WIP: Initial attempt to port ed25519 to SVP64

diff --git a/crypto/ed25519-donna/.gitignore b/crypto/ed25519-donna/.gitignore
new file mode 100644 (file)
index 0000000..308beba
--- /dev/null
+++ b/crypto/ed25519-donna/.gitignore
@@ -0,0 +1,5 @@
+*.o
+*.elf
+*.bin
+*.out
+test-ed25519

diff --git a/crypto/ed25519-donna/Makefile b/crypto/ed25519-donna/Makefile
new file mode 100644 (file)
index 0000000..0c68b4a
--- /dev/null
+++ b/crypto/ed25519-donna/Makefile
@@ -0,0 +1,47 @@
+# A simple Makefile, to build run: make all
+TARGET = test-ed25519
+
+AS = powerpc64le-linux-gnu-as
+CC = gcc
+LD = ld
+CROSSOBJCOPY = powerpc64le-linux-gnu-objcopy
+CROSSLD = powerpc64le-linux-gnu-ld
+
+#compiler flags here
+CFLAGS = -DED25519_SVP64 -DED25519_TEST -g3 -O -Wall -I../../media/pypowersim_wrapper -I/usr/include/python3.7m
+
+# assembler flags here
+ASFLAGS= -mlibresoc -mregnames -Isrc
+
+#linker flags here
+LDFLAGS = -Wall -pthread -lpython3.7m -lssl -lcrypto
+
+SRCDIR = src
+BINDIR  = bin
+
+CFILES := $(SRCDIR)/ed25519.c $(SRCDIR)/test.c $(SRCDIR)/curve25519-donna-64bit_wrappers.c
+ASFILES := $(SRCDIR)/curve25519-donna-64bit_svp64.s
+INCLUDES := $(wildcard $(SRCDIR)/*.h))
+SVP64OBJECTS := $(ASFILES:$(SRCDIR)/%.s=$(SRCDIR)/%.o)
+OBJECTS := $(CFILES:$(SRCDIR)/%.c=$(SRCDIR)/%.o)
+BINFILES := $(BINDIR)/curve25519-donna-64bit_svp64.bin
+ELFFILES := $(BINDIR)/curve25519-donna-64bit_svp64.elf
+
+$(BINDIR)/%.elf: $(SRCDIR)/%.o
+       mkdir -p $(BINDIR)
+       $(CROSSLD) -EL -o $@ -T memmap $^
+
+$(BINDIR)/%.bin: $(BINDIR)/%.elf
+       $(CROSSOBJCOPY) -I elf64-little -O binary $< $@
+
+.PHONY: all clean remove
+all: ${TARGET}
+
+$(TARGET): $(OBJECTS) $(SVP64OBJECTS) $(ELFFILES) $(BINFILES)
+       $(CC) -o $@ $(OBJECTS) $(LDFLAGS)
+
+clean:
+       $ rm -f $(OBJECTS) $(SVP64OBJECTS) $(BINFILES) $(ELFFILES)
+
+remove: clean
+       $ rm -f $(TARGET)

diff --git a/crypto/ed25519-donna/README.md b/crypto/ed25519-donna/README.md
new file mode 100644 (file)
index 0000000..e09fc27
--- /dev/null
+++ b/crypto/ed25519-donna/README.md
@@ -0,0 +1,183 @@
+[ed25519](http://ed25519.cr.yp.to/) is an 
+[Elliptic Curve Digital Signature Algortithm](http://en.wikipedia.org/wiki/Elliptic_Curve_DSA), 
+developed by [Dan Bernstein](http://cr.yp.to/djb.html), 
+[Niels Duif](http://www.nielsduif.nl/), 
+[Tanja Lange](http://hyperelliptic.org/tanja), 
+[Peter Schwabe](http://www.cryptojedi.org/users/peter/), 
+and [Bo-Yin Yang](http://www.iis.sinica.edu.tw/pages/byyang/).
+
+This project provides performant, portable 32-bit & 64-bit implementations. All implementations are 
+of course constant time in regard to secret data.
+
+#### Performance
+
+SSE2 code and benches have not been updated yet. I will do those next.
+
+Compilers versions are gcc 4.6.3, icc 13.1.1, clang 3.4-1~exp1.
+
+Batch verification time (in parentheses) is the average time per 1 verification in a batch of 64 signatures. Counts are in thousands of cycles.
+
+Note that SSE2 performance may be less impressive on AMD & older CPUs with slower SSE ops!
+
+Visual Studio performance for `ge25519_scalarmult_base_niels` will lag behind a bit until optimized assembler versions of `ge25519_scalarmult_base_choose_niels`
+are made.
+
+##### E5200 @ 2.5ghz, march=core2
+
+<table>
+<thead><tr><th>Implementation</th><th>Sign</th><th>gcc</th><th>icc</th><th>clang</th><th>Verify</th><th>gcc</th><th>icc</th><th>clang</th></tr></thead>
+<tbody>
+<tr><td>ed25519-donna 64bit     </td><td></td><td>100k</td><td>110k</td><td>137k</td><td></td><td>327k (144k) </td><td>342k (163k) </td><td>422k (194k) </td></tr>
+<tr><td>amd64-64-24k            </td><td></td><td>102k</td><td>    </td><td>    </td><td></td><td>355k (158k) </td><td>            </td><td>            </td></tr>
+<tr><td>ed25519-donna-sse2 64bit</td><td></td><td>108k</td><td>111k</td><td>116k</td><td></td><td>353k (155k) </td><td>345k (154k) </td><td>360k (161k) </td></tr>
+<tr><td>amd64-51-32k            </td><td></td><td>116k</td><td>    </td><td>    </td><td></td><td>380k (175k) </td><td>            </td><td>            </td></tr>
+<tr><td>ed25519-donna-sse2 32bit</td><td></td><td>147k</td><td>147k</td><td>156k</td><td></td><td>380k (178k) </td><td>381k (173k) </td><td>430k (192k) </td></tr>
+<tr><td>ed25519-donna 32bit     </td><td></td><td>597k</td><td>335k</td><td>380k</td><td></td><td>1693k (720k)</td><td>1052k (453k)</td><td>1141k (493k)</td></tr>
+</tbody>
+</table>
+
+##### E3-1270 @ 3.4ghz, march=corei7-avx
+
+<table>
+<thead><tr><th>Implementation</th><th>Sign</th><th>gcc</th><th>icc</th><th>clang</th><th>Verify</th><th>gcc</th><th>icc</th><th>clang</th></tr></thead>
+<tbody>
+<tr><td>amd64-64-24k            </td><td></td><td> 68k</td><td>    </td><td>    </td><td></td><td>225k (104k) </td><td>            </td><td>            </td></tr>
+<tr><td>ed25519-donna 64bit     </td><td></td><td> 71k</td><td> 75k</td><td> 90k</td><td></td><td>226k (105k) </td><td>226k (112k) </td><td>277k (125k) </td></tr>
+<tr><td>amd64-51-32k            </td><td></td><td> 72k</td><td>    </td><td>    </td><td></td><td>218k (107k) </td><td>            </td><td>            </td></tr>
+<tr><td>ed25519-donna-sse2 64bit</td><td></td><td> 79k</td><td> 82k</td><td> 92k</td><td></td><td>252k (122k) </td><td>259k (124k) </td><td>282k (131k) </td></tr>
+<tr><td>ed25519-donna-sse2 32bit</td><td></td><td> 94k</td><td> 95k</td><td>103k</td><td></td><td>296k (146k) </td><td>294k (137k) </td><td>306k (147k) </td></tr>
+<tr><td>ed25519-donna 32bit     </td><td></td><td>525k</td><td>299k</td><td>316k</td><td></td><td>1502k (645k)</td><td>959k (418k) </td><td>954k (416k) </td></tr>
+</tbody>
+</table>
+
+#### Compilation
+
+No configuration is needed **if you are compiling against OpenSSL**. 
+
+##### Hash Options
+
+If you are not compiling aginst OpenSSL, you will need a hash function.
+
+To use a simple/**slow** implementation of SHA-512, use `-DED25519_REFHASH` when compiling `ed25519.c`. 
+This should never be used except to verify the code works when OpenSSL is not available.
+
+To use a custom hash function, use `-DED25519_CUSTOMHASH` when compiling `ed25519.c` and put your 
+custom hash implementation in ed25519-hash-custom.h. The hash must have a 512bit digest and implement
+
+       struct ed25519_hash_context;
+
+       void ed25519_hash_init(ed25519_hash_context *ctx);
+       void ed25519_hash_update(ed25519_hash_context *ctx, const uint8_t *in, size_t inlen);
+       void ed25519_hash_final(ed25519_hash_context *ctx, uint8_t *hash);
+       void ed25519_hash(uint8_t *hash, const uint8_t *in, size_t inlen);
+
+##### Random Options
+
+If you are not compiling aginst OpenSSL, you will need a random function for batch verification.
+
+To use a custom random function, use `-DED25519_CUSTOMRANDOM` when compiling `ed25519.c` and put your 
+custom hash implementation in ed25519-randombytes-custom.h. The random function must implement:
+
+       void ED25519_FN(ed25519_randombytes_unsafe) (void *p, size_t len);
+
+Use `-DED25519_TEST` when compiling `ed25519.c` to use a deterministically seeded, non-thread safe CSPRNG 
+variant of Bob Jenkins [ISAAC](http://en.wikipedia.org/wiki/ISAAC_%28cipher%29)
+
+##### Minor options
+
+Use `-DED25519_INLINE_ASM` to disable the use of custom assembler routines and instead rely on portable C.
+
+Use `-DED25519_FORCE_32BIT` to force the use of 32 bit routines even when compiling for 64 bit.
+
+##### 32-bit
+
+       gcc ed25519.c -m32 -O3 -c
+
+##### 64-bit
+
+       gcc ed25519.c -m64 -O3 -c
+
+##### SSE2
+
+       gcc ed25519.c -m32 -O3 -c -DED25519_SSE2 -msse2
+       gcc ed25519.c -m64 -O3 -c -DED25519_SSE2
+
+clang and icc are also supported
+
+
+#### Usage
+
+To use the code, link against `ed25519.o -mbits` and:
+
+       #include "ed25519.h"
+
+Add `-lssl -lcrypto` when using OpenSSL (Some systems don't need -lcrypto? It might be trial and error).
+
+To generate a private key, simply generate 32 bytes from a secure
+cryptographic source:
+
+       ed25519_secret_key sk;
+       randombytes(sk, sizeof(ed25519_secret_key));
+
+To generate a public key:
+
+       ed25519_public_key pk;
+       ed25519_publickey(sk, pk);
+
+To sign a message:
+
+       ed25519_signature sig;
+       ed25519_sign(message, message_len, sk, pk, signature);
+
+To verify a signature:
+
+       int valid = ed25519_sign_open(message, message_len, pk, signature) == 0;
+
+To batch verify signatures:
+
+       const unsigned char *mp[num] = {message1, message2..}
+       size_t ml[num] = {message_len1, message_len2..}
+       const unsigned char *pkp[num] = {pk1, pk2..}
+       const unsigned char *sigp[num] = {signature1, signature2..}
+       int valid[num]
+
+       /* valid[i] will be set to 1 if the individual signature was valid, 0 otherwise */
+       int all_valid = ed25519_sign_open_batch(mp, ml, pkp, sigp, num, valid) == 0;
+
+**Note**: Batch verification uses `ed25519_randombytes_unsafe`, implemented in 
+`ed25519-randombytes.h`, to generate random scalars for the verification code. 
+The default implementation now uses OpenSSLs `RAND_bytes`.
+
+Unlike the [SUPERCOP](http://bench.cr.yp.to/supercop.html) version, signatures are
+not appended to messages, and there is no need for padding in front of messages. 
+Additionally, the secret key does not contain a copy of the public key, so it is 
+32 bytes instead of 64 bytes, and the public key must be provided to the signing
+function.
+
+##### Curve25519
+
+Curve25519 public keys can be generated thanks to 
+[Adam Langley](http://www.imperialviolet.org/2013/05/10/fastercurve25519.html) 
+leveraging Ed25519's precomputed basepoint scalar multiplication.
+
+       curved25519_key sk, pk;
+       randombytes(sk, sizeof(curved25519_key));
+       curved25519_scalarmult_basepoint(pk, sk);
+
+Note the name is curved25519, a combination of curve and ed25519, to prevent 
+name clashes. Performance is slightly faster than short message ed25519
+signing due to both using the same code for the scalar multiply.
+
+#### Testing
+
+Fuzzing against reference implemenations is now available. See [fuzz/README](fuzz/README.md).
+
+Building `ed25519.c` with `-DED25519_TEST` and linking with `test.c` will run basic sanity tests
+and benchmark each function. `test-batch.c` has been incorporated in to `test.c`.
+
+`test-internals.c` is standalone and built the same way as `ed25519.c`. It tests the math primitives
+with extreme values to ensure they function correctly. SSE2 is now supported.
+
+#### Papers
+
+[Available on the Ed25519 website](http://ed25519.cr.yp.to/papers.html)
\ No newline at end of file

diff --git a/crypto/ed25519-donna/memmap b/crypto/ed25519-donna/memmap
new file mode 100644 (file)
index 0000000..da68813
--- /dev/null
+++ b/crypto/ed25519-donna/memmap
@@ -0,0 +1,20 @@
+
+MEMORY
+{
+    ram  : ORIGIN = 0x20001000, LENGTH = 512M
+    fixedaddr  : ORIGIN = 0x20000000, LENGTH = 0x1000
+}
+
+
+SECTIONS
+{
+    .fixedaddr :
+    {
+    . = ALIGN(4);
+    __fixedaddr_start__ = .;
+    *(.fixedaddr*)
+    __fixedaddr_end__ = .;
+    } > fixedaddr
+   .text : { *(.text*) } > ram
+   .bss  : { *(.text*) } > ram
+}

diff --git a/crypto/ed25519-donna/src/curve25519-donna-32bit.h b/crypto/ed25519-donna/src/curve25519-donna-32bit.h
new file mode 100644 (file)
index 0000000..b0861ac
--- /dev/null
+++ b/crypto/ed25519-donna/src/curve25519-donna-32bit.h
@@ -0,0 +1,579 @@
+/*
+       Public domain by Andrew M. <liquidsun@gmail.com>
+       See: https://github.com/floodyberry/curve25519-donna
+
+       32 bit integer curve25519 implementation
+*/
+
+typedef uint32_t bignum25519[10];
+typedef uint32_t bignum25519align16[12];
+
+static const uint32_t reduce_mask_25 = (1 << 25) - 1;
+static const uint32_t reduce_mask_26 = (1 << 26) - 1;
+
+
+/* out = in */
+DONNA_INLINE static void
+curve25519_copy(bignum25519 out, const bignum25519 in) {
+       out[0] = in[0];
+       out[1] = in[1];
+       out[2] = in[2];
+       out[3] = in[3];
+       out[4] = in[4];
+       out[5] = in[5];
+       out[6] = in[6];
+       out[7] = in[7];
+       out[8] = in[8];
+       out[9] = in[9];
+}
+
+/* out = a + b */
+DONNA_INLINE static void
+curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) {
+       out[0] = a[0] + b[0];
+       out[1] = a[1] + b[1];
+       out[2] = a[2] + b[2];
+       out[3] = a[3] + b[3];
+       out[4] = a[4] + b[4];
+       out[5] = a[5] + b[5];
+       out[6] = a[6] + b[6];
+       out[7] = a[7] + b[7];
+       out[8] = a[8] + b[8];
+       out[9] = a[9] + b[9];
+}
+
+DONNA_INLINE static void 
+curve25519_add_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
+       uint32_t c;
+       out[0] = a[0] + b[0]    ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
+       out[1] = a[1] + b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
+       out[2] = a[2] + b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
+       out[3] = a[3] + b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
+       out[4] = a[4] + b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
+       out[5] = a[5] + b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
+       out[6] = a[6] + b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
+       out[7] = a[7] + b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
+       out[8] = a[8] + b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
+       out[9] = a[9] + b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
+       out[0] += 19 * c;
+}
+
+DONNA_INLINE static void
+curve25519_add_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
+       uint32_t c;
+       out[0] = a[0] + b[0]    ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
+       out[1] = a[1] + b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
+       out[2] = a[2] + b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
+       out[3] = a[3] + b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
+       out[4] = a[4] + b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
+       out[5] = a[5] + b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
+       out[6] = a[6] + b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
+       out[7] = a[7] + b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
+       out[8] = a[8] + b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
+       out[9] = a[9] + b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
+       out[0] += 19 * c;
+}
+
+/* multiples of p */
+static const uint32_t twoP0       = 0x07ffffda;
+static const uint32_t twoP13579   = 0x03fffffe;
+static const uint32_t twoP2468    = 0x07fffffe;
+static const uint32_t fourP0      = 0x0fffffb4;
+static const uint32_t fourP13579  = 0x07fffffc;
+static const uint32_t fourP2468   = 0x0ffffffc;
+
+/* out = a - b */
+DONNA_INLINE static void
+curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) {
+       uint32_t c;
+       out[0] = twoP0     + a[0] - b[0]    ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
+       out[1] = twoP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
+       out[2] = twoP2468  + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
+       out[3] = twoP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
+       out[4] = twoP2468  + a[4] - b[4] + c;
+       out[5] = twoP13579 + a[5] - b[5]    ;
+       out[6] = twoP2468  + a[6] - b[6]    ;
+       out[7] = twoP13579 + a[7] - b[7]    ;
+       out[8] = twoP2468  + a[8] - b[8]    ;
+       out[9] = twoP13579 + a[9] - b[9]    ;
+}
+
+/* out = a - b, where a is the result of a basic op (add,sub) */
+DONNA_INLINE static void
+curve25519_sub_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
+       uint32_t c;
+       out[0] = fourP0     + a[0] - b[0]    ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
+       out[1] = fourP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
+       out[2] = fourP2468  + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
+       out[3] = fourP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
+       out[4] = fourP2468  + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
+       out[5] = fourP13579 + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
+       out[6] = fourP2468  + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
+       out[7] = fourP13579 + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
+       out[8] = fourP2468  + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
+       out[9] = fourP13579 + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
+       out[0] += 19 * c;
+}
+
+DONNA_INLINE static void
+curve25519_sub_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
+       uint32_t c;
+       out[0] = fourP0     + a[0] - b[0]    ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
+       out[1] = fourP13579 + a[1] - b[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
+       out[2] = fourP2468  + a[2] - b[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
+       out[3] = fourP13579 + a[3] - b[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
+       out[4] = fourP2468  + a[4] - b[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
+       out[5] = fourP13579 + a[5] - b[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
+       out[6] = fourP2468  + a[6] - b[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
+       out[7] = fourP13579 + a[7] - b[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
+       out[8] = fourP2468  + a[8] - b[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
+       out[9] = fourP13579 + a[9] - b[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
+       out[0] += 19 * c;
+}
+
+/* out = -a */
+DONNA_INLINE static void
+curve25519_neg(bignum25519 out, const bignum25519 a) {
+       uint32_t c;
+       out[0] = twoP0     - a[0]    ; c = (out[0] >> 26); out[0] &= reduce_mask_26;
+       out[1] = twoP13579 - a[1] + c; c = (out[1] >> 25); out[1] &= reduce_mask_25;
+       out[2] = twoP2468  - a[2] + c; c = (out[2] >> 26); out[2] &= reduce_mask_26;
+       out[3] = twoP13579 - a[3] + c; c = (out[3] >> 25); out[3] &= reduce_mask_25;
+       out[4] = twoP2468  - a[4] + c; c = (out[4] >> 26); out[4] &= reduce_mask_26;
+       out[5] = twoP13579 - a[5] + c; c = (out[5] >> 25); out[5] &= reduce_mask_25;
+       out[6] = twoP2468  - a[6] + c; c = (out[6] >> 26); out[6] &= reduce_mask_26;
+       out[7] = twoP13579 - a[7] + c; c = (out[7] >> 25); out[7] &= reduce_mask_25;
+       out[8] = twoP2468  - a[8] + c; c = (out[8] >> 26); out[8] &= reduce_mask_26;
+       out[9] = twoP13579 - a[9] + c; c = (out[9] >> 25); out[9] &= reduce_mask_25;
+       out[0] += 19 * c;
+}
+
+/* out = a * b */
+#define curve25519_mul_noinline curve25519_mul
+static void
+curve25519_mul(bignum25519 out, const bignum25519 a, const bignum25519 b) {
+       uint32_t r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
+       uint32_t s0,s1,s2,s3,s4,s5,s6,s7,s8,s9;
+       uint64_t m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
+       uint32_t p;
+
+       r0 = b[0];
+       r1 = b[1];
+       r2 = b[2];
+       r3 = b[3];
+       r4 = b[4];
+       r5 = b[5];
+       r6 = b[6];
+       r7 = b[7];
+       r8 = b[8];
+       r9 = b[9];
+
+       s0 = a[0];
+       s1 = a[1];
+       s2 = a[2];
+       s3 = a[3];
+       s4 = a[4];
+       s5 = a[5];
+       s6 = a[6];
+       s7 = a[7];
+       s8 = a[8];
+       s9 = a[9];
+
+       m1 = mul32x32_64(r0, s1) + mul32x32_64(r1, s0);
+       m3 = mul32x32_64(r0, s3) + mul32x32_64(r1, s2) + mul32x32_64(r2, s1) + mul32x32_64(r3, s0);
+       m5 = mul32x32_64(r0, s5) + mul32x32_64(r1, s4) + mul32x32_64(r2, s3) + mul32x32_64(r3, s2) + mul32x32_64(r4, s1) + mul32x32_64(r5, s0);
+       m7 = mul32x32_64(r0, s7) + mul32x32_64(r1, s6) + mul32x32_64(r2, s5) + mul32x32_64(r3, s4) + mul32x32_64(r4, s3) + mul32x32_64(r5, s2) + mul32x32_64(r6, s1) + mul32x32_64(r7, s0);
+       m9 = mul32x32_64(r0, s9) + mul32x32_64(r1, s8) + mul32x32_64(r2, s7) + mul32x32_64(r3, s6) + mul32x32_64(r4, s5) + mul32x32_64(r5, s4) + mul32x32_64(r6, s3) + mul32x32_64(r7, s2) + mul32x32_64(r8, s1) + mul32x32_64(r9, s0);
+
+       r1 *= 2;
+       r3 *= 2;
+       r5 *= 2;
+       r7 *= 2;
+
+       m0 = mul32x32_64(r0, s0);
+       m2 = mul32x32_64(r0, s2) + mul32x32_64(r1, s1) + mul32x32_64(r2, s0);
+       m4 = mul32x32_64(r0, s4) + mul32x32_64(r1, s3) + mul32x32_64(r2, s2) + mul32x32_64(r3, s1) + mul32x32_64(r4, s0);
+       m6 = mul32x32_64(r0, s6) + mul32x32_64(r1, s5) + mul32x32_64(r2, s4) + mul32x32_64(r3, s3) + mul32x32_64(r4, s2) + mul32x32_64(r5, s1) + mul32x32_64(r6, s0);
+       m8 = mul32x32_64(r0, s8) + mul32x32_64(r1, s7) + mul32x32_64(r2, s6) + mul32x32_64(r3, s5) + mul32x32_64(r4, s4) + mul32x32_64(r5, s3) + mul32x32_64(r6, s2) + mul32x32_64(r7, s1) + mul32x32_64(r8, s0);
+
+       r1 *= 19;
+       r2 *= 19;
+       r3 = (r3 / 2) * 19;
+       r4 *= 19;
+       r5 = (r5 / 2) * 19;
+       r6 *= 19;
+       r7 = (r7 / 2) * 19;
+       r8 *= 19;
+       r9 *= 19;
+
+       m1 += (mul32x32_64(r9, s2) + mul32x32_64(r8, s3) + mul32x32_64(r7, s4) + mul32x32_64(r6, s5) + mul32x32_64(r5, s6) + mul32x32_64(r4, s7) + mul32x32_64(r3, s8) + mul32x32_64(r2, s9));
+       m3 += (mul32x32_64(r9, s4) + mul32x32_64(r8, s5) + mul32x32_64(r7, s6) + mul32x32_64(r6, s7) + mul32x32_64(r5, s8) + mul32x32_64(r4, s9));
+       m5 += (mul32x32_64(r9, s6) + mul32x32_64(r8, s7) + mul32x32_64(r7, s8) + mul32x32_64(r6, s9));
+       m7 += (mul32x32_64(r9, s8) + mul32x32_64(r8, s9));
+
+       r3 *= 2;
+       r5 *= 2;
+       r7 *= 2;
+       r9 *= 2;
+
+       m0 += (mul32x32_64(r9, s1) + mul32x32_64(r8, s2) + mul32x32_64(r7, s3) + mul32x32_64(r6, s4) + mul32x32_64(r5, s5) + mul32x32_64(r4, s6) + mul32x32_64(r3, s7) + mul32x32_64(r2, s8) + mul32x32_64(r1, s9));
+       m2 += (mul32x32_64(r9, s3) + mul32x32_64(r8, s4) + mul32x32_64(r7, s5) + mul32x32_64(r6, s6) + mul32x32_64(r5, s7) + mul32x32_64(r4, s8) + mul32x32_64(r3, s9));
+       m4 += (mul32x32_64(r9, s5) + mul32x32_64(r8, s6) + mul32x32_64(r7, s7) + mul32x32_64(r6, s8) + mul32x32_64(r5, s9));
+       m6 += (mul32x32_64(r9, s7) + mul32x32_64(r8, s8) + mul32x32_64(r7, s9));
+       m8 += (mul32x32_64(r9, s9));
+
+                                    r0 = (uint32_t)m0 & reduce_mask_26; c = (m0 >> 26);
+       m1 += c;                     r1 = (uint32_t)m1 & reduce_mask_25; c = (m1 >> 25);
+       m2 += c;                     r2 = (uint32_t)m2 & reduce_mask_26; c = (m2 >> 26);
+       m3 += c;                     r3 = (uint32_t)m3 & reduce_mask_25; c = (m3 >> 25);
+       m4 += c;                     r4 = (uint32_t)m4 & reduce_mask_26; c = (m4 >> 26);
+       m5 += c;                     r5 = (uint32_t)m5 & reduce_mask_25; c = (m5 >> 25);
+       m6 += c;                     r6 = (uint32_t)m6 & reduce_mask_26; c = (m6 >> 26);
+       m7 += c;                     r7 = (uint32_t)m7 & reduce_mask_25; c = (m7 >> 25);
+       m8 += c;                     r8 = (uint32_t)m8 & reduce_mask_26; c = (m8 >> 26);
+       m9 += c;                     r9 = (uint32_t)m9 & reduce_mask_25; p = (uint32_t)(m9 >> 25);
+       m0 = r0 + mul32x32_64(p,19); r0 = (uint32_t)m0 & reduce_mask_26; p = (uint32_t)(m0 >> 26);
+       r1 += p;
+
+       out[0] = r0;
+       out[1] = r1;
+       out[2] = r2;
+       out[3] = r3;
+       out[4] = r4;
+       out[5] = r5;
+       out[6] = r6;
+       out[7] = r7;
+       out[8] = r8;
+       out[9] = r9;
+}
+
+/* out = in*in */
+static void
+curve25519_square(bignum25519 out, const bignum25519 in) {
+       uint32_t r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
+       uint32_t d6,d7,d8,d9;
+       uint64_t m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
+       uint32_t p;
+
+       r0 = in[0];
+       r1 = in[1];
+       r2 = in[2];
+       r3 = in[3];
+       r4 = in[4];
+       r5 = in[5];
+       r6 = in[6];
+       r7 = in[7];
+       r8 = in[8];
+       r9 = in[9];
+
+       m0 = mul32x32_64(r0, r0);
+       r0 *= 2;
+       m1 = mul32x32_64(r0, r1);
+       m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
+       r1 *= 2;
+       m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2    );
+       m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
+       r2 *= 2;
+       m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4    ) + mul32x32_64(r2, r3);
+       m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
+       r3 *= 2;
+       m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6    ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4    );
+       m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4    );
+       m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8    ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6    ) + mul32x32_64(r4, r5 * 2);
+
+       d6 = r6 * 19;
+       d7 = r7 * 2 * 19;
+       d8 = r8 * 19;
+       d9 = r9 * 2 * 19;
+
+       m0 += (mul32x32_64(d9, r1    ) + mul32x32_64(d8, r2    ) + mul32x32_64(d7, r3    ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
+       m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3    ) + mul32x32_64(d7, r4    ) + mul32x32_64(d6, r5 * 2));
+       m2 += (mul32x32_64(d9, r3    ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6    ));
+       m3 += (mul32x32_64(d9, r4    ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6    ));
+       m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7    ));
+       m5 += (mul32x32_64(d9, r6    ) + mul32x32_64(d8, r7 * 2));
+       m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8    ));
+       m7 += (mul32x32_64(d9, r8    ));
+       m8 += (mul32x32_64(d9, r9    ));
+
+                                    r0 = (uint32_t)m0 & reduce_mask_26; c = (m0 >> 26);
+       m1 += c;                     r1 = (uint32_t)m1 & reduce_mask_25; c = (m1 >> 25);
+       m2 += c;                     r2 = (uint32_t)m2 & reduce_mask_26; c = (m2 >> 26);
+       m3 += c;                     r3 = (uint32_t)m3 & reduce_mask_25; c = (m3 >> 25);
+       m4 += c;                     r4 = (uint32_t)m4 & reduce_mask_26; c = (m4 >> 26);
+       m5 += c;                     r5 = (uint32_t)m5 & reduce_mask_25; c = (m5 >> 25);
+       m6 += c;                     r6 = (uint32_t)m6 & reduce_mask_26; c = (m6 >> 26);
+       m7 += c;                     r7 = (uint32_t)m7 & reduce_mask_25; c = (m7 >> 25);
+       m8 += c;                     r8 = (uint32_t)m8 & reduce_mask_26; c = (m8 >> 26);
+       m9 += c;                     r9 = (uint32_t)m9 & reduce_mask_25; p = (uint32_t)(m9 >> 25);
+       m0 = r0 + mul32x32_64(p,19); r0 = (uint32_t)m0 & reduce_mask_26; p = (uint32_t)(m0 >> 26);
+       r1 += p;
+
+       out[0] = r0;
+       out[1] = r1;
+       out[2] = r2;
+       out[3] = r3;
+       out[4] = r4;
+       out[5] = r5;
+       out[6] = r6;
+       out[7] = r7;
+       out[8] = r8;
+       out[9] = r9;
+}
+
+
+/* out = in ^ (2 * count) */
+static void
+curve25519_square_times(bignum25519 out, const bignum25519 in, int count) {
+       uint32_t r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
+       uint32_t d6,d7,d8,d9;
+       uint64_t m0,m1,m2,m3,m4,m5,m6,m7,m8,m9,c;
+       uint32_t p;
+
+       r0 = in[0];
+       r1 = in[1];
+       r2 = in[2];
+       r3 = in[3];
+       r4 = in[4];
+       r5 = in[5];
+       r6 = in[6];
+       r7 = in[7];
+       r8 = in[8];
+       r9 = in[9];
+
+       do {
+               m0 = mul32x32_64(r0, r0);
+               r0 *= 2;
+               m1 = mul32x32_64(r0, r1);
+               m2 = mul32x32_64(r0, r2) + mul32x32_64(r1, r1 * 2);
+               r1 *= 2;
+               m3 = mul32x32_64(r0, r3) + mul32x32_64(r1, r2    );
+               m4 = mul32x32_64(r0, r4) + mul32x32_64(r1, r3 * 2) + mul32x32_64(r2, r2);
+               r2 *= 2;
+               m5 = mul32x32_64(r0, r5) + mul32x32_64(r1, r4    ) + mul32x32_64(r2, r3);
+               m6 = mul32x32_64(r0, r6) + mul32x32_64(r1, r5 * 2) + mul32x32_64(r2, r4) + mul32x32_64(r3, r3 * 2);
+               r3 *= 2;
+               m7 = mul32x32_64(r0, r7) + mul32x32_64(r1, r6    ) + mul32x32_64(r2, r5) + mul32x32_64(r3, r4    );
+               m8 = mul32x32_64(r0, r8) + mul32x32_64(r1, r7 * 2) + mul32x32_64(r2, r6) + mul32x32_64(r3, r5 * 2) + mul32x32_64(r4, r4    );
+               m9 = mul32x32_64(r0, r9) + mul32x32_64(r1, r8    ) + mul32x32_64(r2, r7) + mul32x32_64(r3, r6    ) + mul32x32_64(r4, r5 * 2);
+
+               d6 = r6 * 19;
+               d7 = r7 * 2 * 19;
+               d8 = r8 * 19;
+               d9 = r9 * 2 * 19;
+
+               m0 += (mul32x32_64(d9, r1    ) + mul32x32_64(d8, r2    ) + mul32x32_64(d7, r3    ) + mul32x32_64(d6, r4 * 2) + mul32x32_64(r5, r5 * 2 * 19));
+               m1 += (mul32x32_64(d9, r2 / 2) + mul32x32_64(d8, r3    ) + mul32x32_64(d7, r4    ) + mul32x32_64(d6, r5 * 2));
+               m2 += (mul32x32_64(d9, r3    ) + mul32x32_64(d8, r4 * 2) + mul32x32_64(d7, r5 * 2) + mul32x32_64(d6, r6    ));
+               m3 += (mul32x32_64(d9, r4    ) + mul32x32_64(d8, r5 * 2) + mul32x32_64(d7, r6    ));
+               m4 += (mul32x32_64(d9, r5 * 2) + mul32x32_64(d8, r6 * 2) + mul32x32_64(d7, r7    ));
+               m5 += (mul32x32_64(d9, r6    ) + mul32x32_64(d8, r7 * 2));
+               m6 += (mul32x32_64(d9, r7 * 2) + mul32x32_64(d8, r8    ));
+               m7 += (mul32x32_64(d9, r8    ));
+               m8 += (mul32x32_64(d9, r9    ));
+
+                                            r0 = (uint32_t)m0 & reduce_mask_26; c = (m0 >> 26);
+               m1 += c;                     r1 = (uint32_t)m1 & reduce_mask_25; c = (m1 >> 25);
+               m2 += c;                     r2 = (uint32_t)m2 & reduce_mask_26; c = (m2 >> 26);
+               m3 += c;                     r3 = (uint32_t)m3 & reduce_mask_25; c = (m3 >> 25);
+               m4 += c;                     r4 = (uint32_t)m4 & reduce_mask_26; c = (m4 >> 26);
+               m5 += c;                     r5 = (uint32_t)m5 & reduce_mask_25; c = (m5 >> 25);
+               m6 += c;                     r6 = (uint32_t)m6 & reduce_mask_26; c = (m6 >> 26);
+               m7 += c;                     r7 = (uint32_t)m7 & reduce_mask_25; c = (m7 >> 25);
+               m8 += c;                     r8 = (uint32_t)m8 & reduce_mask_26; c = (m8 >> 26);
+               m9 += c;                     r9 = (uint32_t)m9 & reduce_mask_25; p = (uint32_t)(m9 >> 25);
+               m0 = r0 + mul32x32_64(p,19); r0 = (uint32_t)m0 & reduce_mask_26; p = (uint32_t)(m0 >> 26);
+               r1 += p;
+       } while (--count);
+
+       out[0] = r0;
+       out[1] = r1;
+       out[2] = r2;
+       out[3] = r3;
+       out[4] = r4;
+       out[5] = r5;
+       out[6] = r6;
+       out[7] = r7;
+       out[8] = r8;
+       out[9] = r9;
+}
+
+/* Take a little-endian, 32-byte number and expand it into polynomial form */
+static void
+curve25519_expand(bignum25519 out, const unsigned char in[32]) {
+       static const union { uint8_t b[2]; uint16_t s; } endian_check = {{1,0}};
+       uint32_t x0,x1,x2,x3,x4,x5,x6,x7;
+
+       if (endian_check.s == 1) {
+               x0 = *(uint32_t *)(in + 0);
+               x1 = *(uint32_t *)(in + 4);
+               x2 = *(uint32_t *)(in + 8);
+               x3 = *(uint32_t *)(in + 12);
+               x4 = *(uint32_t *)(in + 16);
+               x5 = *(uint32_t *)(in + 20);
+               x6 = *(uint32_t *)(in + 24);
+               x7 = *(uint32_t *)(in + 28);
+    } else {
+               #define F(s)                         \
+                       ((((uint32_t)in[s + 0])      ) | \
+                        (((uint32_t)in[s + 1]) <<  8) | \
+                        (((uint32_t)in[s + 2]) << 16) | \
+                        (((uint32_t)in[s + 3]) << 24))
+               x0 = F(0);
+               x1 = F(4);
+               x2 = F(8);
+               x3 = F(12);
+               x4 = F(16);
+               x5 = F(20);
+               x6 = F(24);
+               x7 = F(28);
+               #undef F
+       }
+
+       out[0] = (                        x0       ) & 0x3ffffff;
+       out[1] = ((((uint64_t)x1 << 32) | x0) >> 26) & 0x1ffffff;
+       out[2] = ((((uint64_t)x2 << 32) | x1) >> 19) & 0x3ffffff;
+       out[3] = ((((uint64_t)x3 << 32) | x2) >> 13) & 0x1ffffff;
+       out[4] = ((                       x3) >>  6) & 0x3ffffff;
+       out[5] = (                        x4       ) & 0x1ffffff;
+       out[6] = ((((uint64_t)x5 << 32) | x4) >> 25) & 0x3ffffff;
+       out[7] = ((((uint64_t)x6 << 32) | x5) >> 19) & 0x1ffffff;
+       out[8] = ((((uint64_t)x7 << 32) | x6) >> 12) & 0x3ffffff;
+       out[9] = ((                       x7) >>  6) & 0x1ffffff;
+}
+
+/* Take a fully reduced polynomial form number and contract it into a
+ * little-endian, 32-byte array
+ */
+static void
+curve25519_contract(unsigned char out[32], const bignum25519 in) {
+       bignum25519 f;
+       curve25519_copy(f, in);
+
+       #define carry_pass() \
+               f[1] += f[0] >> 26; f[0] &= reduce_mask_26; \
+               f[2] += f[1] >> 25; f[1] &= reduce_mask_25; \
+               f[3] += f[2] >> 26; f[2] &= reduce_mask_26; \
+               f[4] += f[3] >> 25; f[3] &= reduce_mask_25; \
+               f[5] += f[4] >> 26; f[4] &= reduce_mask_26; \
+               f[6] += f[5] >> 25; f[5] &= reduce_mask_25; \
+               f[7] += f[6] >> 26; f[6] &= reduce_mask_26; \
+               f[8] += f[7] >> 25; f[7] &= reduce_mask_25; \
+               f[9] += f[8] >> 26; f[8] &= reduce_mask_26;
+
+       #define carry_pass_full() \
+               carry_pass() \
+               f[0] += 19 * (f[9] >> 25); f[9] &= reduce_mask_25;
+
+       #define carry_pass_final() \
+               carry_pass() \
+               f[9] &= reduce_mask_25;
+
+       carry_pass_full()
+       carry_pass_full()
+
+       /* now t is between 0 and 2^255-1, properly carried. */
+       /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
+       f[0] += 19;
+       carry_pass_full()
+
+       /* now between 19 and 2^255-1 in both cases, and offset by 19. */
+       f[0] += (reduce_mask_26 + 1) - 19;
+       f[1] += (reduce_mask_25 + 1) - 1;
+       f[2] += (reduce_mask_26 + 1) - 1;
+       f[3] += (reduce_mask_25 + 1) - 1;
+       f[4] += (reduce_mask_26 + 1) - 1;
+       f[5] += (reduce_mask_25 + 1) - 1;
+       f[6] += (reduce_mask_26 + 1) - 1;
+       f[7] += (reduce_mask_25 + 1) - 1;
+       f[8] += (reduce_mask_26 + 1) - 1;
+       f[9] += (reduce_mask_25 + 1) - 1;
+
+       /* now between 2^255 and 2^256-20, and offset by 2^255. */
+       carry_pass_final()
+
+       #undef carry_pass
+       #undef carry_full
+       #undef carry_final
+
+       f[1] <<= 2;
+       f[2] <<= 3;
+       f[3] <<= 5;
+       f[4] <<= 6;
+       f[6] <<= 1;
+       f[7] <<= 3;
+       f[8] <<= 4;
+       f[9] <<= 6;
+
+       #define F(i, s) \
+               out[s+0] |= (unsigned char )(f[i] & 0xff); \
+               out[s+1] = (unsigned char )((f[i] >> 8) & 0xff); \
+               out[s+2] = (unsigned char )((f[i] >> 16) & 0xff); \
+               out[s+3] = (unsigned char )((f[i] >> 24) & 0xff);
+
+       out[0] = 0;
+       out[16] = 0;
+       F(0,0);
+       F(1,3);
+       F(2,6);
+       F(3,9);
+       F(4,12);
+       F(5,16);
+       F(6,19);
+       F(7,22);
+       F(8,25);
+       F(9,28);
+       #undef F
+}
+
+
+/* out = (flag) ? in : out */
+DONNA_INLINE static void
+curve25519_move_conditional_bytes(uint8_t out[96], const uint8_t in[96], uint32_t flag) {
+       const uint32_t nb = flag - 1, b = ~nb;
+       const uint32_t *inl = (const uint32_t *)in;
+       uint32_t *outl = (uint32_t *)out;
+       outl[0] = (outl[0] & nb) | (inl[0] & b);
+       outl[1] = (outl[1] & nb) | (inl[1] & b);
+       outl[2] = (outl[2] & nb) | (inl[2] & b);
+       outl[3] = (outl[3] & nb) | (inl[3] & b);
+       outl[4] = (outl[4] & nb) | (inl[4] & b);
+       outl[5] = (outl[5] & nb) | (inl[5] & b);
+       outl[6] = (outl[6] & nb) | (inl[6] & b);
+       outl[7] = (outl[7] & nb) | (inl[7] & b);
+       outl[8] = (outl[8] & nb) | (inl[8] & b);
+       outl[9] = (outl[9] & nb) | (inl[9] & b);
+       outl[10] = (outl[10] & nb) | (inl[10] & b);
+       outl[11] = (outl[11] & nb) | (inl[11] & b);
+       outl[12] = (outl[12] & nb) | (inl[12] & b);
+       outl[13] = (outl[13] & nb) | (inl[13] & b);
+       outl[14] = (outl[14] & nb) | (inl[14] & b);
+       outl[15] = (outl[15] & nb) | (inl[15] & b);
+       outl[16] = (outl[16] & nb) | (inl[16] & b);
+       outl[17] = (outl[17] & nb) | (inl[17] & b);
+       outl[18] = (outl[18] & nb) | (inl[18] & b);
+       outl[19] = (outl[19] & nb) | (inl[19] & b);
+       outl[20] = (outl[20] & nb) | (inl[20] & b);
+       outl[21] = (outl[21] & nb) | (inl[21] & b);
+       outl[22] = (outl[22] & nb) | (inl[22] & b);
+       outl[23] = (outl[23] & nb) | (inl[23] & b);
+
+}
+
+/* if (iswap) swap(a, b) */
+DONNA_INLINE static void
+curve25519_swap_conditional(bignum25519 a, bignum25519 b, uint32_t iswap) {
+       const uint32_t swap = (uint32_t)(-(int32_t)iswap);
+       uint32_t x0,x1,x2,x3,x4,x5,x6,x7,x8,x9;
+
+       x0 = swap & (a[0] ^ b[0]); a[0] ^= x0; b[0] ^= x0;
+       x1 = swap & (a[1] ^ b[1]); a[1] ^= x1; b[1] ^= x1;
+       x2 = swap & (a[2] ^ b[2]); a[2] ^= x2; b[2] ^= x2;
+       x3 = swap & (a[3] ^ b[3]); a[3] ^= x3; b[3] ^= x3;
+       x4 = swap & (a[4] ^ b[4]); a[4] ^= x4; b[4] ^= x4;
+       x5 = swap & (a[5] ^ b[5]); a[5] ^= x5; b[5] ^= x5;
+       x6 = swap & (a[6] ^ b[6]); a[6] ^= x6; b[6] ^= x6;
+       x7 = swap & (a[7] ^ b[7]); a[7] ^= x7; b[7] ^= x7;
+       x8 = swap & (a[8] ^ b[8]); a[8] ^= x8; b[8] ^= x8;
+       x9 = swap & (a[9] ^ b[9]); a[9] ^= x9; b[9] ^= x9;
+}

diff --git a/crypto/ed25519-donna/src/curve25519-donna-64bit.h b/crypto/ed25519-donna/src/curve25519-donna-64bit.h
new file mode 100644 (file)
index 0000000..eb2aff8
--- /dev/null
+++ b/crypto/ed25519-donna/src/curve25519-donna-64bit.h
@@ -0,0 +1,421 @@
+/*
+       Public domain by Adam Langley <agl@imperialviolet.org> &
+                        Andrew M. <liquidsun@gmail.com>
+       See: https://github.com/floodyberry/curve25519-donna
+
+       64bit integer curve25519 implementation
+*/
+
+typedef uint64_t bignum25519[5];
+
+static const uint64_t reduce_mask_40 = ((uint64_t)1 << 40) - 1;
+static const uint64_t reduce_mask_51 = ((uint64_t)1 << 51) - 1;
+static const uint64_t reduce_mask_56 = ((uint64_t)1 << 56) - 1;
+
+
+#ifdef ED25519_SVP64
+#include "curve25519-donna-64bit_wrappers.h"
+#define curve25519_copy     curve25519_copy_svp64
+#else
+/* out = in */
+static void
+curve25519_copy_c(bignum25519 out, const bignum25519 in) {
+       out[0] = in[0];
+       out[1] = in[1];
+       out[2] = in[2];
+       out[3] = in[3];
+       out[4] = in[4];
+}
+
+#define curve25519_copy     curve25519_copy_c
+#endif
+
+/* out = a + b */
+DONNA_INLINE static void
+curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) {
+       out[0] = a[0] + b[0];
+       out[1] = a[1] + b[1];
+       out[2] = a[2] + b[2];
+       out[3] = a[3] + b[3];
+       out[4] = a[4] + b[4];
+}
+
+/* out = a + b, where a and/or b are the result of a basic op (add,sub) */
+DONNA_INLINE static void
+curve25519_add_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
+       out[0] = a[0] + b[0];
+       out[1] = a[1] + b[1];
+       out[2] = a[2] + b[2];
+       out[3] = a[3] + b[3];
+       out[4] = a[4] + b[4];
+}
+
+DONNA_INLINE static void
+curve25519_add_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
+       uint64_t c;
+       out[0] = a[0] + b[0]    ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
+       out[1] = a[1] + b[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
+       out[2] = a[2] + b[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
+       out[3] = a[3] + b[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
+       out[4] = a[4] + b[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
+       out[0] += c * 19;
+}
+
+/* multiples of p */
+static const uint64_t twoP0      = 0x0fffffffffffda;
+static const uint64_t twoP1234   = 0x0ffffffffffffe;
+static const uint64_t fourP0     = 0x1fffffffffffb4;
+static const uint64_t fourP1234  = 0x1ffffffffffffc;
+
+/* out = a - b */
+DONNA_INLINE static void
+curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) {
+       out[0] = a[0] + twoP0    - b[0];
+       out[1] = a[1] + twoP1234 - b[1];
+       out[2] = a[2] + twoP1234 - b[2];
+       out[3] = a[3] + twoP1234 - b[3];
+       out[4] = a[4] + twoP1234 - b[4];
+}
+
+/* out = a - b, where a and/or b are the result of a basic op (add,sub) */
+DONNA_INLINE static void
+curve25519_sub_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
+       out[0] = a[0] + fourP0    - b[0];
+       out[1] = a[1] + fourP1234 - b[1];
+       out[2] = a[2] + fourP1234 - b[2];
+       out[3] = a[3] + fourP1234 - b[3];
+       out[4] = a[4] + fourP1234 - b[4];
+}
+
+DONNA_INLINE static void
+curve25519_sub_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
+       uint64_t c;
+       out[0] = a[0] + fourP0    - b[0]    ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
+       out[1] = a[1] + fourP1234 - b[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
+       out[2] = a[2] + fourP1234 - b[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
+       out[3] = a[3] + fourP1234 - b[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
+       out[4] = a[4] + fourP1234 - b[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
+       out[0] += c * 19;
+}
+
+/* out = -a */
+DONNA_INLINE static void
+curve25519_neg(bignum25519 out, const bignum25519 a) {
+       uint64_t c;
+       out[0] = twoP0    - a[0]    ; c = (out[0] >> 51); out[0] &= reduce_mask_51;
+       out[1] = twoP1234 - a[1] + c; c = (out[1] >> 51); out[1] &= reduce_mask_51;
+       out[2] = twoP1234 - a[2] + c; c = (out[2] >> 51); out[2] &= reduce_mask_51;
+       out[3] = twoP1234 - a[3] + c; c = (out[3] >> 51); out[3] &= reduce_mask_51;
+       out[4] = twoP1234 - a[4] + c; c = (out[4] >> 51); out[4] &= reduce_mask_51;
+       out[0] += c * 19;
+}
+
+/* out = a * b */
+DONNA_INLINE static void
+curve25519_mul(bignum25519 out, const bignum25519 in2, const bignum25519 in) {
+#if !defined(HAVE_NATIVE_UINT128)
+       uint128_t mul;
+#endif
+       uint128_t t[5];
+       uint64_t r0,r1,r2,r3,r4,s0,s1,s2,s3,s4,c;
+
+       r0 = in[0];
+       r1 = in[1];
+       r2 = in[2];
+       r3 = in[3];
+       r4 = in[4];
+
+       s0 = in2[0];
+       s1 = in2[1];
+       s2 = in2[2];
+       s3 = in2[3];
+       s4 = in2[4];
+
+#if defined(HAVE_NATIVE_UINT128)
+       t[0]  =  ((uint128_t) r0) * s0;
+       t[1]  =  ((uint128_t) r0) * s1 + ((uint128_t) r1) * s0;
+       t[2]  =  ((uint128_t) r0) * s2 + ((uint128_t) r2) * s0 + ((uint128_t) r1) * s1;
+       t[3]  =  ((uint128_t) r0) * s3 + ((uint128_t) r3) * s0 + ((uint128_t) r1) * s2 + ((uint128_t) r2) * s1;
+       t[4]  =  ((uint128_t) r0) * s4 + ((uint128_t) r4) * s0 + ((uint128_t) r3) * s1 + ((uint128_t) r1) * s3 + ((uint128_t) r2) * s2;
+#else
+       mul64x64_128(t[0], r0, s0)
+       mul64x64_128(t[1], r0, s1) mul64x64_128(mul, r1, s0) add128(t[1], mul)
+       mul64x64_128(t[2], r0, s2) mul64x64_128(mul, r2, s0) add128(t[2], mul) mul64x64_128(mul, r1, s1) add128(t[2], mul)
+       mul64x64_128(t[3], r0, s3) mul64x64_128(mul, r3, s0) add128(t[3], mul) mul64x64_128(mul, r1, s2) add128(t[3], mul) mul64x64_128(mul, r2, s1) add128(t[3], mul)
+       mul64x64_128(t[4], r0, s4) mul64x64_128(mul, r4, s0) add128(t[4], mul) mul64x64_128(mul, r3, s1) add128(t[4], mul) mul64x64_128(mul, r1, s3) add128(t[4], mul) mul64x64_128(mul, r2, s2) add128(t[4], mul)
+#endif
+
+       r1 *= 19;
+       r2 *= 19;
+       r3 *= 19;
+       r4 *= 19;
+
+#if defined(HAVE_NATIVE_UINT128)
+       t[0] += ((uint128_t) r4) * s1 + ((uint128_t) r1) * s4 + ((uint128_t) r2) * s3 + ((uint128_t) r3) * s2;
+       t[1] += ((uint128_t) r4) * s2 + ((uint128_t) r2) * s4 + ((uint128_t) r3) * s3;
+       t[2] += ((uint128_t) r4) * s3 + ((uint128_t) r3) * s4;
+       t[3] += ((uint128_t) r4) * s4;
+#else
+       mul64x64_128(mul, r4, s1) add128(t[0], mul) mul64x64_128(mul, r1, s4) add128(t[0], mul) mul64x64_128(mul, r2, s3) add128(t[0], mul) mul64x64_128(mul, r3, s2) add128(t[0], mul)
+       mul64x64_128(mul, r4, s2) add128(t[1], mul) mul64x64_128(mul, r2, s4) add128(t[1], mul) mul64x64_128(mul, r3, s3) add128(t[1], mul)
+       mul64x64_128(mul, r4, s3) add128(t[2], mul) mul64x64_128(mul, r3, s4) add128(t[2], mul)
+       mul64x64_128(mul, r4, s4) add128(t[3], mul)
+#endif
+
+
+                            r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
+       add128_64(t[1], c)   r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
+       add128_64(t[2], c)   r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
+       add128_64(t[3], c)   r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
+       add128_64(t[4], c)   r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
+       r0 +=   c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
+       r1 +=   c;
+
+       out[0] = r0;
+       out[1] = r1;
+       out[2] = r2;
+       out[3] = r3;
+       out[4] = r4;
+}
+
+DONNA_NOINLINE static void
+curve25519_mul_noinline(bignum25519 out, const bignum25519 in2, const bignum25519 in) {
+       curve25519_mul(out, in2, in);
+}
+
+/* out = in^(2 * count) */
+DONNA_NOINLINE static void
+curve25519_square_times(bignum25519 out, const bignum25519 in, uint64_t count) {
+#if !defined(HAVE_NATIVE_UINT128)
+       uint128_t mul;
+#endif
+       uint128_t t[5];
+       uint64_t r0,r1,r2,r3,r4,c;
+       uint64_t d0,d1,d2,d4,d419;
+
+       r0 = in[0];
+       r1 = in[1];
+       r2 = in[2];
+       r3 = in[3];
+       r4 = in[4];
+
+       do {
+               d0 = r0 * 2;
+               d1 = r1 * 2;
+               d2 = r2 * 2 * 19;
+               d419 = r4 * 19;
+               d4 = d419 * 2;
+
+#if defined(HAVE_NATIVE_UINT128)
+               t[0] = ((uint128_t) r0) * r0 + ((uint128_t) d4) * r1 + (((uint128_t) d2) * (r3     ));
+               t[1] = ((uint128_t) d0) * r1 + ((uint128_t) d4) * r2 + (((uint128_t) r3) * (r3 * 19));
+               t[2] = ((uint128_t) d0) * r2 + ((uint128_t) r1) * r1 + (((uint128_t) d4) * (r3     ));
+               t[3] = ((uint128_t) d0) * r3 + ((uint128_t) d1) * r2 + (((uint128_t) r4) * (d419   ));
+               t[4] = ((uint128_t) d0) * r4 + ((uint128_t) d1) * r3 + (((uint128_t) r2) * (r2     ));
+#else
+               mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2,      r3) add128(t[0], mul)
+               mul64x64_128(t[1], d0, r1) mul64x64_128(mul, d4, r2) add128(t[1], mul) mul64x64_128(mul, r3, r3 * 19) add128(t[1], mul)
+               mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4,      r3) add128(t[2], mul)
+               mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4,    d419) add128(t[3], mul)
+               mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2,      r2) add128(t[4], mul)
+#endif
+
+               r0 = lo128(t[0]) & reduce_mask_51;
+               r1 = lo128(t[1]) & reduce_mask_51; shl128(c, t[0], 13); r1 += c;
+               r2 = lo128(t[2]) & reduce_mask_51; shl128(c, t[1], 13); r2 += c;
+               r3 = lo128(t[3]) & reduce_mask_51; shl128(c, t[2], 13); r3 += c;
+               r4 = lo128(t[4]) & reduce_mask_51; shl128(c, t[3], 13); r4 += c; 
+                                                  shl128(c, t[4], 13); r0 += c * 19;
+                              c = r0 >> 51; r0 &= reduce_mask_51;
+               r1 += c     ;  c = r1 >> 51; r1 &= reduce_mask_51;
+               r2 += c     ;  c = r2 >> 51; r2 &= reduce_mask_51;
+               r3 += c     ;  c = r3 >> 51; r3 &= reduce_mask_51;
+               r4 += c     ;  c = r4 >> 51; r4 &= reduce_mask_51;
+               r0 += c * 19;
+       } while(--count);
+
+       out[0] = r0;
+       out[1] = r1;
+       out[2] = r2;
+       out[3] = r3;
+       out[4] = r4;
+}
+
+DONNA_INLINE static void
+curve25519_square(bignum25519 out, const bignum25519 in) {
+#if !defined(HAVE_NATIVE_UINT128)
+       uint128_t mul;
+#endif
+       uint128_t t[5];
+       uint64_t r0,r1,r2,r3,r4,c;
+       uint64_t d0,d1,d2,d4,d419;
+
+       r0 = in[0];
+       r1 = in[1];
+       r2 = in[2];
+       r3 = in[3];
+       r4 = in[4];
+
+       d0 = r0 * 2;
+       d1 = r1 * 2;
+       d2 = r2 * 2 * 19;
+       d419 = r4 * 19;
+       d4 = d419 * 2;
+
+#if defined(HAVE_NATIVE_UINT128)
+       t[0] = ((uint128_t) r0) * r0 + ((uint128_t) d4) * r1 + (((uint128_t) d2) * (r3     ));
+       t[1] = ((uint128_t) d0) * r1 + ((uint128_t) d4) * r2 + (((uint128_t) r3) * (r3 * 19));
+       t[2] = ((uint128_t) d0) * r2 + ((uint128_t) r1) * r1 + (((uint128_t) d4) * (r3     ));
+       t[3] = ((uint128_t) d0) * r3 + ((uint128_t) d1) * r2 + (((uint128_t) r4) * (d419   ));
+       t[4] = ((uint128_t) d0) * r4 + ((uint128_t) d1) * r3 + (((uint128_t) r2) * (r2     ));
+#else
+       mul64x64_128(t[0], r0, r0) mul64x64_128(mul, d4, r1) add128(t[0], mul) mul64x64_128(mul, d2,      r3) add128(t[0], mul)
+       mul64x64_128(t[1], d0, r1) mul64x64_128(mul, d4, r2) add128(t[1], mul) mul64x64_128(mul, r3, r3 * 19) add128(t[1], mul)
+       mul64x64_128(t[2], d0, r2) mul64x64_128(mul, r1, r1) add128(t[2], mul) mul64x64_128(mul, d4,      r3) add128(t[2], mul)
+       mul64x64_128(t[3], d0, r3) mul64x64_128(mul, d1, r2) add128(t[3], mul) mul64x64_128(mul, r4,    d419) add128(t[3], mul)
+       mul64x64_128(t[4], d0, r4) mul64x64_128(mul, d1, r3) add128(t[4], mul) mul64x64_128(mul, r2,      r2) add128(t[4], mul)
+#endif
+
+                            r0 = lo128(t[0]) & reduce_mask_51; shr128(c, t[0], 51);
+       add128_64(t[1], c)   r1 = lo128(t[1]) & reduce_mask_51; shr128(c, t[1], 51);
+       add128_64(t[2], c)   r2 = lo128(t[2]) & reduce_mask_51; shr128(c, t[2], 51);
+       add128_64(t[3], c)   r3 = lo128(t[3]) & reduce_mask_51; shr128(c, t[3], 51);
+       add128_64(t[4], c)   r4 = lo128(t[4]) & reduce_mask_51; shr128(c, t[4], 51);
+       r0 +=   c * 19; c = r0 >> 51; r0 = r0 & reduce_mask_51;
+       r1 +=   c;
+
+       out[0] = r0;
+       out[1] = r1;
+       out[2] = r2;
+       out[3] = r3;
+       out[4] = r4;
+}
+
+/* Take a little-endian, 32-byte number and expand it into polynomial form */
+DONNA_INLINE static void
+curve25519_expand(bignum25519 out, const unsigned char *in) {
+       static const union { uint8_t b[2]; uint16_t s; } endian_check = {{1,0}};
+       uint64_t x0,x1,x2,x3;
+
+       if (endian_check.s == 1) {
+               x0 = *(uint64_t *)(in + 0);
+               x1 = *(uint64_t *)(in + 8);
+               x2 = *(uint64_t *)(in + 16);
+               x3 = *(uint64_t *)(in + 24);
+       } else {
+               #define F(s)                         \
+                       ((((uint64_t)in[s + 0])      ) | \
+                        (((uint64_t)in[s + 1]) <<  8) | \
+                        (((uint64_t)in[s + 2]) << 16) | \
+                        (((uint64_t)in[s + 3]) << 24) | \
+                        (((uint64_t)in[s + 4]) << 32) | \
+                        (((uint64_t)in[s + 5]) << 40) | \
+                        (((uint64_t)in[s + 6]) << 48) | \
+                        (((uint64_t)in[s + 7]) << 56))
+
+               x0 = F(0);
+               x1 = F(8);
+               x2 = F(16);
+               x3 = F(24);
+       }
+
+       out[0] = x0 & reduce_mask_51; x0 = (x0 >> 51) | (x1 << 13);
+       out[1] = x0 & reduce_mask_51; x1 = (x1 >> 38) | (x2 << 26);
+       out[2] = x1 & reduce_mask_51; x2 = (x2 >> 25) | (x3 << 39);
+       out[3] = x2 & reduce_mask_51; x3 = (x3 >> 12);
+       out[4] = x3 & reduce_mask_51;
+}
+
+/* Take a fully reduced polynomial form number and contract it into a
+ * little-endian, 32-byte array
+ */
+DONNA_INLINE static void
+curve25519_contract(unsigned char *out, const bignum25519 input) {
+       uint64_t t[5];
+       uint64_t f, i;
+
+       t[0] = input[0];
+       t[1] = input[1];
+       t[2] = input[2];
+       t[3] = input[3];
+       t[4] = input[4];
+
+       #define curve25519_contract_carry() \
+               t[1] += t[0] >> 51; t[0] &= reduce_mask_51; \
+               t[2] += t[1] >> 51; t[1] &= reduce_mask_51; \
+               t[3] += t[2] >> 51; t[2] &= reduce_mask_51; \
+               t[4] += t[3] >> 51; t[3] &= reduce_mask_51;
+
+       #define curve25519_contract_carry_full() curve25519_contract_carry() \
+               t[0] += 19 * (t[4] >> 51); t[4] &= reduce_mask_51;
+
+       #define curve25519_contract_carry_final() curve25519_contract_carry() \
+               t[4] &= reduce_mask_51;
+
+       curve25519_contract_carry_full()
+       curve25519_contract_carry_full()
+
+       /* now t is between 0 and 2^255-1, properly carried. */
+       /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
+       t[0] += 19;
+       curve25519_contract_carry_full()
+
+       /* now between 19 and 2^255-1 in both cases, and offset by 19. */
+       t[0] += (reduce_mask_51 + 1) - 19;
+       t[1] += (reduce_mask_51 + 1) - 1;
+       t[2] += (reduce_mask_51 + 1) - 1;
+       t[3] += (reduce_mask_51 + 1) - 1;
+       t[4] += (reduce_mask_51 + 1) - 1;
+
+       /* now between 2^255 and 2^256-20, and offset by 2^255. */
+       curve25519_contract_carry_final()
+
+       #define write51full(n,shift) \
+               f = ((t[n] >> shift) | (t[n+1] << (51 - shift))); \
+               for (i = 0; i < 8; i++, f >>= 8) *out++ = (unsigned char)f;
+       #define write51(n) write51full(n,13*n)
+       write51(0)
+       write51(1)
+       write51(2)
+       write51(3)
+}
+
+#if !defined(ED25519_GCC_64BIT_CHOOSE)
+
+/* out = (flag) ? in : out */
+DONNA_INLINE static void
+curve25519_move_conditional_bytes(uint8_t out[96], const uint8_t in[96], uint64_t flag) {
+       const uint64_t nb = flag - 1, b = ~nb;
+       const uint64_t *inq = (const uint64_t *)in;
+       uint64_t *outq = (uint64_t *)out;
+       outq[0] = (outq[0] & nb) | (inq[0] & b);
+       outq[1] = (outq[1] & nb) | (inq[1] & b);
+       outq[2] = (outq[2] & nb) | (inq[2] & b);
+       outq[3] = (outq[3] & nb) | (inq[3] & b);
+       outq[4] = (outq[4] & nb) | (inq[4] & b);
+       outq[5] = (outq[5] & nb) | (inq[5] & b);
+       outq[6] = (outq[6] & nb) | (inq[6] & b);
+       outq[7] = (outq[7] & nb) | (inq[7] & b);
+       outq[8] = (outq[8] & nb) | (inq[8] & b);
+       outq[9] = (outq[9] & nb) | (inq[9] & b);
+       outq[10] = (outq[10] & nb) | (inq[10] & b);
+       outq[11] = (outq[11] & nb) | (inq[11] & b);
+}
+
+/* if (iswap) swap(a, b) */
+DONNA_INLINE static void
+curve25519_swap_conditional(bignum25519 a, bignum25519 b, uint64_t iswap) {
+       const uint64_t swap = (uint64_t)(-(int64_t)iswap);
+       uint64_t x0,x1,x2,x3,x4;
+
+       x0 = swap & (a[0] ^ b[0]); a[0] ^= x0; b[0] ^= x0;
+       x1 = swap & (a[1] ^ b[1]); a[1] ^= x1; b[1] ^= x1;
+       x2 = swap & (a[2] ^ b[2]); a[2] ^= x2; b[2] ^= x2;
+       x3 = swap & (a[3] ^ b[3]); a[3] ^= x3; b[3] ^= x3;
+       x4 = swap & (a[4] ^ b[4]); a[4] ^= x4; b[4] ^= x4;
+}
+
+#endif /* ED25519_GCC_64BIT_CHOOSE */
+
+#define ED25519_64BIT_TABLES
+

diff --git a/crypto/ed25519-donna/src/curve25519-donna-64bit_svp64.s b/crypto/ed25519-donna/src/curve25519-donna-64bit_svp64.s
new file mode 100644 (file)
index 0000000..2c6defe
--- /dev/null
+++ b/crypto/ed25519-donna/src/curve25519-donna-64bit_svp64.s
@@ -0,0 +1,31 @@
+    .machine libresoc
+    .file      "curve25519-donna-64bit_svp64.s"
+    .abiversion 2
+    .section   ".text"
+    .align 2
+
+    .include "curve25519_svp64_macros.s"
+
+    .set out_ptr, 2
+    .set in_ptr, 3
+    .set j, 8
+
+    .globl  curve25519_copy_svp64_asm
+    .type   curve25519_copy_svp64_asm, @function
+curve25519_copy_svp64_asm:
+    .cfi_startproc
+
+    # Load 5 x 64-bit values from in
+    setvl                  0,0,5,0,1,1                     # Set VL to 5 elements
+    sv.ld               *j, 0(in_ptr)
+    sv.std              *j, 0(out_ptr)
+
+    blr
+
+    .long 0
+    .cfi_endproc
+
+.LFE0:
+    .size      curve25519_copy_svp64_asm,.-curve25519_copy_svp64_asm
+    .ident     "GCC: (Debian 8.3.0-6) 8.3.0"
+    .section   .note.GNU-stack,"",@progbits

diff --git a/crypto/ed25519-donna/src/curve25519-donna-64bit_wrappers.c b/crypto/ed25519-donna/src/curve25519-donna-64bit_wrappers.c
new file mode 100644 (file)
index 0000000..d1dacd7
--- /dev/null
+++ b/crypto/ed25519-donna/src/curve25519-donna-64bit_wrappers.c
@@ -0,0 +1,74 @@
+#include <Python.h>
+#include <stdint.h>
+#include <stdio.h>
+
+#include "pypowersim_wrapper_common.h"
+#include "curve25519-donna-64bit_wrappers.h"
+
+const char *curve25519_donna_64bit_svp64_filename = "./bin/curve25519-donna-64bit_svp64.bin";
+
+void
+curve25519_copy_svp64(bignum25519 out, const bignum25519 in) {
+
+    // These cannot be the same pointer as the original function, as it is really a separate CPU/RAM
+    // we have to memcpy from input to this pointer, the address was chosen arbitrarily
+    uint64_t outptr_svp64  = 0x100000;
+    uint64_t inptr_svp64 = 0x200000;
+
+    // Create the pypowersim_state
+    pypowersim_state_t *state = pypowersim_prepare();
+
+    // Change the relevant elements
+    state->binary = PyBytes_FromStringAndSize(curve25519_donna_64bit_svp64_filename, strlen(curve25519_donna_64bit_svp64_filename));
+
+    // Set GPR #3 to the out bignum25519 pointer
+    PyObject *outptr_address = PyLong_FromUnsignedLongLong(outptr_svp64);
+    PyList_SetItem(state->initial_regs, 2, outptr_address);
+
+    // Set GPR #4 to the input pointer
+    PyObject *inptr_address = PyLong_FromUnsignedLongLong(inptr_svp64);
+    PyList_SetItem(state->initial_regs, 3, inptr_address);
+
+    // Load data into buffer from real memory
+    for (size_t i = 0; i < sizeof(bignum25519)/sizeof(uint64_t); i++) {
+      PyObject *svp64_address = PyLong_FromUnsignedLongLong(inptr_svp64 + i*8);
+      uint64_t inptr64 = in[i];
+      printf("val \t: %016lx -> %016lx\n", inptr64, inptr_svp64);
+      PyObject *word = PyLong_FromUnsignedLongLong(inptr64);
+      PyDict_SetItem(state->initial_mem, svp64_address, word);
+    }
+
+    // Prepare the arguments object for the call
+    pypowersim_prepareargs(state);
+
+    // Call the function and get the resulting object
+    state->result_obj = PyObject_CallObject(state->simulator, state->args);
+    if (!state->result_obj) {
+        PyErr_Print();
+        printf("Error invoking 'run_a_simulation'\n");
+        pypowersim_finalize(state);
+       exit(1);
+    }
+
+    PyObject *memobj = PyObject_GetAttrString(state->result_obj, "mem");
+    if (!memobj) {
+        PyErr_Print();
+        Py_DECREF(state->result_obj);
+        printf("Error getting mem object\n");
+    }
+
+    PyObject *mem = PyObject_GetAttrString(memobj, "mem");
+    if (!mem) {
+        PyErr_Print();
+        Py_DECREF(state->result_obj);
+        printf("Error getting mem dict\n");
+    }
+
+    for (size_t i = 0; i < sizeof(bignum25519)/sizeof(uint64_t); i++) {
+      PyObject *svp64_address = PyLong_FromUnsignedLongLong((outptr_svp64 + i*8)/8);
+      PyObject *pyval = PyDict_GetItem(mem, svp64_address);
+      uint64_t val = PyLong_AsUnsignedLongLong(pyval);
+      out[i] = val;
+      printf("out[%ld]: %016lx\t val: %016lx -> %lx\n", i, out[i], val, outptr_svp64 + i*8);
+    }
+}

diff --git a/crypto/ed25519-donna/src/curve25519-donna-64bit_wrappers.h b/crypto/ed25519-donna/src/curve25519-donna-64bit_wrappers.h
new file mode 100644 (file)
index 0000000..ab3a108
--- /dev/null
+++ b/crypto/ed25519-donna/src/curve25519-donna-64bit_wrappers.h
@@ -0,0 +1,7 @@
+#include <stdint.h>
+
+typedef uint64_t bignum25519[5];
+
+void curve25519_copy_svp64(bignum25519 out, const bignum25519 in);
+void curve25519_copy_svp64_asm(bignum25519 out, const bignum25519 in);
+

diff --git a/crypto/ed25519-donna/src/curve25519-donna-helpers.h b/crypto/ed25519-donna/src/curve25519-donna-helpers.h
new file mode 100644 (file)
index 0000000..e4058ff
--- /dev/null
+++ b/crypto/ed25519-donna/src/curve25519-donna-helpers.h
@@ -0,0 +1,67 @@
+/*
+       Public domain by Andrew M. <liquidsun@gmail.com>
+       See: https://github.com/floodyberry/curve25519-donna
+
+       Curve25519 implementation agnostic helpers
+*/
+
+/*
+ * In:  b =   2^5 - 2^0
+ * Out: b = 2^250 - 2^0
+ */
+static void
+curve25519_pow_two5mtwo0_two250mtwo0(bignum25519 b) {
+       bignum25519 ALIGN(16) t0,c;
+
+       /* 2^5  - 2^0 */ /* b */
+       /* 2^10 - 2^5 */ curve25519_square_times(t0, b, 5);
+       /* 2^10 - 2^0 */ curve25519_mul_noinline(b, t0, b);
+       /* 2^20 - 2^10 */ curve25519_square_times(t0, b, 10);
+       /* 2^20 - 2^0 */ curve25519_mul_noinline(c, t0, b);
+       /* 2^40 - 2^20 */ curve25519_square_times(t0, c, 20);
+       /* 2^40 - 2^0 */ curve25519_mul_noinline(t0, t0, c);
+       /* 2^50 - 2^10 */ curve25519_square_times(t0, t0, 10);
+       /* 2^50 - 2^0 */ curve25519_mul_noinline(b, t0, b);
+       /* 2^100 - 2^50 */ curve25519_square_times(t0, b, 50);
+       /* 2^100 - 2^0 */ curve25519_mul_noinline(c, t0, b);
+       /* 2^200 - 2^100 */ curve25519_square_times(t0, c, 100);
+       /* 2^200 - 2^0 */ curve25519_mul_noinline(t0, t0, c);
+       /* 2^250 - 2^50 */ curve25519_square_times(t0, t0, 50);
+       /* 2^250 - 2^0 */ curve25519_mul_noinline(b, t0, b);
+}
+
+/*
+ * z^(p - 2) = z(2^255 - 21)
+ */
+static void
+curve25519_recip(bignum25519 out, const bignum25519 z) {
+       bignum25519 ALIGN(16) a,t0,b;
+
+       /* 2 */ curve25519_square_times(a, z, 1); /* a = 2 */
+       /* 8 */ curve25519_square_times(t0, a, 2);
+       /* 9 */ curve25519_mul_noinline(b, t0, z); /* b = 9 */
+       /* 11 */ curve25519_mul_noinline(a, b, a); /* a = 11 */
+       /* 22 */ curve25519_square_times(t0, a, 1);
+       /* 2^5 - 2^0 = 31 */ curve25519_mul_noinline(b, t0, b);
+       /* 2^250 - 2^0 */ curve25519_pow_two5mtwo0_two250mtwo0(b);
+       /* 2^255 - 2^5 */ curve25519_square_times(b, b, 5);
+       /* 2^255 - 21 */ curve25519_mul_noinline(out, b, a);
+}
+
+/*
+ * z^((p-5)/8) = z^(2^252 - 3)
+ */
+static void
+curve25519_pow_two252m3(bignum25519 two252m3, const bignum25519 z) {
+       bignum25519 ALIGN(16) b,c,t0;
+
+       /* 2 */ curve25519_square_times(c, z, 1); /* c = 2 */
+       /* 8 */ curve25519_square_times(t0, c, 2); /* t0 = 8 */
+       /* 9 */ curve25519_mul_noinline(b, t0, z); /* b = 9 */
+       /* 11 */ curve25519_mul_noinline(c, b, c); /* c = 11 */
+       /* 22 */ curve25519_square_times(t0, c, 1);
+       /* 2^5 - 2^0 = 31 */ curve25519_mul_noinline(b, t0, b);
+       /* 2^250 - 2^0 */ curve25519_pow_two5mtwo0_two250mtwo0(b);
+       /* 2^252 - 2^2 */ curve25519_square_times(b, b, 2);
+       /* 2^252 - 3 */ curve25519_mul_noinline(two252m3, b, z);
+}

diff --git a/crypto/ed25519-donna/src/curve25519-donna-sse2.h b/crypto/ed25519-donna/src/curve25519-donna-sse2.h
new file mode 100644 (file)
index 0000000..1dbfd44
--- /dev/null
+++ b/crypto/ed25519-donna/src/curve25519-donna-sse2.h
@@ -0,0 +1,1112 @@
+/*
+       Public domain by Andrew M. <liquidsun@gmail.com>
+       See: https://github.com/floodyberry/curve25519-donna
+
+       SSE2 curve25519 implementation
+*/
+
+#include <emmintrin.h>
+typedef __m128i xmmi;
+
+typedef union packedelem8_t {
+       unsigned char u[16];
+       xmmi v;
+} packedelem8;
+
+typedef union packedelem32_t {
+       uint32_t u[4];
+       xmmi v;
+} packedelem32;
+
+typedef union packedelem64_t {
+       uint64_t u[2];
+       xmmi v;
+} packedelem64;
+
+/* 10 elements + an extra 2 to fit in 3 xmm registers */
+typedef uint32_t bignum25519[12];
+typedef packedelem32 packed32bignum25519[5];
+typedef packedelem64 packed64bignum25519[10];
+
+static const packedelem32 bot32bitmask = {{0xffffffff, 0x00000000, 0xffffffff, 0x00000000}};
+static const packedelem32 top32bitmask = {{0x00000000, 0xffffffff, 0x00000000, 0xffffffff}};
+static const packedelem32 top64bitmask = {{0x00000000, 0x00000000, 0xffffffff, 0xffffffff}};
+static const packedelem32 bot64bitmask = {{0xffffffff, 0xffffffff, 0x00000000, 0x00000000}};
+
+/* reduction masks */
+static const packedelem64 packedmask26 = {{0x03ffffff, 0x03ffffff}};
+static const packedelem64 packedmask25 = {{0x01ffffff, 0x01ffffff}};
+static const packedelem32 packedmask2625 = {{0x3ffffff,0,0x1ffffff,0}};
+static const packedelem32 packedmask26262626 = {{0x03ffffff, 0x03ffffff, 0x03ffffff, 0x03ffffff}};
+static const packedelem32 packedmask25252525 = {{0x01ffffff, 0x01ffffff, 0x01ffffff, 0x01ffffff}};
+
+/* multipliers */
+static const packedelem64 packednineteen = {{19, 19}};
+static const packedelem64 packednineteenone = {{19, 1}};
+static const packedelem64 packedthirtyeight = {{38, 38}};
+static const packedelem64 packed3819 = {{19*2,19}};
+static const packedelem64 packed9638 = {{19*4,19*2}};
+
+/* 121666,121665 */
+static const packedelem64 packed121666121665 = {{121666, 121665}};
+
+/* 2*(2^255 - 19) = 0 mod p */
+static const packedelem32 packed2p0 = {{0x7ffffda,0x3fffffe,0x7fffffe,0x3fffffe}};
+static const packedelem32 packed2p1 = {{0x7fffffe,0x3fffffe,0x7fffffe,0x3fffffe}};
+static const packedelem32 packed2p2 = {{0x7fffffe,0x3fffffe,0x0000000,0x0000000}};
+
+static const packedelem32 packed32packed2p0 = {{0x7ffffda,0x7ffffda,0x3fffffe,0x3fffffe}};
+static const packedelem32 packed32packed2p1 = {{0x7fffffe,0x7fffffe,0x3fffffe,0x3fffffe}};
+
+/* 4*(2^255 - 19) = 0 mod p */
+static const packedelem32 packed4p0 = {{0xfffffb4,0x7fffffc,0xffffffc,0x7fffffc}};
+static const packedelem32 packed4p1 = {{0xffffffc,0x7fffffc,0xffffffc,0x7fffffc}};
+static const packedelem32 packed4p2 = {{0xffffffc,0x7fffffc,0x0000000,0x0000000}};
+
+static const packedelem32 packed32packed4p0 = {{0xfffffb4,0xfffffb4,0x7fffffc,0x7fffffc}};
+static const packedelem32 packed32packed4p1 = {{0xffffffc,0xffffffc,0x7fffffc,0x7fffffc}};
+
+/* out = in */
+DONNA_INLINE static void
+curve25519_copy(bignum25519 out, const bignum25519 in) {
+       xmmi x0,x1,x2;
+       x0 = _mm_load_si128((xmmi*)in + 0);
+       x1 = _mm_load_si128((xmmi*)in + 1);
+       x2 = _mm_load_si128((xmmi*)in + 2);
+       _mm_store_si128((xmmi*)out + 0, x0);
+       _mm_store_si128((xmmi*)out + 1, x1);
+       _mm_store_si128((xmmi*)out + 2, x2);
+}
+
+/* out = a + b */
+DONNA_INLINE static void
+curve25519_add(bignum25519 out, const bignum25519 a, const bignum25519 b) {
+       xmmi a0,a1,a2,b0,b1,b2;
+       a0 = _mm_load_si128((xmmi*)a + 0);
+       a1 = _mm_load_si128((xmmi*)a + 1);
+       a2 = _mm_load_si128((xmmi*)a + 2);
+       b0 = _mm_load_si128((xmmi*)b + 0);
+       b1 = _mm_load_si128((xmmi*)b + 1);
+       b2 = _mm_load_si128((xmmi*)b + 2);
+       a0 = _mm_add_epi32(a0, b0);
+       a1 = _mm_add_epi32(a1, b1);
+       a2 = _mm_add_epi32(a2, b2);
+       _mm_store_si128((xmmi*)out + 0, a0);
+       _mm_store_si128((xmmi*)out + 1, a1);
+       _mm_store_si128((xmmi*)out + 2, a2);
+}
+
+#define curve25519_add_after_basic curve25519_add_reduce
+DONNA_INLINE static void
+curve25519_add_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
+       xmmi a0,a1,a2,b0,b1,b2;
+       xmmi c1,c2,c3;
+       xmmi r0,r1,r2,r3,r4,r5;
+
+       a0 = _mm_load_si128((xmmi*)a + 0);
+       a1 = _mm_load_si128((xmmi*)a + 1);
+       a2 = _mm_load_si128((xmmi*)a + 2);
+       b0 = _mm_load_si128((xmmi*)b + 0);
+       b1 = _mm_load_si128((xmmi*)b + 1);
+       b2 = _mm_load_si128((xmmi*)b + 2);
+       a0 = _mm_add_epi32(a0, b0);
+       a1 = _mm_add_epi32(a1, b1);
+       a2 = _mm_add_epi32(a2, b2);
+
+       r0 = _mm_and_si128(_mm_unpacklo_epi64(a0, a1), bot32bitmask.v);
+       r1 = _mm_srli_epi64(_mm_unpacklo_epi64(a0, a1), 32);
+       r2 = _mm_and_si128(_mm_unpackhi_epi64(a0, a1), bot32bitmask.v);
+       r3 = _mm_srli_epi64(_mm_unpackhi_epi64(a0, a1), 32);
+       r4 = _mm_and_si128(_mm_unpacklo_epi64(_mm_setzero_si128(), a2), bot32bitmask.v);
+       r5 = _mm_srli_epi64(_mm_unpacklo_epi64(_mm_setzero_si128(), a2), 32);
+
+       c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);
+       c1 = _mm_srli_epi64(r1, 25); c2 = _mm_srli_epi64(r3, 25); r1 = _mm_and_si128(r1, packedmask25.v); r3 = _mm_and_si128(r3, packedmask25.v); r2 = _mm_add_epi64(r2, c1); r4 = _mm_add_epi64(r4, c2); c3 = _mm_slli_si128(c2, 8);
+       c1 = _mm_srli_epi64(r4, 26);                                                                      r4 = _mm_and_si128(r4, packedmask26.v);                             r5 = _mm_add_epi64(r5, c1); 
+       c1 = _mm_srli_epi64(r5, 25);                                                                      r5 = _mm_and_si128(r5, packedmask25.v);                             r0 = _mm_add_epi64(r0, _mm_unpackhi_epi64(_mm_mul_epu32(c1, packednineteen.v), c3));
+       c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);
+
+       _mm_store_si128((xmmi*)out + 0, _mm_unpacklo_epi64(_mm_unpacklo_epi32(r0, r1), _mm_unpacklo_epi32(r2, r3)));
+       _mm_store_si128((xmmi*)out + 1, _mm_unpacklo_epi64(_mm_unpackhi_epi32(r0, r1), _mm_unpackhi_epi32(r2, r3)));
+       _mm_store_si128((xmmi*)out + 2, _mm_unpackhi_epi32(r4, r5));
+}
+
+DONNA_INLINE static void
+curve25519_sub(bignum25519 out, const bignum25519 a, const bignum25519 b) {
+       xmmi a0,a1,a2,b0,b1,b2;
+       xmmi c1,c2;
+       xmmi r0,r1;
+
+       a0 = _mm_load_si128((xmmi*)a + 0);
+       a1 = _mm_load_si128((xmmi*)a + 1);
+       a2 = _mm_load_si128((xmmi*)a + 2);
+       a0 = _mm_add_epi32(a0, packed2p0.v);
+       a1 = _mm_add_epi32(a1, packed2p1.v);
+       a2 = _mm_add_epi32(a2, packed2p2.v);
+       b0 = _mm_load_si128((xmmi*)b + 0);
+       b1 = _mm_load_si128((xmmi*)b + 1);
+       b2 = _mm_load_si128((xmmi*)b + 2);
+       a0 = _mm_sub_epi32(a0, b0);
+       a1 = _mm_sub_epi32(a1, b1);
+       a2 = _mm_sub_epi32(a2, b2);
+
+       r0 = _mm_and_si128(_mm_shuffle_epi32(a0, _MM_SHUFFLE(2,2,0,0)), bot32bitmask.v);
+       r1 = _mm_and_si128(_mm_shuffle_epi32(a0, _MM_SHUFFLE(3,3,1,1)), bot32bitmask.v);
+
+       c1 = _mm_srli_epi32(r0, 26); 
+       c2 = _mm_srli_epi32(r1, 25); 
+       r0 = _mm_and_si128(r0, packedmask26.v); 
+       r1 = _mm_and_si128(r1, packedmask25.v); 
+       r0 = _mm_add_epi32(r0, _mm_slli_si128(c2, 8));
+       r1 = _mm_add_epi32(r1, c1);
+
+       a0 = _mm_unpacklo_epi64(_mm_unpacklo_epi32(r0, r1), _mm_unpackhi_epi32(r0, r1));
+       a1 = _mm_add_epi32(a1, _mm_srli_si128(c2, 8));
+
+       _mm_store_si128((xmmi*)out + 0, a0);
+       _mm_store_si128((xmmi*)out + 1, a1);
+       _mm_store_si128((xmmi*)out + 2, a2);
+}
+
+DONNA_INLINE static void
+curve25519_sub_after_basic(bignum25519 out, const bignum25519 a, const bignum25519 b) {
+       xmmi a0,a1,a2,b0,b1,b2;
+       xmmi c1,c2,c3;
+       xmmi r0,r1,r2,r3,r4,r5;
+
+       a0 = _mm_load_si128((xmmi*)a + 0);
+       a1 = _mm_load_si128((xmmi*)a + 1);
+       a2 = _mm_load_si128((xmmi*)a + 2);
+       a0 = _mm_add_epi32(a0, packed4p0.v);
+       a1 = _mm_add_epi32(a1, packed4p1.v);
+       a2 = _mm_add_epi32(a2, packed4p2.v);
+       b0 = _mm_load_si128((xmmi*)b + 0);
+       b1 = _mm_load_si128((xmmi*)b + 1);
+       b2 = _mm_load_si128((xmmi*)b + 2);
+       a0 = _mm_sub_epi32(a0, b0);
+       a1 = _mm_sub_epi32(a1, b1);
+       a2 = _mm_sub_epi32(a2, b2);
+
+       r0 = _mm_and_si128(_mm_unpacklo_epi64(a0, a1), bot32bitmask.v);
+       r1 = _mm_srli_epi64(_mm_unpacklo_epi64(a0, a1), 32);
+       r2 = _mm_and_si128(_mm_unpackhi_epi64(a0, a1), bot32bitmask.v);
+       r3 = _mm_srli_epi64(_mm_unpackhi_epi64(a0, a1), 32);
+       r4 = _mm_and_si128(_mm_unpacklo_epi64(_mm_setzero_si128(), a2), bot32bitmask.v);
+       r5 = _mm_srli_epi64(_mm_unpacklo_epi64(_mm_setzero_si128(), a2), 32);
+
+       c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);
+       c1 = _mm_srli_epi64(r1, 25); c2 = _mm_srli_epi64(r3, 25); r1 = _mm_and_si128(r1, packedmask25.v); r3 = _mm_and_si128(r3, packedmask25.v); r2 = _mm_add_epi64(r2, c1); r4 = _mm_add_epi64(r4, c2); c3 = _mm_slli_si128(c2, 8);
+       c1 = _mm_srli_epi64(r4, 26);                                                                      r4 = _mm_and_si128(r4, packedmask26.v);                             r5 = _mm_add_epi64(r5, c1); 
+       c1 = _mm_srli_epi64(r5, 25);                                                                      r5 = _mm_and_si128(r5, packedmask25.v);                             r0 = _mm_add_epi64(r0, _mm_unpackhi_epi64(_mm_mul_epu32(c1, packednineteen.v), c3));
+       c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);
+
+       _mm_store_si128((xmmi*)out + 0, _mm_unpacklo_epi64(_mm_unpacklo_epi32(r0, r1), _mm_unpacklo_epi32(r2, r3)));
+       _mm_store_si128((xmmi*)out + 1, _mm_unpacklo_epi64(_mm_unpackhi_epi32(r0, r1), _mm_unpackhi_epi32(r2, r3)));
+       _mm_store_si128((xmmi*)out + 2, _mm_unpackhi_epi32(r4, r5));
+}
+
+DONNA_INLINE static void
+curve25519_sub_reduce(bignum25519 out, const bignum25519 a, const bignum25519 b) {
+       xmmi a0,a1,a2,b0,b1,b2;
+       xmmi c1,c2,c3;
+       xmmi r0,r1,r2,r3,r4,r5;
+
+       a0 = _mm_load_si128((xmmi*)a + 0);
+       a1 = _mm_load_si128((xmmi*)a + 1);
+       a2 = _mm_load_si128((xmmi*)a + 2);
+       a0 = _mm_add_epi32(a0, packed2p0.v);
+       a1 = _mm_add_epi32(a1, packed2p1.v);
+       a2 = _mm_add_epi32(a2, packed2p2.v);
+       b0 = _mm_load_si128((xmmi*)b + 0);
+       b1 = _mm_load_si128((xmmi*)b + 1);
+       b2 = _mm_load_si128((xmmi*)b + 2);
+       a0 = _mm_sub_epi32(a0, b0);
+       a1 = _mm_sub_epi32(a1, b1);
+       a2 = _mm_sub_epi32(a2, b2);
+
+       r0 = _mm_and_si128(_mm_unpacklo_epi64(a0, a1), bot32bitmask.v);
+       r1 = _mm_srli_epi64(_mm_unpacklo_epi64(a0, a1), 32);
+       r2 = _mm_and_si128(_mm_unpackhi_epi64(a0, a1), bot32bitmask.v);
+       r3 = _mm_srli_epi64(_mm_unpackhi_epi64(a0, a1), 32);
+       r4 = _mm_and_si128(_mm_unpacklo_epi64(_mm_setzero_si128(), a2), bot32bitmask.v);
+       r5 = _mm_srli_epi64(_mm_unpacklo_epi64(_mm_setzero_si128(), a2), 32);
+
+       c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);
+       c1 = _mm_srli_epi64(r1, 25); c2 = _mm_srli_epi64(r3, 25); r1 = _mm_and_si128(r1, packedmask25.v); r3 = _mm_and_si128(r3, packedmask25.v); r2 = _mm_add_epi64(r2, c1); r4 = _mm_add_epi64(r4, c2); c3 = _mm_slli_si128(c2, 8);
+       c1 = _mm_srli_epi64(r4, 26);                                                                      r4 = _mm_and_si128(r4, packedmask26.v);                             r5 = _mm_add_epi64(r5, c1); 
+       c1 = _mm_srli_epi64(r5, 25);                                                                      r5 = _mm_and_si128(r5, packedmask25.v);                             r0 = _mm_add_epi64(r0, _mm_unpackhi_epi64(_mm_mul_epu32(c1, packednineteen.v), c3));
+       c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);
+
+       _mm_store_si128((xmmi*)out + 0, _mm_unpacklo_epi64(_mm_unpacklo_epi32(r0, r1), _mm_unpacklo_epi32(r2, r3)));
+       _mm_store_si128((xmmi*)out + 1, _mm_unpacklo_epi64(_mm_unpackhi_epi32(r0, r1), _mm_unpackhi_epi32(r2, r3)));
+       _mm_store_si128((xmmi*)out + 2, _mm_unpackhi_epi32(r4, r5));
+}
+
+
+DONNA_INLINE static void
+curve25519_neg(bignum25519 out, const bignum25519 b) {
+       xmmi a0,a1,a2,b0,b1,b2;
+       xmmi c1,c2,c3;
+       xmmi r0,r1,r2,r3,r4,r5;
+
+       a0 = packed2p0.v;
+       a1 = packed2p1.v;
+       a2 = packed2p2.v;
+       b0 = _mm_load_si128((xmmi*)b + 0);
+       b1 = _mm_load_si128((xmmi*)b + 1);
+       b2 = _mm_load_si128((xmmi*)b + 2);
+       a0 = _mm_sub_epi32(a0, b0);
+       a1 = _mm_sub_epi32(a1, b1);
+       a2 = _mm_sub_epi32(a2, b2);
+
+       r0 = _mm_and_si128(_mm_unpacklo_epi64(a0, a1), bot32bitmask.v);
+       r1 = _mm_srli_epi64(_mm_unpacklo_epi64(a0, a1), 32);
+       r2 = _mm_and_si128(_mm_unpackhi_epi64(a0, a1), bot32bitmask.v);
+       r3 = _mm_srli_epi64(_mm_unpackhi_epi64(a0, a1), 32);
+       r4 = _mm_and_si128(_mm_unpacklo_epi64(_mm_setzero_si128(), a2), bot32bitmask.v);
+       r5 = _mm_srli_epi64(_mm_unpacklo_epi64(_mm_setzero_si128(), a2), 32);
+
+       c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);
+       c1 = _mm_srli_epi64(r1, 25); c2 = _mm_srli_epi64(r3, 25); r1 = _mm_and_si128(r1, packedmask25.v); r3 = _mm_and_si128(r3, packedmask25.v); r2 = _mm_add_epi64(r2, c1); r4 = _mm_add_epi64(r4, c2); c3 = _mm_slli_si128(c2, 8);
+       c1 = _mm_srli_epi64(r4, 26);                                                                      r4 = _mm_and_si128(r4, packedmask26.v);                             r5 = _mm_add_epi64(r5, c1); 
+       c1 = _mm_srli_epi64(r5, 25);                                                                      r5 = _mm_and_si128(r5, packedmask25.v);                             r0 = _mm_add_epi64(r0, _mm_unpackhi_epi64(_mm_mul_epu32(c1, packednineteen.v), c3));
+       c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);
+
+       _mm_store_si128((xmmi*)out + 0, _mm_unpacklo_epi64(_mm_unpacklo_epi32(r0, r1), _mm_unpacklo_epi32(r2, r3)));
+       _mm_store_si128((xmmi*)out + 1, _mm_unpacklo_epi64(_mm_unpackhi_epi32(r0, r1), _mm_unpackhi_epi32(r2, r3)));
+       _mm_store_si128((xmmi*)out + 2, _mm_unpackhi_epi32(r4, r5));
+}
+
+
+/* Multiply two numbers: out = in2 * in */
+static void 
+curve25519_mul(bignum25519 out, const bignum25519 r, const bignum25519 s) {
+       xmmi m01,m23,m45,m67,m89;
+       xmmi m0123,m4567;
+       xmmi s0123,s4567;
+       xmmi s01,s23,s45,s67,s89;
+       xmmi s12,s34,s56,s78,s9;
+       xmmi r0,r2,r4,r6,r8;
+       xmmi r1,r3,r5,r7,r9;
+       xmmi r119,r219,r319,r419,r519,r619,r719,r819,r919;
+       xmmi c1,c2,c3;
+
+       s0123 = _mm_load_si128((xmmi*)s + 0);
+       s01 = _mm_shuffle_epi32(s0123,_MM_SHUFFLE(3,1,2,0));
+       s12 = _mm_shuffle_epi32(s0123, _MM_SHUFFLE(2,2,1,1));
+       s23 = _mm_shuffle_epi32(s0123,_MM_SHUFFLE(3,3,2,2));
+       s4567 = _mm_load_si128((xmmi*)s + 1);
+       s34 = _mm_unpacklo_epi64(_mm_srli_si128(s0123,12),s4567);
+       s45 = _mm_shuffle_epi32(s4567,_MM_SHUFFLE(3,1,2,0));
+       s56 = _mm_shuffle_epi32(s4567, _MM_SHUFFLE(2,2,1,1));
+       s67 = _mm_shuffle_epi32(s4567,_MM_SHUFFLE(3,3,2,2));
+       s89 = _mm_load_si128((xmmi*)s + 2);
+       s78 = _mm_unpacklo_epi64(_mm_srli_si128(s4567,12),s89);
+       s89 = _mm_shuffle_epi32(s89,_MM_SHUFFLE(3,1,2,0));
+       s9 = _mm_shuffle_epi32(s89, _MM_SHUFFLE(3,3,2,2));
+
+       r0 = _mm_load_si128((xmmi*)r + 0);
+       r1 = _mm_shuffle_epi32(r0, _MM_SHUFFLE(1,1,1,1));
+       r1 = _mm_add_epi64(r1, _mm_and_si128(r1, top64bitmask.v));
+       r2 = _mm_shuffle_epi32(r0, _MM_SHUFFLE(2,2,2,2));
+       r3 = _mm_shuffle_epi32(r0, _MM_SHUFFLE(3,3,3,3));
+       r3 = _mm_add_epi64(r3, _mm_and_si128(r3, top64bitmask.v));
+       r0 = _mm_shuffle_epi32(r0, _MM_SHUFFLE(0,0,0,0));
+       r4 = _mm_load_si128((xmmi*)r + 1);
+       r5 = _mm_shuffle_epi32(r4, _MM_SHUFFLE(1,1,1,1));
+       r5 = _mm_add_epi64(r5, _mm_and_si128(r5, top64bitmask.v));
+       r6 = _mm_shuffle_epi32(r4, _MM_SHUFFLE(2,2,2,2));
+       r7 = _mm_shuffle_epi32(r4, _MM_SHUFFLE(3,3,3,3));
+       r7 = _mm_add_epi64(r7, _mm_and_si128(r7, top64bitmask.v));
+       r4 = _mm_shuffle_epi32(r4, _MM_SHUFFLE(0,0,0,0));
+       r8 = _mm_load_si128((xmmi*)r + 2);
+       r9 = _mm_shuffle_epi32(r8, _MM_SHUFFLE(3,1,3,1));
+       r9 = _mm_add_epi64(r9, _mm_and_si128(r9, top64bitmask.v));
+       r8 = _mm_shuffle_epi32(r8, _MM_SHUFFLE(3,0,3,0));
+
+       m01 = _mm_mul_epu32(r1,s01);
+       m23 = _mm_mul_epu32(r1,s23);
+       m45 = _mm_mul_epu32(r1,s45);
+       m67 = _mm_mul_epu32(r1,s67);
+       m23 = _mm_add_epi64(m23,_mm_mul_epu32(r3,s01));
+       m45 = _mm_add_epi64(m45,_mm_mul_epu32(r3,s23));
+       m67 = _mm_add_epi64(m67,_mm_mul_epu32(r3,s45));
+       m89 = _mm_mul_epu32(r1,s89);
+       m45 = _mm_add_epi64(m45,_mm_mul_epu32(r5,s01));
+       m67 = _mm_add_epi64(m67,_mm_mul_epu32(r5,s23));
+       m89 = _mm_add_epi64(m89,_mm_mul_epu32(r3,s67));
+       m67 = _mm_add_epi64(m67,_mm_mul_epu32(r7,s01));
+       m89 = _mm_add_epi64(m89,_mm_mul_epu32(r5,s45));
+       m89 = _mm_add_epi64(m89,_mm_mul_epu32(r7,s23));
+       m89 = _mm_add_epi64(m89,_mm_mul_epu32(r9,s01));
+
+       /* shift up */
+       m89 = _mm_unpackhi_epi64(m67,_mm_slli_si128(m89,8));
+       m67 = _mm_unpackhi_epi64(m45,_mm_slli_si128(m67,8));
+       m45 = _mm_unpackhi_epi64(m23,_mm_slli_si128(m45,8));
+       m23 = _mm_unpackhi_epi64(m01,_mm_slli_si128(m23,8));
+       m01 = _mm_unpackhi_epi64(_mm_setzero_si128(),_mm_slli_si128(m01,8));
+
+       m01 = _mm_add_epi64(m01,_mm_mul_epu32(r0,s01));
+       m23 = _mm_add_epi64(m23,_mm_mul_epu32(r0,s23));
+       m45 = _mm_add_epi64(m45,_mm_mul_epu32(r0,s45));
+       m67 = _mm_add_epi64(m67,_mm_mul_epu32(r0,s67));
+       m23 = _mm_add_epi64(m23,_mm_mul_epu32(r2,s01));
+       m45 = _mm_add_epi64(m45,_mm_mul_epu32(r2,s23));
+       m67 = _mm_add_epi64(m67,_mm_mul_epu32(r4,s23));
+       m89 = _mm_add_epi64(m89,_mm_mul_epu32(r0,s89));
+       m45 = _mm_add_epi64(m45,_mm_mul_epu32(r4,s01));
+       m67 = _mm_add_epi64(m67,_mm_mul_epu32(r2,s45));
+       m89 = _mm_add_epi64(m89,_mm_mul_epu32(r2,s67));
+       m67 = _mm_add_epi64(m67,_mm_mul_epu32(r6,s01));
+       m89 = _mm_add_epi64(m89,_mm_mul_epu32(r4,s45));
+       m89 = _mm_add_epi64(m89,_mm_mul_epu32(r6,s23));
+       m89 = _mm_add_epi64(m89,_mm_mul_epu32(r8,s01));
+
+       r219 = _mm_mul_epu32(r2, packednineteen.v);
+       r419 = _mm_mul_epu32(r4, packednineteen.v);
+       r619 = _mm_mul_epu32(r6, packednineteen.v);
+       r819 = _mm_mul_epu32(r8, packednineteen.v);
+       r119 = _mm_shuffle_epi32(r1,_MM_SHUFFLE(0,0,2,2)); r119 = _mm_mul_epu32(r119, packednineteen.v);
+       r319 = _mm_shuffle_epi32(r3,_MM_SHUFFLE(0,0,2,2)); r319 = _mm_mul_epu32(r319, packednineteen.v);
+       r519 = _mm_shuffle_epi32(r5,_MM_SHUFFLE(0,0,2,2)); r519 = _mm_mul_epu32(r519, packednineteen.v);
+       r719 = _mm_shuffle_epi32(r7,_MM_SHUFFLE(0,0,2,2)); r719 = _mm_mul_epu32(r719, packednineteen.v);
+       r919 = _mm_shuffle_epi32(r9,_MM_SHUFFLE(0,0,2,2)); r919 = _mm_mul_epu32(r919, packednineteen.v);
+
+       m01 = _mm_add_epi64(m01,_mm_mul_epu32(r919,s12));
+       m23 = _mm_add_epi64(m23,_mm_mul_epu32(r919,s34));
+       m45 = _mm_add_epi64(m45,_mm_mul_epu32(r919,s56));
+       m67 = _mm_add_epi64(m67,_mm_mul_epu32(r919,s78));
+       m01 = _mm_add_epi64(m01,_mm_mul_epu32(r719,s34));
+       m23 = _mm_add_epi64(m23,_mm_mul_epu32(r719,s56));
+       m45 = _mm_add_epi64(m45,_mm_mul_epu32(r719,s78));
+       m67 = _mm_add_epi64(m67,_mm_mul_epu32(r719,s9));
+       m01 = _mm_add_epi64(m01,_mm_mul_epu32(r519,s56));
+       m23 = _mm_add_epi64(m23,_mm_mul_epu32(r519,s78));
+       m45 = _mm_add_epi64(m45,_mm_mul_epu32(r519,s9));
+       m67 = _mm_add_epi64(m67,_mm_mul_epu32(r819,s89));
+       m01 = _mm_add_epi64(m01,_mm_mul_epu32(r319,s78));
+       m23 = _mm_add_epi64(m23,_mm_mul_epu32(r319,s9));
+       m45 = _mm_add_epi64(m45,_mm_mul_epu32(r619,s89));
+       m89 = _mm_add_epi64(m89,_mm_mul_epu32(r919,s9));
+       m01 = _mm_add_epi64(m01,_mm_mul_epu32(r819,s23));
+       m23 = _mm_add_epi64(m23,_mm_mul_epu32(r819,s45));
+       m45 = _mm_add_epi64(m45,_mm_mul_epu32(r819,s67));
+       m01 = _mm_add_epi64(m01,_mm_mul_epu32(r619,s45));
+       m23 = _mm_add_epi64(m23,_mm_mul_epu32(r619,s67));
+       m01 = _mm_add_epi64(m01,_mm_mul_epu32(r419,s67));
+       m23 = _mm_add_epi64(m23,_mm_mul_epu32(r419,s89));
+       m01 = _mm_add_epi64(m01,_mm_mul_epu32(r219,s89));
+       m01 = _mm_add_epi64(m01,_mm_mul_epu32(r119,s9));
+
+       r0 = _mm_unpacklo_epi64(m01, m45);
+       r1 = _mm_unpackhi_epi64(m01, m45);
+       r2 = _mm_unpacklo_epi64(m23, m67);
+       r3 = _mm_unpackhi_epi64(m23, m67);
+       r4 = _mm_unpacklo_epi64(m89, m89);
+       r5 = _mm_unpackhi_epi64(m89, m89);
+
+       c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);
+       c1 = _mm_srli_epi64(r1, 25); c2 = _mm_srli_epi64(r3, 25); r1 = _mm_and_si128(r1, packedmask25.v); r3 = _mm_and_si128(r3, packedmask25.v); r2 = _mm_add_epi64(r2, c1); r4 = _mm_add_epi64(r4, c2); c3 = _mm_slli_si128(c2, 8);
+       c1 = _mm_srli_epi64(r4, 26);                                                                      r4 = _mm_and_si128(r4, packedmask26.v);                             r5 = _mm_add_epi64(r5, c1); 
+       c1 = _mm_srli_epi64(r5, 25);                                                                      r5 = _mm_and_si128(r5, packedmask25.v);                             r0 = _mm_add_epi64(r0, _mm_unpackhi_epi64(_mm_mul_epu32(c1, packednineteen.v), c3));
+       c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);
+
+       m0123 = _mm_unpacklo_epi32(r0, r1);
+       m4567 = _mm_unpackhi_epi32(r0, r1);
+       m0123 = _mm_unpacklo_epi64(m0123, _mm_unpacklo_epi32(r2, r3));
+       m4567 = _mm_unpacklo_epi64(m4567, _mm_unpackhi_epi32(r2, r3));
+       m89 = _mm_unpackhi_epi32(r4, r5);
+
+       _mm_store_si128((xmmi*)out + 0, m0123);
+       _mm_store_si128((xmmi*)out + 1, m4567);
+       _mm_store_si128((xmmi*)out + 2, m89);
+}
+
+DONNA_NOINLINE static void
+curve25519_mul_noinline(bignum25519 out, const bignum25519 r, const bignum25519 s) {
+       curve25519_mul(out, r, s);
+}
+
+#define curve25519_square(r, n) curve25519_square_times(r, n, 1)
+static void
+curve25519_square_times(bignum25519 r, const bignum25519 in, int count) {
+       xmmi m01,m23,m45,m67,m89;
+       xmmi r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
+       xmmi r0a,r1a,r2a,r3a,r7a,r9a;
+       xmmi r0123,r4567;
+       xmmi r01,r23,r45,r67,r6x,r89,r8x;
+       xmmi r12,r34,r56,r78,r9x;
+       xmmi r5619;
+       xmmi c1,c2,c3;
+
+       r0123 = _mm_load_si128((xmmi*)in + 0);
+       r01 = _mm_shuffle_epi32(r0123,_MM_SHUFFLE(3,1,2,0));
+       r23 = _mm_shuffle_epi32(r0123,_MM_SHUFFLE(3,3,2,2));
+       r4567 = _mm_load_si128((xmmi*)in + 1);
+       r45 = _mm_shuffle_epi32(r4567,_MM_SHUFFLE(3,1,2,0));
+       r67 = _mm_shuffle_epi32(r4567,_MM_SHUFFLE(3,3,2,2));
+       r89 = _mm_load_si128((xmmi*)in + 2);
+       r89 = _mm_shuffle_epi32(r89,_MM_SHUFFLE(3,1,2,0));
+
+       do {
+               r12 = _mm_unpackhi_epi64(r01, _mm_slli_si128(r23, 8));
+               r0 = _mm_shuffle_epi32(r01, _MM_SHUFFLE(0,0,0,0));
+               r0 = _mm_add_epi64(r0, _mm_and_si128(r0, top64bitmask.v));
+               r0a = _mm_shuffle_epi32(r0,_MM_SHUFFLE(3,2,1,2));
+               r1 = _mm_shuffle_epi32(r01, _MM_SHUFFLE(2,2,2,2));
+               r2 = _mm_shuffle_epi32(r23, _MM_SHUFFLE(0,0,0,0));
+               r2 = _mm_add_epi64(r2, _mm_and_si128(r2, top64bitmask.v));
+               r2a = _mm_shuffle_epi32(r2,_MM_SHUFFLE(3,2,1,2));
+               r3 = _mm_shuffle_epi32(r23, _MM_SHUFFLE(2,2,2,2));
+               r34 = _mm_unpackhi_epi64(r23, _mm_slli_si128(r45, 8));
+               r4 = _mm_shuffle_epi32(r45, _MM_SHUFFLE(0,0,0,0));
+               r4 = _mm_add_epi64(r4, _mm_and_si128(r4, top64bitmask.v));
+               r56 = _mm_unpackhi_epi64(r45, _mm_slli_si128(r67, 8));
+               r5619 = _mm_mul_epu32(r56, packednineteen.v);
+               r5 = _mm_shuffle_epi32(r5619, _MM_SHUFFLE(1,1,1,0));
+               r6 = _mm_shuffle_epi32(r5619, _MM_SHUFFLE(3,2,3,2));            
+               r78 = _mm_unpackhi_epi64(r67, _mm_slli_si128(r89, 8));
+               r6x = _mm_unpacklo_epi64(r67, _mm_setzero_si128());
+               r7 = _mm_shuffle_epi32(r67, _MM_SHUFFLE(2,2,2,2));
+               r7 = _mm_mul_epu32(r7, packed3819.v);
+               r7a = _mm_shuffle_epi32(r7, _MM_SHUFFLE(3,3,3,2));
+               r8x = _mm_unpacklo_epi64(r89, _mm_setzero_si128());
+               r8 = _mm_shuffle_epi32(r89, _MM_SHUFFLE(0,0,0,0));
+               r8 = _mm_mul_epu32(r8, packednineteen.v);
+               r9  = _mm_shuffle_epi32(r89, _MM_SHUFFLE(2,2,2,2));
+               r9x  = _mm_slli_epi32(_mm_shuffle_epi32(r89, _MM_SHUFFLE(3,3,3,2)), 1);
+               r9 = _mm_mul_epu32(r9, packed3819.v);
+               r9a = _mm_shuffle_epi32(r9, _MM_SHUFFLE(2,2,2,2));
+
+               m01 = _mm_mul_epu32(r01, r0);
+               m23 = _mm_mul_epu32(r23, r0a);
+               m45 = _mm_mul_epu32(r45, r0a);
+               m45 = _mm_add_epi64(m45, _mm_mul_epu32(r23, r2));
+               r23 = _mm_slli_epi32(r23, 1);
+               m67 = _mm_mul_epu32(r67, r0a);
+               m67 = _mm_add_epi64(m67, _mm_mul_epu32(r45, r2a));
+               m89 = _mm_mul_epu32(r89, r0a);
+               m89 = _mm_add_epi64(m89, _mm_mul_epu32(r67, r2a));
+               r67 = _mm_slli_epi32(r67, 1);
+               m89 = _mm_add_epi64(m89, _mm_mul_epu32(r45, r4));
+               r45 = _mm_slli_epi32(r45, 1);
+
+               r1 = _mm_slli_epi32(r1, 1);
+               r3 = _mm_slli_epi32(r3, 1);
+               r1a = _mm_add_epi64(r1, _mm_and_si128(r1, bot64bitmask.v));
+               r3a = _mm_add_epi64(r3, _mm_and_si128(r3, bot64bitmask.v));
+
+               m23 = _mm_add_epi64(m23, _mm_mul_epu32(r12, r1));
+               m45 = _mm_add_epi64(m45, _mm_mul_epu32(r34, r1a));
+               m67 = _mm_add_epi64(m67, _mm_mul_epu32(r56, r1a));
+               m67 = _mm_add_epi64(m67, _mm_mul_epu32(r34, r3));
+               r34 = _mm_slli_epi32(r34, 1);
+               m89 = _mm_add_epi64(m89, _mm_mul_epu32(r78, r1a));
+               r78 = _mm_slli_epi32(r78, 1);
+               m89 = _mm_add_epi64(m89, _mm_mul_epu32(r56, r3a));
+               r56 = _mm_slli_epi32(r56, 1);
+
+               m01 = _mm_add_epi64(m01, _mm_mul_epu32(_mm_slli_epi32(r12, 1), r9));
+               m01 = _mm_add_epi64(m01, _mm_mul_epu32(r34, r7));
+               m23 = _mm_add_epi64(m23, _mm_mul_epu32(r34, r9));
+               m01 = _mm_add_epi64(m01, _mm_mul_epu32(r56, r5));
+               m23 = _mm_add_epi64(m23, _mm_mul_epu32(r56, r7));
+               m45 = _mm_add_epi64(m45, _mm_mul_epu32(r56, r9));
+               m01 = _mm_add_epi64(m01, _mm_mul_epu32(r23, r8));
+               m01 = _mm_add_epi64(m01, _mm_mul_epu32(r45, r6));
+               m23 = _mm_add_epi64(m23, _mm_mul_epu32(r45, r8));
+               m23 = _mm_add_epi64(m23, _mm_mul_epu32(r6x, r6));
+               m45 = _mm_add_epi64(m45, _mm_mul_epu32(r78, r7a));
+               m67 = _mm_add_epi64(m67, _mm_mul_epu32(r78, r9));
+               m45 = _mm_add_epi64(m45, _mm_mul_epu32(r67, r8));               
+               m67 = _mm_add_epi64(m67, _mm_mul_epu32(r8x, r8));
+               m89 = _mm_add_epi64(m89, _mm_mul_epu32(r9x, r9a));
+
+               r0 = _mm_unpacklo_epi64(m01, m45);
+               r1 = _mm_unpackhi_epi64(m01, m45);
+               r2 = _mm_unpacklo_epi64(m23, m67);
+               r3 = _mm_unpackhi_epi64(m23, m67);
+               r4 = _mm_unpacklo_epi64(m89, m89);
+               r5 = _mm_unpackhi_epi64(m89, m89);
+
+               c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);
+               c1 = _mm_srli_epi64(r1, 25); c2 = _mm_srli_epi64(r3, 25); r1 = _mm_and_si128(r1, packedmask25.v); r3 = _mm_and_si128(r3, packedmask25.v); r2 = _mm_add_epi64(r2, c1); r4 = _mm_add_epi64(r4, c2); c3 = _mm_slli_si128(c2, 8);
+               c1 = _mm_srli_epi64(r4, 26);                                                                      r4 = _mm_and_si128(r4, packedmask26.v);                             r5 = _mm_add_epi64(r5, c1); 
+               c1 = _mm_srli_epi64(r5, 25);                                                                      r5 = _mm_and_si128(r5, packedmask25.v);                             r0 = _mm_add_epi64(r0, _mm_unpackhi_epi64(_mm_mul_epu32(c1, packednineteen.v), c3));
+               c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);
+
+               r01 = _mm_unpacklo_epi64(r0, r1);
+               r45 = _mm_unpackhi_epi64(r0, r1);
+               r23 = _mm_unpacklo_epi64(r2, r3);
+               r67 = _mm_unpackhi_epi64(r2, r3);
+               r89 = _mm_unpackhi_epi64(r4, r5);
+       } while (--count);
+
+       r0123 = _mm_shuffle_epi32(r23, _MM_SHUFFLE(2,0,3,3));
+       r4567 = _mm_shuffle_epi32(r67, _MM_SHUFFLE(2,0,3,3));
+       r0123 = _mm_or_si128(r0123, _mm_shuffle_epi32(r01, _MM_SHUFFLE(3,3,2,0)));
+       r4567 = _mm_or_si128(r4567, _mm_shuffle_epi32(r45, _MM_SHUFFLE(3,3,2,0)));
+       r89 = _mm_shuffle_epi32(r89, _MM_SHUFFLE(3,3,2,0));
+
+       _mm_store_si128((xmmi*)r + 0, r0123);
+       _mm_store_si128((xmmi*)r + 1, r4567);
+       _mm_store_si128((xmmi*)r + 2, r89);
+}
+
+DONNA_INLINE static void
+curve25519_tangle32(packedelem32 *out, const bignum25519 x, const bignum25519 z) {
+       xmmi x0,x1,x2,z0,z1,z2;
+
+       x0 = _mm_load_si128((xmmi *)(x + 0));
+       x1 = _mm_load_si128((xmmi *)(x + 4));
+       x2 = _mm_load_si128((xmmi *)(x + 8));
+       z0 = _mm_load_si128((xmmi *)(z + 0));
+       z1 = _mm_load_si128((xmmi *)(z + 4));
+       z2 = _mm_load_si128((xmmi *)(z + 8));
+
+       out[0].v = _mm_unpacklo_epi32(x0, z0);
+       out[1].v = _mm_unpackhi_epi32(x0, z0);
+       out[2].v = _mm_unpacklo_epi32(x1, z1);
+       out[3].v = _mm_unpackhi_epi32(x1, z1);
+       out[4].v = _mm_unpacklo_epi32(x2, z2);
+}
+
+DONNA_INLINE static void
+curve25519_untangle32(bignum25519 x, bignum25519 z, const packedelem32 *in) {
+       xmmi t0,t1,t2,t3,t4,zero;
+
+       t0 = _mm_shuffle_epi32(in[0].v, _MM_SHUFFLE(3,1,2,0));
+       t1 = _mm_shuffle_epi32(in[1].v, _MM_SHUFFLE(3,1,2,0));
+       t2 = _mm_shuffle_epi32(in[2].v, _MM_SHUFFLE(3,1,2,0));
+       t3 = _mm_shuffle_epi32(in[3].v, _MM_SHUFFLE(3,1,2,0));
+       t4 = _mm_shuffle_epi32(in[4].v, _MM_SHUFFLE(3,1,2,0));
+       zero = _mm_setzero_si128();
+       _mm_store_si128((xmmi *)x + 0, _mm_unpacklo_epi64(t0, t1));
+       _mm_store_si128((xmmi *)x + 1, _mm_unpacklo_epi64(t2, t3));
+       _mm_store_si128((xmmi *)x + 2, _mm_unpacklo_epi64(t4, zero));
+       _mm_store_si128((xmmi *)z + 0, _mm_unpackhi_epi64(t0, t1));
+       _mm_store_si128((xmmi *)z + 1, _mm_unpackhi_epi64(t2, t3));
+       _mm_store_si128((xmmi *)z + 2, _mm_unpackhi_epi64(t4, zero));
+}
+
+DONNA_INLINE static void
+curve25519_add_reduce_packed32(packedelem32 *out, const packedelem32 *r, const packedelem32 *s) {
+       xmmi r0,r1,r2,r3,r4;
+       xmmi s0,s1,s2,s3,s4,s5;
+       xmmi c1,c2;
+
+       r0 = _mm_add_epi32(r[0].v, s[0].v);
+       r1 = _mm_add_epi32(r[1].v, s[1].v);
+       r2 = _mm_add_epi32(r[2].v, s[2].v);
+       r3 = _mm_add_epi32(r[3].v, s[3].v);
+       r4 = _mm_add_epi32(r[4].v, s[4].v);
+
+       s0 = _mm_unpacklo_epi64(r0, r2); /* 00 44 */
+       s1 = _mm_unpackhi_epi64(r0, r2); /* 11 55 */
+       s2 = _mm_unpacklo_epi64(r1, r3); /* 22 66 */
+       s3 = _mm_unpackhi_epi64(r1, r3); /* 33 77 */
+       s4 = _mm_unpacklo_epi64(_mm_setzero_si128(), r4);  /* 00 88 */
+       s5 = _mm_unpackhi_epi64(_mm_setzero_si128(), r4);  /* 00 99 */
+
+       c1 = _mm_srli_epi32(s0, 26); c2 = _mm_srli_epi32(s2, 26); s0 = _mm_and_si128(s0, packedmask26262626.v); s2 = _mm_and_si128(s2, packedmask26262626.v); s1 = _mm_add_epi32(s1, c1); s3 = _mm_add_epi32(s3, c2);
+       c1 = _mm_srli_epi32(s1, 25); c2 = _mm_srli_epi32(s3, 25); s1 = _mm_and_si128(s1, packedmask25252525.v); s3 = _mm_and_si128(s3, packedmask25252525.v); s2 = _mm_add_epi32(s2, c1); s4 = _mm_add_epi32(s4, _mm_unpackhi_epi64(_mm_setzero_si128(), c2)); s0 = _mm_add_epi32(s0, _mm_unpacklo_epi64(_mm_setzero_si128(), c2));
+       c1 = _mm_srli_epi32(s2, 26); c2 = _mm_srli_epi32(s4, 26); s2 = _mm_and_si128(s2, packedmask26262626.v); s4 = _mm_and_si128(s4, packedmask26262626.v); s3 = _mm_add_epi32(s3, c1); s5 = _mm_add_epi32(s5, c2);
+       c1 = _mm_srli_epi32(s3, 25); c2 = _mm_srli_epi32(s5, 25); s3 = _mm_and_si128(s3, packedmask25252525.v); s5 = _mm_and_si128(s5, packedmask25252525.v); s4 = _mm_add_epi32(s4, c1); s0 = _mm_add_epi32(s0, _mm_or_si128(_mm_slli_si128(c1, 8), _mm_srli_si128(_mm_add_epi32(_mm_add_epi32(_mm_slli_epi32(c2, 4), _mm_slli_epi32(c2, 1)), c2), 8)));
+       c1 = _mm_srli_epi32(s0, 26); c2 = _mm_srli_epi32(s2, 26); s0 = _mm_and_si128(s0, packedmask26262626.v); s2 = _mm_and_si128(s2, packedmask26262626.v); s1 = _mm_add_epi32(s1, c1); s3 = _mm_add_epi32(s3, c2);
+
+       out[0].v = _mm_unpacklo_epi64(s0, s1); /* 00 11 */
+       out[1].v = _mm_unpacklo_epi64(s2, s3); /* 22 33 */
+       out[2].v = _mm_unpackhi_epi64(s0, s1); /* 44 55 */
+       out[3].v = _mm_unpackhi_epi64(s2, s3); /* 66 77 */
+       out[4].v = _mm_unpackhi_epi64(s4, s5); /* 88 99 */
+}
+
+DONNA_INLINE static void
+curve25519_add_packed32(packedelem32 *out, const packedelem32 *r, const packedelem32 *s) {
+       out[0].v = _mm_add_epi32(r[0].v, s[0].v);
+       out[1].v = _mm_add_epi32(r[1].v, s[1].v);
+       out[2].v = _mm_add_epi32(r[2].v, s[2].v);
+       out[3].v = _mm_add_epi32(r[3].v, s[3].v);
+       out[4].v = _mm_add_epi32(r[4].v, s[4].v);
+}
+
+DONNA_INLINE static void
+curve25519_sub_packed32(packedelem32 *out, const packedelem32 *r, const packedelem32 *s) {
+       xmmi r0,r1,r2,r3,r4;
+       xmmi s0,s1,s2,s3;
+       xmmi c1,c2;
+
+       r0 = _mm_add_epi32(r[0].v, packed32packed2p0.v);
+       r1 = _mm_add_epi32(r[1].v, packed32packed2p1.v);
+       r2 = _mm_add_epi32(r[2].v, packed32packed2p1.v);
+       r3 = _mm_add_epi32(r[3].v, packed32packed2p1.v);
+       r4 = _mm_add_epi32(r[4].v, packed32packed2p1.v);
+       r0 = _mm_sub_epi32(r0, s[0].v); /* 00 11 */
+       r1 = _mm_sub_epi32(r1, s[1].v); /* 22 33 */
+       r2 = _mm_sub_epi32(r2, s[2].v); /* 44 55 */
+       r3 = _mm_sub_epi32(r3, s[3].v); /* 66 77 */
+       r4 = _mm_sub_epi32(r4, s[4].v); /* 88 99 */
+
+       s0 = _mm_unpacklo_epi64(r0, r2); /* 00 44 */
+       s1 = _mm_unpackhi_epi64(r0, r2); /* 11 55 */
+       s2 = _mm_unpacklo_epi64(r1, r3); /* 22 66 */
+       s3 = _mm_unpackhi_epi64(r1, r3); /* 33 77 */
+
+       c1 = _mm_srli_epi32(s0, 26); c2 = _mm_srli_epi32(s2, 26); s0 = _mm_and_si128(s0, packedmask26262626.v); s2 = _mm_and_si128(s2, packedmask26262626.v); s1 = _mm_add_epi32(s1, c1); s3 = _mm_add_epi32(s3, c2);
+       c1 = _mm_srli_epi32(s1, 25); c2 = _mm_srli_epi32(s3, 25); s1 = _mm_and_si128(s1, packedmask25252525.v); s3 = _mm_and_si128(s3, packedmask25252525.v); s2 = _mm_add_epi32(s2, c1); r4 = _mm_add_epi32(r4, _mm_srli_si128(c2, 8)); s0 = _mm_add_epi32(s0,  _mm_slli_si128(c2, 8));
+
+       out[0].v = _mm_unpacklo_epi64(s0, s1); /* 00 11 */
+       out[1].v = _mm_unpacklo_epi64(s2, s3); /* 22 33 */
+       out[2].v = _mm_unpackhi_epi64(s0, s1); /* 44 55 */
+       out[3].v = _mm_unpackhi_epi64(s2, s3); /* 66 77 */
+       out[4].v = r4;
+}
+
+DONNA_INLINE static void
+curve25519_sub_after_basic_packed32(packedelem32 *out, const packedelem32 *r, const packedelem32 *s) {
+       xmmi r0,r1,r2,r3,r4;
+       xmmi s0,s1,s2,s3,s4,s5;
+       xmmi c1,c2;
+
+       r0 = _mm_add_epi32(r[0].v, packed32packed4p0.v);
+       r1 = _mm_add_epi32(r[1].v, packed32packed4p1.v);
+       r2 = _mm_add_epi32(r[2].v, packed32packed4p1.v);
+       r3 = _mm_add_epi32(r[3].v, packed32packed4p1.v);
+       r4 = _mm_add_epi32(r[4].v, packed32packed4p1.v);
+       r0 = _mm_sub_epi32(r0, s[0].v); /* 00 11 */
+       r1 = _mm_sub_epi32(r1, s[1].v); /* 22 33 */
+       r2 = _mm_sub_epi32(r2, s[2].v); /* 44 55 */
+       r3 = _mm_sub_epi32(r3, s[3].v); /* 66 77 */
+       r4 = _mm_sub_epi32(r4, s[4].v); /* 88 99 */
+
+       s0 = _mm_unpacklo_epi64(r0, r2); /* 00 44 */
+       s1 = _mm_unpackhi_epi64(r0, r2); /* 11 55 */
+       s2 = _mm_unpacklo_epi64(r1, r3); /* 22 66 */
+       s3 = _mm_unpackhi_epi64(r1, r3); /* 33 77 */
+       s4 = _mm_unpacklo_epi64(_mm_setzero_si128(), r4);  /* 00 88 */
+       s5 = _mm_unpackhi_epi64(_mm_setzero_si128(), r4);  /* 00 99 */
+
+       c1 = _mm_srli_epi32(s0, 26); c2 = _mm_srli_epi32(s2, 26); s0 = _mm_and_si128(s0, packedmask26262626.v); s2 = _mm_and_si128(s2, packedmask26262626.v); s1 = _mm_add_epi32(s1, c1); s3 = _mm_add_epi32(s3, c2);
+       c1 = _mm_srli_epi32(s1, 25); c2 = _mm_srli_epi32(s3, 25); s1 = _mm_and_si128(s1, packedmask25252525.v); s3 = _mm_and_si128(s3, packedmask25252525.v); s2 = _mm_add_epi32(s2, c1); s4 = _mm_add_epi32(s4, _mm_unpackhi_epi64(_mm_setzero_si128(), c2)); s0 = _mm_add_epi32(s0, _mm_unpacklo_epi64(_mm_setzero_si128(), c2));
+       c1 = _mm_srli_epi32(s2, 26); c2 = _mm_srli_epi32(s4, 26); s2 = _mm_and_si128(s2, packedmask26262626.v); s4 = _mm_and_si128(s4, packedmask26262626.v); s3 = _mm_add_epi32(s3, c1); s5 = _mm_add_epi32(s5, c2);
+       c1 = _mm_srli_epi32(s3, 25); c2 = _mm_srli_epi32(s5, 25); s3 = _mm_and_si128(s3, packedmask25252525.v); s5 = _mm_and_si128(s5, packedmask25252525.v); s4 = _mm_add_epi32(s4, c1); s0 = _mm_add_epi32(s0, _mm_or_si128(_mm_slli_si128(c1, 8), _mm_srli_si128(_mm_add_epi32(_mm_add_epi32(_mm_slli_epi32(c2, 4), _mm_slli_epi32(c2, 1)), c2), 8)));
+       c1 = _mm_srli_epi32(s0, 26); c2 = _mm_srli_epi32(s2, 26); s0 = _mm_and_si128(s0, packedmask26262626.v); s2 = _mm_and_si128(s2, packedmask26262626.v); s1 = _mm_add_epi32(s1, c1); s3 = _mm_add_epi32(s3, c2);
+
+       out[0].v = _mm_unpacklo_epi64(s0, s1); /* 00 11 */
+       out[1].v = _mm_unpacklo_epi64(s2, s3); /* 22 33 */
+       out[2].v = _mm_unpackhi_epi64(s0, s1); /* 44 55 */
+       out[3].v = _mm_unpackhi_epi64(s2, s3); /* 66 77 */
+       out[4].v = _mm_unpackhi_epi64(s4, s5); /* 88 99 */
+}
+
+DONNA_INLINE static void
+curve25519_tangle64_from32(packedelem64 *a, packedelem64 *b, const packedelem32 *c, const packedelem32 *d) {
+       xmmi c0,c1,c2,c3,c4,c5,t;
+       xmmi d0,d1,d2,d3,d4,d5;
+       xmmi t0,t1,t2,t3,t4,zero;
+
+       t0 = _mm_shuffle_epi32(c[0].v, _MM_SHUFFLE(3,1,2,0));
+       t1 = _mm_shuffle_epi32(c[1].v, _MM_SHUFFLE(3,1,2,0));
+       t2 = _mm_shuffle_epi32(d[0].v, _MM_SHUFFLE(3,1,2,0));
+       t3 = _mm_shuffle_epi32(d[1].v, _MM_SHUFFLE(3,1,2,0));
+       c0 = _mm_unpacklo_epi64(t0, t1);
+       c3 = _mm_unpackhi_epi64(t0, t1);
+       d0 = _mm_unpacklo_epi64(t2, t3);
+       d3 = _mm_unpackhi_epi64(t2, t3);
+       t = _mm_unpacklo_epi64(c0, d0); a[0].v = t; a[1].v = _mm_srli_epi64(t, 32);
+       t = _mm_unpackhi_epi64(c0, d0); a[2].v = t; a[3].v = _mm_srli_epi64(t, 32);
+       t = _mm_unpacklo_epi64(c3, d3); b[0].v = t; b[1].v = _mm_srli_epi64(t, 32);
+       t = _mm_unpackhi_epi64(c3, d3); b[2].v = t; b[3].v = _mm_srli_epi64(t, 32);
+
+       t0 = _mm_shuffle_epi32(c[2].v, _MM_SHUFFLE(3,1,2,0));
+       t1 = _mm_shuffle_epi32(c[3].v, _MM_SHUFFLE(3,1,2,0));
+       t2 = _mm_shuffle_epi32(d[2].v, _MM_SHUFFLE(3,1,2,0));
+       t3 = _mm_shuffle_epi32(d[3].v, _MM_SHUFFLE(3,1,2,0));
+       c1 = _mm_unpacklo_epi64(t0, t1);
+       c4 = _mm_unpackhi_epi64(t0, t1);
+       d1 = _mm_unpacklo_epi64(t2, t3);
+       d4 = _mm_unpackhi_epi64(t2, t3);
+       t = _mm_unpacklo_epi64(c1, d1); a[4].v = t; a[5].v = _mm_srli_epi64(t, 32);
+       t = _mm_unpackhi_epi64(c1, d1); a[6].v = t; a[7].v = _mm_srli_epi64(t, 32);
+       t = _mm_unpacklo_epi64(c4, d4); b[4].v = t; b[5].v = _mm_srli_epi64(t, 32);
+       t = _mm_unpackhi_epi64(c4, d4); b[6].v = t; b[7].v = _mm_srli_epi64(t, 32);
+
+       t4 = _mm_shuffle_epi32(c[4].v, _MM_SHUFFLE(3,1,2,0));
+       zero = _mm_setzero_si128();
+       c2 = _mm_unpacklo_epi64(t4, zero);
+       c5 = _mm_unpackhi_epi64(t4, zero);
+       t4 = _mm_shuffle_epi32(d[4].v, _MM_SHUFFLE(3,1,2,0));
+       d2 = _mm_unpacklo_epi64(t4, zero);
+       d5 = _mm_unpackhi_epi64(t4, zero);
+       t = _mm_unpacklo_epi64(c2, d2); a[8].v = t; a[9].v = _mm_srli_epi64(t, 32);
+       t = _mm_unpacklo_epi64(c5, d5); b[8].v = t; b[9].v = _mm_srli_epi64(t, 32);
+}
+
+DONNA_INLINE static void
+curve25519_tangle64(packedelem64 *out, const bignum25519 x, const bignum25519 z) {
+       xmmi x0,x1,x2,z0,z1,z2,t;
+
+       x0 = _mm_load_si128((xmmi *)x + 0);
+       x1 = _mm_load_si128((xmmi *)x + 1);
+       x2 = _mm_load_si128((xmmi *)x + 2);
+       z0 = _mm_load_si128((xmmi *)z + 0);
+       z1 = _mm_load_si128((xmmi *)z + 1);
+       z2 = _mm_load_si128((xmmi *)z + 2);
+
+       t = _mm_unpacklo_epi64(x0, z0); out[0].v = t; out[1].v = _mm_srli_epi64(t, 32);
+       t = _mm_unpackhi_epi64(x0, z0); out[2].v = t; out[3].v = _mm_srli_epi64(t, 32);
+       t = _mm_unpacklo_epi64(x1, z1); out[4].v = t; out[5].v = _mm_srli_epi64(t, 32);
+       t = _mm_unpackhi_epi64(x1, z1); out[6].v = t; out[7].v = _mm_srli_epi64(t, 32);
+       t = _mm_unpacklo_epi64(x2, z2); out[8].v = t; out[9].v = _mm_srli_epi64(t, 32);
+}
+
+DONNA_INLINE static void
+curve25519_tangleone64(packedelem64 *out, const bignum25519 x) {
+       xmmi x0,x1,x2;
+
+       x0 = _mm_load_si128((xmmi *)(x + 0));
+       x1 = _mm_load_si128((xmmi *)(x + 4));
+       x2 = _mm_load_si128((xmmi *)(x + 8));
+
+       out[0].v = _mm_shuffle_epi32(x0, _MM_SHUFFLE(0,0,0,0));
+       out[1].v = _mm_shuffle_epi32(x0, _MM_SHUFFLE(1,1,1,1));
+       out[2].v = _mm_shuffle_epi32(x0, _MM_SHUFFLE(2,2,2,2));
+       out[3].v = _mm_shuffle_epi32(x0, _MM_SHUFFLE(3,3,3,3));
+       out[4].v = _mm_shuffle_epi32(x1, _MM_SHUFFLE(0,0,0,0));
+       out[5].v = _mm_shuffle_epi32(x1, _MM_SHUFFLE(1,1,1,1));
+       out[6].v = _mm_shuffle_epi32(x1, _MM_SHUFFLE(2,2,2,2));
+       out[7].v = _mm_shuffle_epi32(x1, _MM_SHUFFLE(3,3,3,3));
+       out[8].v = _mm_shuffle_epi32(x2, _MM_SHUFFLE(0,0,0,0));
+       out[9].v = _mm_shuffle_epi32(x2, _MM_SHUFFLE(1,1,1,1));
+}
+
+DONNA_INLINE static void
+curve25519_swap64(packedelem64 *out) {
+       out[0].v = _mm_shuffle_epi32(out[0].v, _MM_SHUFFLE(1,0,3,2));
+       out[1].v = _mm_shuffle_epi32(out[1].v, _MM_SHUFFLE(1,0,3,2));
+       out[2].v = _mm_shuffle_epi32(out[2].v, _MM_SHUFFLE(1,0,3,2));
+       out[3].v = _mm_shuffle_epi32(out[3].v, _MM_SHUFFLE(1,0,3,2));
+       out[4].v = _mm_shuffle_epi32(out[4].v, _MM_SHUFFLE(1,0,3,2));
+       out[5].v = _mm_shuffle_epi32(out[5].v, _MM_SHUFFLE(1,0,3,2));
+       out[6].v = _mm_shuffle_epi32(out[6].v, _MM_SHUFFLE(1,0,3,2));
+       out[7].v = _mm_shuffle_epi32(out[7].v, _MM_SHUFFLE(1,0,3,2));
+       out[8].v = _mm_shuffle_epi32(out[8].v, _MM_SHUFFLE(1,0,3,2));
+       out[9].v = _mm_shuffle_epi32(out[9].v, _MM_SHUFFLE(1,0,3,2));
+}
+
+DONNA_INLINE static void
+curve25519_untangle64(bignum25519 x, bignum25519 z, const packedelem64 *in) {
+       _mm_store_si128((xmmi *)(x + 0), _mm_unpacklo_epi64(_mm_unpacklo_epi32(in[0].v, in[1].v), _mm_unpacklo_epi32(in[2].v, in[3].v)));
+       _mm_store_si128((xmmi *)(x + 4), _mm_unpacklo_epi64(_mm_unpacklo_epi32(in[4].v, in[5].v), _mm_unpacklo_epi32(in[6].v, in[7].v)));
+       _mm_store_si128((xmmi *)(x + 8), _mm_unpacklo_epi32(in[8].v, in[9].v)                                                          );
+       _mm_store_si128((xmmi *)(z + 0), _mm_unpacklo_epi64(_mm_unpackhi_epi32(in[0].v, in[1].v), _mm_unpackhi_epi32(in[2].v, in[3].v)));
+       _mm_store_si128((xmmi *)(z + 4), _mm_unpacklo_epi64(_mm_unpackhi_epi32(in[4].v, in[5].v), _mm_unpackhi_epi32(in[6].v, in[7].v)));
+       _mm_store_si128((xmmi *)(z + 8), _mm_unpackhi_epi32(in[8].v, in[9].v)                                                          );
+}
+
+DONNA_INLINE static void
+curve25519_mul_packed64(packedelem64 *out, const packedelem64 *r, const packedelem64 *s) {
+       xmmi r1,r2,r3,r4,r5,r6,r7,r8,r9;
+       xmmi r1_2,r3_2,r5_2,r7_2,r9_2;
+       xmmi c1,c2;
+
+       out[0].v = _mm_mul_epu32(r[0].v, s[0].v);
+       out[1].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[1].v), _mm_mul_epu32(r[1].v, s[0].v));
+       r1_2 = _mm_slli_epi32(r[1].v, 1);
+       out[2].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r1_2  , s[1].v), _mm_mul_epu32(r[2].v, s[0].v)));
+       out[3].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[3].v), _mm_add_epi64(_mm_mul_epu32(r[1].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[1].v), _mm_mul_epu32(r[3].v, s[0].v))));
+       r3_2 = _mm_slli_epi32(r[3].v, 1);
+       out[4].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r1_2  , s[3].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r3_2  , s[1].v), _mm_mul_epu32(r[4].v, s[0].v)))));
+       out[5].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[5].v), _mm_add_epi64(_mm_mul_epu32(r[1].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[3].v), _mm_add_epi64(_mm_mul_epu32(r[3].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r[4].v, s[1].v), _mm_mul_epu32(r[5].v, s[0].v))))));
+       r5_2 = _mm_slli_epi32(r[5].v, 1);
+       out[6].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[6].v), _mm_add_epi64(_mm_mul_epu32(r1_2  , s[5].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r3_2  , s[3].v), _mm_add_epi64(_mm_mul_epu32(r[4].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r5_2  , s[1].v), _mm_mul_epu32(r[6].v, s[0].v)))))));
+       out[7].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[7].v), _mm_add_epi64(_mm_mul_epu32(r[1].v, s[6].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[5].v), _mm_add_epi64(_mm_mul_epu32(r[3].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r[4].v, s[3].v), _mm_add_epi64(_mm_mul_epu32(r[5].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r[6].v, s[1].v), _mm_mul_epu32(r[7].v  , s[0].v))))))));
+       r7_2 = _mm_slli_epi32(r[7].v, 1);
+       out[8].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[8].v), _mm_add_epi64(_mm_mul_epu32(r1_2  , s[7].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[6].v), _mm_add_epi64(_mm_mul_epu32(r3_2  , s[5].v), _mm_add_epi64(_mm_mul_epu32(r[4].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r5_2  , s[3].v), _mm_add_epi64(_mm_mul_epu32(r[6].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r7_2  , s[1].v), _mm_mul_epu32(r[8].v, s[0].v)))))))));
+       out[9].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[9].v), _mm_add_epi64(_mm_mul_epu32(r[1].v, s[8].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[7].v), _mm_add_epi64(_mm_mul_epu32(r[3].v, s[6].v), _mm_add_epi64(_mm_mul_epu32(r[4].v, s[5].v), _mm_add_epi64(_mm_mul_epu32(r[5].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r[6].v, s[3].v), _mm_add_epi64(_mm_mul_epu32(r[7].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r[8].v, s[1].v), _mm_mul_epu32(r[9].v, s[0].v))))))))));
+
+       r1 = _mm_mul_epu32(r[1].v, packednineteen.v);
+       r2 = _mm_mul_epu32(r[2].v, packednineteen.v);
+       r1_2 = _mm_slli_epi32(r1, 1);
+       r3 = _mm_mul_epu32(r[3].v, packednineteen.v);
+       r4 = _mm_mul_epu32(r[4].v, packednineteen.v);
+       r3_2 = _mm_slli_epi32(r3, 1);
+       r5 = _mm_mul_epu32(r[5].v, packednineteen.v);
+       r6 = _mm_mul_epu32(r[6].v, packednineteen.v);
+       r5_2 = _mm_slli_epi32(r5, 1);
+       r7 = _mm_mul_epu32(r[7].v, packednineteen.v);
+       r8 = _mm_mul_epu32(r[8].v, packednineteen.v);
+       r7_2 = _mm_slli_epi32(r7, 1);
+       r9 = _mm_mul_epu32(r[9].v, packednineteen.v);
+       r9_2 = _mm_slli_epi32(r9, 1);
+
+       out[0].v = _mm_add_epi64(out[0].v, _mm_add_epi64(_mm_mul_epu32(r9_2, s[1].v), _mm_add_epi64(_mm_mul_epu32(r8, s[2].v), _mm_add_epi64(_mm_mul_epu32(r7_2, s[3].v), _mm_add_epi64(_mm_mul_epu32(r6, s[4].v), _mm_add_epi64(_mm_mul_epu32(r5_2, s[5].v), _mm_add_epi64(_mm_mul_epu32(r4, s[6].v), _mm_add_epi64(_mm_mul_epu32(r3_2, s[7].v), _mm_add_epi64(_mm_mul_epu32(r2, s[8].v), _mm_mul_epu32(r1_2, s[9].v))))))))));
+       out[1].v = _mm_add_epi64(out[1].v, _mm_add_epi64(_mm_mul_epu32(r9  , s[2].v), _mm_add_epi64(_mm_mul_epu32(r8, s[3].v), _mm_add_epi64(_mm_mul_epu32(r7  , s[4].v), _mm_add_epi64(_mm_mul_epu32(r6, s[5].v), _mm_add_epi64(_mm_mul_epu32(r5  , s[6].v), _mm_add_epi64(_mm_mul_epu32(r4, s[7].v), _mm_add_epi64(_mm_mul_epu32(r3  , s[8].v), _mm_mul_epu32(r2, s[9].v)))))))));
+       out[2].v = _mm_add_epi64(out[2].v, _mm_add_epi64(_mm_mul_epu32(r9_2, s[3].v), _mm_add_epi64(_mm_mul_epu32(r8, s[4].v), _mm_add_epi64(_mm_mul_epu32(r7_2, s[5].v), _mm_add_epi64(_mm_mul_epu32(r6, s[6].v), _mm_add_epi64(_mm_mul_epu32(r5_2, s[7].v), _mm_add_epi64(_mm_mul_epu32(r4, s[8].v), _mm_mul_epu32(r3_2, s[9].v))))))));
+       out[3].v = _mm_add_epi64(out[3].v, _mm_add_epi64(_mm_mul_epu32(r9  , s[4].v), _mm_add_epi64(_mm_mul_epu32(r8, s[5].v), _mm_add_epi64(_mm_mul_epu32(r7  , s[6].v), _mm_add_epi64(_mm_mul_epu32(r6, s[7].v), _mm_add_epi64(_mm_mul_epu32(r5  , s[8].v), _mm_mul_epu32(r4, s[9].v)))))));
+       out[4].v = _mm_add_epi64(out[4].v, _mm_add_epi64(_mm_mul_epu32(r9_2, s[5].v), _mm_add_epi64(_mm_mul_epu32(r8, s[6].v), _mm_add_epi64(_mm_mul_epu32(r7_2, s[7].v), _mm_add_epi64(_mm_mul_epu32(r6, s[8].v), _mm_mul_epu32(r5_2, s[9].v))))));
+       out[5].v = _mm_add_epi64(out[5].v, _mm_add_epi64(_mm_mul_epu32(r9  , s[6].v), _mm_add_epi64(_mm_mul_epu32(r8, s[7].v), _mm_add_epi64(_mm_mul_epu32(r7  , s[8].v), _mm_mul_epu32(r6, s[9].v)))));
+       out[6].v = _mm_add_epi64(out[6].v, _mm_add_epi64(_mm_mul_epu32(r9_2, s[7].v), _mm_add_epi64(_mm_mul_epu32(r8, s[8].v), _mm_mul_epu32(r7_2, s[9].v))));
+       out[7].v = _mm_add_epi64(out[7].v, _mm_add_epi64(_mm_mul_epu32(r9  , s[8].v), _mm_mul_epu32(r8, s[9].v)));
+       out[8].v = _mm_add_epi64(out[8].v, _mm_mul_epu32(r9_2, s[9].v));
+
+       c1 = _mm_srli_epi64(out[0].v, 26); c2 = _mm_srli_epi64(out[4].v, 26); out[0].v = _mm_and_si128(out[0].v, packedmask26.v); out[4].v = _mm_and_si128(out[4].v, packedmask26.v); out[1].v = _mm_add_epi64(out[1].v, c1); out[5].v = _mm_add_epi64(out[5].v, c2);
+       c1 = _mm_srli_epi64(out[1].v, 25); c2 = _mm_srli_epi64(out[5].v, 25); out[1].v = _mm_and_si128(out[1].v, packedmask25.v); out[5].v = _mm_and_si128(out[5].v, packedmask25.v); out[2].v = _mm_add_epi64(out[2].v, c1); out[6].v = _mm_add_epi64(out[6].v, c2);
+       c1 = _mm_srli_epi64(out[2].v, 26); c2 = _mm_srli_epi64(out[6].v, 26); out[2].v = _mm_and_si128(out[2].v, packedmask26.v); out[6].v = _mm_and_si128(out[6].v, packedmask26.v); out[3].v = _mm_add_epi64(out[3].v, c1); out[7].v = _mm_add_epi64(out[7].v, c2);
+       c1 = _mm_srli_epi64(out[3].v, 25); c2 = _mm_srli_epi64(out[7].v, 25); out[3].v = _mm_and_si128(out[3].v, packedmask25.v); out[7].v = _mm_and_si128(out[7].v, packedmask25.v); out[4].v = _mm_add_epi64(out[4].v, c1); out[8].v = _mm_add_epi64(out[8].v, c2);
+                                          c2 = _mm_srli_epi64(out[8].v, 26);                                                     out[8].v = _mm_and_si128(out[8].v, packedmask26.v);                                         out[9].v = _mm_add_epi64(out[9].v, c2);
+                                          c2 = _mm_srli_epi64(out[9].v, 25);                                                     out[9].v = _mm_and_si128(out[9].v, packedmask25.v);                                         out[0].v = _mm_add_epi64(out[0].v, _mm_mul_epu32(c2, packednineteen.v));
+       c1 = _mm_srli_epi64(out[0].v, 26); c2 = _mm_srli_epi64(out[4].v, 26); out[0].v = _mm_and_si128(out[0].v, packedmask26.v); out[4].v = _mm_and_si128(out[4].v, packedmask26.v); out[1].v = _mm_add_epi64(out[1].v, c1); out[5].v = _mm_add_epi64(out[5].v, c2);
+}
+
+DONNA_INLINE static void
+curve25519_square_packed64(packedelem64 *out, const packedelem64 *r) {
+       xmmi r0,r1,r2,r3;
+       xmmi r1_2,r3_2,r4_2,r5_2,r6_2,r7_2;
+       xmmi d5,d6,d7,d8,d9;
+       xmmi c1,c2;
+
+       r0 = r[0].v;
+       r1 = r[1].v;
+       r2 = r[2].v;
+       r3 = r[3].v;
+
+       out[0].v = _mm_mul_epu32(r0, r0);
+       r0 = _mm_slli_epi32(r0, 1);
+       out[1].v = _mm_mul_epu32(r0, r1);
+       r1_2 = _mm_slli_epi32(r1, 1);
+       out[2].v = _mm_add_epi64(_mm_mul_epu32(r0, r2    ), _mm_mul_epu32(r1, r1_2));
+       r1 = r1_2;
+       out[3].v = _mm_add_epi64(_mm_mul_epu32(r0, r3    ), _mm_mul_epu32(r1, r2  ));
+       r3_2 = _mm_slli_epi32(r3, 1);
+       out[4].v = _mm_add_epi64(_mm_mul_epu32(r0, r[4].v), _mm_add_epi64(_mm_mul_epu32(r1, r3_2  ), _mm_mul_epu32(r2, r2)));
+       r2 = _mm_slli_epi32(r2, 1);
+       out[5].v = _mm_add_epi64(_mm_mul_epu32(r0, r[5].v), _mm_add_epi64(_mm_mul_epu32(r1, r[4].v), _mm_mul_epu32(r2, r3)));
+       r5_2 = _mm_slli_epi32(r[5].v, 1);
+       out[6].v = _mm_add_epi64(_mm_mul_epu32(r0, r[6].v), _mm_add_epi64(_mm_mul_epu32(r1, r5_2  ), _mm_add_epi64(_mm_mul_epu32(r2, r[4].v), _mm_mul_epu32(r3, r3_2  ))));
+       r3 = r3_2;
+       out[7].v = _mm_add_epi64(_mm_mul_epu32(r0, r[7].v), _mm_add_epi64(_mm_mul_epu32(r1, r[6].v), _mm_add_epi64(_mm_mul_epu32(r2, r[5].v), _mm_mul_epu32(r3, r[4].v))));
+       r7_2 = _mm_slli_epi32(r[7].v, 1);
+       out[8].v = _mm_add_epi64(_mm_mul_epu32(r0, r[8].v), _mm_add_epi64(_mm_mul_epu32(r1, r7_2  ), _mm_add_epi64(_mm_mul_epu32(r2, r[6].v), _mm_add_epi64(_mm_mul_epu32(r3, r5_2  ), _mm_mul_epu32(r[4].v, r[4].v)))));
+       out[9].v = _mm_add_epi64(_mm_mul_epu32(r0, r[9].v), _mm_add_epi64(_mm_mul_epu32(r1, r[8].v), _mm_add_epi64(_mm_mul_epu32(r2, r[7].v), _mm_add_epi64(_mm_mul_epu32(r3, r[6].v), _mm_mul_epu32(r[4].v, r5_2  )))));
+
+       d5 = _mm_mul_epu32(r[5].v, packedthirtyeight.v);
+       d6 = _mm_mul_epu32(r[6].v, packednineteen.v);
+       d7 = _mm_mul_epu32(r[7].v, packedthirtyeight.v);
+       d8 = _mm_mul_epu32(r[8].v, packednineteen.v);
+       d9 = _mm_mul_epu32(r[9].v, packedthirtyeight.v);
+
+       r4_2 = _mm_slli_epi32(r[4].v, 1);
+       r6_2 = _mm_slli_epi32(r[6].v, 1);
+       out[0].v = _mm_add_epi64(out[0].v, _mm_add_epi64(_mm_mul_epu32(d9, r1                   ), _mm_add_epi64(_mm_mul_epu32(d8, r2  ), _mm_add_epi64(_mm_mul_epu32(d7, r3    ), _mm_add_epi64(_mm_mul_epu32(d6, r4_2), _mm_mul_epu32(d5, r[5].v))))));
+       out[1].v = _mm_add_epi64(out[1].v, _mm_add_epi64(_mm_mul_epu32(d9, _mm_srli_epi32(r2, 1)), _mm_add_epi64(_mm_mul_epu32(d8, r3  ), _mm_add_epi64(_mm_mul_epu32(d7, r[4].v), _mm_mul_epu32(d6, r5_2  )))));
+       out[2].v = _mm_add_epi64(out[2].v, _mm_add_epi64(_mm_mul_epu32(d9, r3                   ), _mm_add_epi64(_mm_mul_epu32(d8, r4_2), _mm_add_epi64(_mm_mul_epu32(d7, r5_2  ), _mm_mul_epu32(d6, r[6].v)))));
+       out[3].v = _mm_add_epi64(out[3].v, _mm_add_epi64(_mm_mul_epu32(d9, r[4].v               ), _mm_add_epi64(_mm_mul_epu32(d8, r5_2), _mm_mul_epu32(d7, r[6].v))));
+       out[4].v = _mm_add_epi64(out[4].v, _mm_add_epi64(_mm_mul_epu32(d9, r5_2                 ), _mm_add_epi64(_mm_mul_epu32(d8, r6_2), _mm_mul_epu32(d7, r[7].v))));
+       out[5].v = _mm_add_epi64(out[5].v, _mm_add_epi64(_mm_mul_epu32(d9, r[6].v               ), _mm_mul_epu32(d8, r7_2  )));
+       out[6].v = _mm_add_epi64(out[6].v, _mm_add_epi64(_mm_mul_epu32(d9, r7_2                 ), _mm_mul_epu32(d8, r[8].v)));
+       out[7].v = _mm_add_epi64(out[7].v, _mm_mul_epu32(d9, r[8].v));
+       out[8].v = _mm_add_epi64(out[8].v, _mm_mul_epu32(d9, r[9].v));
+
+       c1 = _mm_srli_epi64(out[0].v, 26); c2 = _mm_srli_epi64(out[4].v, 26); out[0].v = _mm_and_si128(out[0].v, packedmask26.v); out[4].v = _mm_and_si128(out[4].v, packedmask26.v); out[1].v = _mm_add_epi64(out[1].v, c1); out[5].v = _mm_add_epi64(out[5].v, c2);
+       c1 = _mm_srli_epi64(out[1].v, 25); c2 = _mm_srli_epi64(out[5].v, 25); out[1].v = _mm_and_si128(out[1].v, packedmask25.v); out[5].v = _mm_and_si128(out[5].v, packedmask25.v); out[2].v = _mm_add_epi64(out[2].v, c1); out[6].v = _mm_add_epi64(out[6].v, c2);
+       c1 = _mm_srli_epi64(out[2].v, 26); c2 = _mm_srli_epi64(out[6].v, 26); out[2].v = _mm_and_si128(out[2].v, packedmask26.v); out[6].v = _mm_and_si128(out[6].v, packedmask26.v); out[3].v = _mm_add_epi64(out[3].v, c1); out[7].v = _mm_add_epi64(out[7].v, c2);
+       c1 = _mm_srli_epi64(out[3].v, 25); c2 = _mm_srli_epi64(out[7].v, 25); out[3].v = _mm_and_si128(out[3].v, packedmask25.v); out[7].v = _mm_and_si128(out[7].v, packedmask25.v); out[4].v = _mm_add_epi64(out[4].v, c1); out[8].v = _mm_add_epi64(out[8].v, c2);
+                                          c2 = _mm_srli_epi64(out[8].v, 26);                                                     out[8].v = _mm_and_si128(out[8].v, packedmask26.v);                                         out[9].v = _mm_add_epi64(out[9].v, c2);
+                                          c2 = _mm_srli_epi64(out[9].v, 25);                                                     out[9].v = _mm_and_si128(out[9].v, packedmask25.v);                                         out[0].v = _mm_add_epi64(out[0].v, _mm_mul_epu32(c2, packednineteen.v));
+       c1 = _mm_srli_epi64(out[0].v, 26); c2 = _mm_srli_epi64(out[4].v, 26); out[0].v = _mm_and_si128(out[0].v, packedmask26.v); out[4].v = _mm_and_si128(out[4].v, packedmask26.v); out[1].v = _mm_add_epi64(out[1].v, c1); out[5].v = _mm_add_epi64(out[5].v, c2);
+}
+
+
+/* Take a little-endian, 32-byte number and expand it into polynomial form */
+static void
+curve25519_expand(bignum25519 out, const unsigned char in[32]) {
+       uint32_t x0,x1,x2,x3,x4,x5,x6,x7;
+
+       x0 = *(uint32_t *)(in + 0);
+       x1 = *(uint32_t *)(in + 4);
+       x2 = *(uint32_t *)(in + 8);
+       x3 = *(uint32_t *)(in + 12);
+       x4 = *(uint32_t *)(in + 16);
+       x5 = *(uint32_t *)(in + 20);
+       x6 = *(uint32_t *)(in + 24);
+       x7 = *(uint32_t *)(in + 28);
+
+       out[0] = (                        x0       ) & 0x3ffffff;
+       out[1] = ((((uint64_t)x1 << 32) | x0) >> 26) & 0x1ffffff;
+       out[2] = ((((uint64_t)x2 << 32) | x1) >> 19) & 0x3ffffff;
+       out[3] = ((((uint64_t)x3 << 32) | x2) >> 13) & 0x1ffffff;
+       out[4] = ((                       x3) >>  6) & 0x3ffffff;
+       out[5] = (                        x4       ) & 0x1ffffff;
+       out[6] = ((((uint64_t)x5 << 32) | x4) >> 25) & 0x3ffffff;
+       out[7] = ((((uint64_t)x6 << 32) | x5) >> 19) & 0x1ffffff;
+       out[8] = ((((uint64_t)x7 << 32) | x6) >> 12) & 0x3ffffff;
+       out[9] = ((                       x7) >>  6) & 0x1ffffff;
+       out[10] = 0;
+       out[11] = 0;
+}
+
+/* Take a fully reduced polynomial form number and contract it into a
+ * little-endian, 32-byte array
+ */
+static void
+curve25519_contract(unsigned char out[32], const bignum25519 in) {
+       bignum25519 ALIGN(16) f;
+       curve25519_copy(f, in);
+
+       #define carry_pass() \
+               f[1] += f[0] >> 26; f[0] &= 0x3ffffff; \
+               f[2] += f[1] >> 25; f[1] &= 0x1ffffff; \
+               f[3] += f[2] >> 26; f[2] &= 0x3ffffff; \
+               f[4] += f[3] >> 25; f[3] &= 0x1ffffff; \
+               f[5] += f[4] >> 26; f[4] &= 0x3ffffff; \
+               f[6] += f[5] >> 25; f[5] &= 0x1ffffff; \
+               f[7] += f[6] >> 26; f[6] &= 0x3ffffff; \
+               f[8] += f[7] >> 25; f[7] &= 0x1ffffff; \
+               f[9] += f[8] >> 26; f[8] &= 0x3ffffff;
+
+       #define carry_pass_full() \
+               carry_pass() \
+               f[0] += 19 * (f[9] >> 25); f[9] &= 0x1ffffff;
+
+       #define carry_pass_final() \
+               carry_pass() \
+               f[9] &= 0x1ffffff;
+
+       carry_pass_full()
+       carry_pass_full()
+
+       /* now t is between 0 and 2^255-1, properly carried. */
+       /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
+       f[0] += 19;
+       carry_pass_full()
+
+       /* now between 19 and 2^255-1 in both cases, and offset by 19. */
+       f[0] += (1 << 26) - 19;
+       f[1] += (1 << 25) - 1;
+       f[2] += (1 << 26) - 1;
+       f[3] += (1 << 25) - 1;
+       f[4] += (1 << 26) - 1;
+       f[5] += (1 << 25) - 1;
+       f[6] += (1 << 26) - 1;
+       f[7] += (1 << 25) - 1;
+       f[8] += (1 << 26) - 1;
+       f[9] += (1 << 25) - 1;
+
+       /* now between 2^255 and 2^256-20, and offset by 2^255. */
+       carry_pass_final()
+
+       #undef carry_pass
+       #undef carry_full
+       #undef carry_final
+
+       f[1] <<= 2;
+       f[2] <<= 3;
+       f[3] <<= 5;
+       f[4] <<= 6;
+       f[6] <<= 1;
+       f[7] <<= 3;
+       f[8] <<= 4;
+       f[9] <<= 6;
+
+       #define F(i, s) \
+               out[s+0] |= (unsigned char )(f[i] & 0xff); \
+               out[s+1] = (unsigned char )((f[i] >> 8) & 0xff); \
+               out[s+2] = (unsigned char )((f[i] >> 16) & 0xff); \
+               out[s+3] = (unsigned char )((f[i] >> 24) & 0xff);
+
+       out[0] = 0;
+       out[16] = 0;
+       F(0,0);
+       F(1,3);
+       F(2,6);
+       F(3,9);
+       F(4,12);
+       F(5,16);
+       F(6,19);
+       F(7,22);
+       F(8,25);
+       F(9,28);
+       #undef F
+}
+
+/* if (iswap) swap(a, b) */
+DONNA_INLINE static void
+curve25519_swap_conditional(bignum25519 a, bignum25519 b, uint32_t iswap) {
+       const uint32_t swap = (uint32_t)(-(int32_t)iswap);
+       xmmi a0,a1,a2,b0,b1,b2,x0,x1,x2;
+       xmmi mask = _mm_cvtsi32_si128(swap);
+       mask = _mm_shuffle_epi32(mask, 0);
+       a0 = _mm_load_si128((xmmi *)a + 0);
+       a1 = _mm_load_si128((xmmi *)a + 1);
+       b0 = _mm_load_si128((xmmi *)b + 0);
+       b1 = _mm_load_si128((xmmi *)b + 1);
+       b0 = _mm_xor_si128(a0, b0);
+       b1 = _mm_xor_si128(a1, b1);
+       x0 = _mm_and_si128(b0, mask);
+       x1 = _mm_and_si128(b1, mask);
+       x0 = _mm_xor_si128(x0, a0);
+       x1 = _mm_xor_si128(x1, a1);
+       a0 = _mm_xor_si128(x0, b0);
+       a1 = _mm_xor_si128(x1, b1);
+       _mm_store_si128((xmmi *)a + 0, x0);
+       _mm_store_si128((xmmi *)a + 1, x1);     
+       _mm_store_si128((xmmi *)b + 0, a0);
+       _mm_store_si128((xmmi *)b + 1, a1);
+
+       a2 = _mm_load_si128((xmmi *)a + 2);
+       b2 = _mm_load_si128((xmmi *)b + 2);
+       b2 = _mm_xor_si128(a2, b2);
+       x2 = _mm_and_si128(b2, mask);
+       x2 = _mm_xor_si128(x2, a2);
+       a2 = _mm_xor_si128(x2, b2);     
+       _mm_store_si128((xmmi *)b + 2, a2);
+       _mm_store_si128((xmmi *)a + 2, x2);
+}
+
+/* out = (flag) ? out : in */
+DONNA_INLINE static void
+curve25519_move_conditional_bytes(uint8_t out[96], const uint8_t in[96], uint32_t flag) {
+       xmmi a0,a1,a2,a3,a4,a5,b0,b1,b2,b3,b4,b5;
+       const uint32_t nb = flag - 1;
+       xmmi masknb = _mm_shuffle_epi32(_mm_cvtsi32_si128(nb),0);
+       a0 = _mm_load_si128((xmmi *)in + 0);
+       a1 = _mm_load_si128((xmmi *)in + 1);
+       a2 = _mm_load_si128((xmmi *)in + 2);
+       b0 = _mm_load_si128((xmmi *)out + 0);
+       b1 = _mm_load_si128((xmmi *)out + 1);
+       b2 = _mm_load_si128((xmmi *)out + 2);
+       a0 = _mm_andnot_si128(masknb, a0);
+       a1 = _mm_andnot_si128(masknb, a1);
+       a2 = _mm_andnot_si128(masknb, a2);
+       b0 = _mm_and_si128(masknb, b0);
+       b1 = _mm_and_si128(masknb, b1);
+       b2 = _mm_and_si128(masknb, b2);
+       a0 = _mm_or_si128(a0, b0);
+       a1 = _mm_or_si128(a1, b1);
+       a2 = _mm_or_si128(a2, b2);
+       _mm_store_si128((xmmi*)out + 0, a0);
+       _mm_store_si128((xmmi*)out + 1, a1);
+       _mm_store_si128((xmmi*)out + 2, a2);
+
+       a3 = _mm_load_si128((xmmi *)in + 3);
+       a4 = _mm_load_si128((xmmi *)in + 4);
+       a5 = _mm_load_si128((xmmi *)in + 5);
+       b3 = _mm_load_si128((xmmi *)out + 3);
+       b4 = _mm_load_si128((xmmi *)out + 4);
+       b5 = _mm_load_si128((xmmi *)out + 5);
+       a3 = _mm_andnot_si128(masknb, a3);
+       a4 = _mm_andnot_si128(masknb, a4);
+       a5 = _mm_andnot_si128(masknb, a5);
+       b3 = _mm_and_si128(masknb, b3);
+       b4 = _mm_and_si128(masknb, b4);
+       b5 = _mm_and_si128(masknb, b5);
+       a3 = _mm_or_si128(a3, b3);
+       a4 = _mm_or_si128(a4, b4);
+       a5 = _mm_or_si128(a5, b5);
+       _mm_store_si128((xmmi*)out + 3, a3);
+       _mm_store_si128((xmmi*)out + 4, a4);
+       _mm_store_si128((xmmi*)out + 5, a5);
+}
+

diff --git a/crypto/ed25519-donna/src/curve25519_svp64_macros.s b/crypto/ed25519-donna/src/curve25519_svp64_macros.s
new file mode 100644 (file)
index 0000000..eb24d2f
--- /dev/null
+++ b/crypto/ed25519-donna/src/curve25519_svp64_macros.s
@@ -0,0 +1,31 @@
+    .machine libresoc
+    .file      "curve25519_svp64_macros.s"
+
+# Helper macros for assembly
+
+# load word immediate for 32-bit constants
+.macro  lwi rD, const
+.if (\const >= -0x8000) && (\const <= 0x7fff)
+    li      \rD, \const
+.else
+    lis     \rD, \const@ha
+    ori     \rD, \rD, \const@l
+.endif
+.endm
+
+# load double word immediate for 64-bit constants
+.macro  ldi rD, const
+.if (\const >= -0x80000000) && (\const <= 0x7fffffff)
+    lwi      \rD, \const
+.else
+    # load high word into the high word of rD
+    lis     \rD,\const@highest       # load msg bits 48-63 into rD bits 16-31
+    ori     \rD,\rD,\const@higher    # load msg bits 32-47 into rD bits  0-15
+
+    rldicr  \rD,\rD,32,31           # rotate r4's low word into rD's high word
+
+    # load low word into the low word of rD
+    oris    \rD,\rD,\const@h         # load msg bits 16-31 into rD bits 16-31
+    ori     \rD,\rD,\const@l         # load msg bits  0-15 into rD bits  0-15
+.endif
+.endm

diff --git a/crypto/ed25519-donna/src/ed25519-donna-32bit-sse2.h b/crypto/ed25519-donna/src/ed25519-donna-32bit-sse2.h
new file mode 100644 (file)
index 0000000..db04a13
--- /dev/null
+++ b/crypto/ed25519-donna/src/ed25519-donna-32bit-sse2.h
@@ -0,0 +1,513 @@
+#if defined(ED25519_GCC_32BIT_SSE_CHOOSE)
+
+#define HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS
+
+DONNA_NOINLINE static void
+ge25519_scalarmult_base_choose_niels(ge25519_niels *t, const uint8_t table[256][96], uint32_t pos, signed char b) {
+       int32_t breg = (int32_t)b;
+       uint32_t sign = (uint32_t)breg >> 31;
+       uint32_t mask = ~(sign - 1);
+       uint32_t u = (breg + mask) ^ mask;
+
+       __asm__ __volatile__ (
+               /* ysubx+xaddy */
+               "movl %0, %%eax                  ;\n"
+               "movd %%eax, %%xmm6              ;\n"
+               "pshufd $0x00, %%xmm6, %%xmm6    ;\n"
+               "pxor %%xmm0, %%xmm0             ;\n"
+               "pxor %%xmm1, %%xmm1             ;\n"
+               "pxor %%xmm2, %%xmm2             ;\n"
+               "pxor %%xmm3, %%xmm3             ;\n"
+
+               /* 0 */
+               "movl $0, %%eax                  ;\n"
+               "movd %%eax, %%xmm7              ;\n"
+               "pshufd $0x00, %%xmm7, %%xmm7    ;\n"
+               "pcmpeqd %%xmm6, %%xmm7          ;\n"
+               "movl $1, %%ecx                  ;\n"
+               "movd %%ecx, %%xmm4              ;\n"
+               "pxor %%xmm5, %%xmm5             ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "pand %%xmm7, %%xmm5             ;\n"
+               "por %%xmm4, %%xmm0              ;\n"
+               "por %%xmm5, %%xmm1              ;\n"
+               "por %%xmm4, %%xmm2              ;\n"
+               "por %%xmm5, %%xmm3              ;\n"
+
+               /* 1 */
+               "movl $1, %%eax                  ;\n"
+               "movd %%eax, %%xmm7              ;\n"
+               "pshufd $0x00, %%xmm7, %%xmm7    ;\n"
+               "pcmpeqd %%xmm6, %%xmm7          ;\n"
+               "movdqa 0(%1), %%xmm4            ;\n"
+               "movdqa 16(%1), %%xmm5           ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "pand %%xmm7, %%xmm5             ;\n"
+               "por %%xmm4, %%xmm0              ;\n"
+               "por %%xmm5, %%xmm1              ;\n"
+               "movdqa 32(%1), %%xmm4           ;\n"
+               "movdqa 48(%1), %%xmm5           ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "pand %%xmm7, %%xmm5             ;\n"
+               "por %%xmm4, %%xmm2              ;\n"
+               "por %%xmm5, %%xmm3              ;\n"
+
+               /* 2 */
+               "movl $2, %%eax                  ;\n"
+               "movd %%eax, %%xmm7              ;\n"
+               "pshufd $0x00, %%xmm7, %%xmm7    ;\n"
+               "pcmpeqd %%xmm6, %%xmm7          ;\n"
+               "movdqa 96(%1), %%xmm4           ;\n"
+               "movdqa 112(%1), %%xmm5          ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "pand %%xmm7, %%xmm5             ;\n"
+               "por %%xmm4, %%xmm0              ;\n"
+               "por %%xmm5, %%xmm1              ;\n"
+               "movdqa 128(%1), %%xmm4          ;\n"
+               "movdqa 144(%1), %%xmm5          ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "pand %%xmm7, %%xmm5             ;\n"
+               "por %%xmm4, %%xmm2              ;\n"
+               "por %%xmm5, %%xmm3              ;\n"
+
+               /* 3 */
+               "movl $3, %%eax                  ;\n"
+               "movd %%eax, %%xmm7              ;\n"
+               "pshufd $0x00, %%xmm7, %%xmm7    ;\n"
+               "pcmpeqd %%xmm6, %%xmm7          ;\n"
+               "movdqa 192(%1), %%xmm4          ;\n"
+               "movdqa 208(%1), %%xmm5          ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "pand %%xmm7, %%xmm5             ;\n"
+               "por %%xmm4, %%xmm0              ;\n"
+               "por %%xmm5, %%xmm1              ;\n"
+               "movdqa 224(%1), %%xmm4          ;\n"
+               "movdqa 240(%1), %%xmm5          ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "pand %%xmm7, %%xmm5             ;\n"
+               "por %%xmm4, %%xmm2              ;\n"
+               "por %%xmm5, %%xmm3              ;\n"
+
+               /* 4 */
+               "movl $4, %%eax                  ;\n"
+               "movd %%eax, %%xmm7              ;\n"
+               "pshufd $0x00, %%xmm7, %%xmm7    ;\n"
+               "pcmpeqd %%xmm6, %%xmm7          ;\n"
+               "movdqa 288(%1), %%xmm4          ;\n"
+               "movdqa 304(%1), %%xmm5          ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "pand %%xmm7, %%xmm5             ;\n"
+               "por %%xmm4, %%xmm0              ;\n"
+               "por %%xmm5, %%xmm1              ;\n"
+               "movdqa 320(%1), %%xmm4          ;\n"
+               "movdqa 336(%1), %%xmm5          ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "pand %%xmm7, %%xmm5             ;\n"
+               "por %%xmm4, %%xmm2              ;\n"
+               "por %%xmm5, %%xmm3              ;\n"
+
+               /* 5 */
+               "movl $5, %%eax                  ;\n"
+               "movd %%eax, %%xmm7              ;\n"
+               "pshufd $0x00, %%xmm7, %%xmm7    ;\n"
+               "pcmpeqd %%xmm6, %%xmm7          ;\n"
+               "movdqa 384(%1), %%xmm4          ;\n"
+               "movdqa 400(%1), %%xmm5          ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "pand %%xmm7, %%xmm5             ;\n"
+               "por %%xmm4, %%xmm0              ;\n"
+               "por %%xmm5, %%xmm1              ;\n"
+               "movdqa 416(%1), %%xmm4          ;\n"
+               "movdqa 432(%1), %%xmm5          ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "pand %%xmm7, %%xmm5             ;\n"
+               "por %%xmm4, %%xmm2              ;\n"
+               "por %%xmm5, %%xmm3              ;\n"
+
+               /* 6 */
+               "movl $6, %%eax                  ;\n"
+               "movd %%eax, %%xmm7              ;\n"
+               "pshufd $0x00, %%xmm7, %%xmm7    ;\n"
+               "pcmpeqd %%xmm6, %%xmm7          ;\n"
+               "movdqa 480(%1), %%xmm4          ;\n"
+               "movdqa 496(%1), %%xmm5          ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "pand %%xmm7, %%xmm5             ;\n"
+               "por %%xmm4, %%xmm0              ;\n"
+               "por %%xmm5, %%xmm1              ;\n"
+               "movdqa 512(%1), %%xmm4          ;\n"
+               "movdqa 528(%1), %%xmm5          ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "pand %%xmm7, %%xmm5             ;\n"
+               "por %%xmm4, %%xmm2              ;\n"
+               "por %%xmm5, %%xmm3              ;\n"
+
+               /* 7 */
+               "movl $7, %%eax                  ;\n"
+               "movd %%eax, %%xmm7              ;\n"
+               "pshufd $0x00, %%xmm7, %%xmm7    ;\n"
+               "pcmpeqd %%xmm6, %%xmm7          ;\n"
+               "movdqa 576(%1), %%xmm4          ;\n"
+               "movdqa 592(%1), %%xmm5          ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "pand %%xmm7, %%xmm5             ;\n"
+               "por %%xmm4, %%xmm0              ;\n"
+               "por %%xmm5, %%xmm1              ;\n"
+               "movdqa 608(%1), %%xmm4          ;\n"
+               "movdqa 624(%1), %%xmm5          ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "pand %%xmm7, %%xmm5             ;\n"
+               "por %%xmm4, %%xmm2              ;\n"
+               "por %%xmm5, %%xmm3              ;\n"
+
+               /* 8 */
+               "movl $8, %%eax                  ;\n"
+               "movd %%eax, %%xmm7              ;\n"
+               "pshufd $0x00, %%xmm7, %%xmm7    ;\n"
+               "pcmpeqd %%xmm6, %%xmm7          ;\n"
+               "movdqa 672(%1), %%xmm4          ;\n"
+               "movdqa 688(%1), %%xmm5          ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "pand %%xmm7, %%xmm5             ;\n"
+               "por %%xmm4, %%xmm0              ;\n"
+               "por %%xmm5, %%xmm1              ;\n"
+               "movdqa 704(%1), %%xmm4          ;\n"
+               "movdqa 720(%1), %%xmm5          ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "pand %%xmm7, %%xmm5             ;\n"
+               "por %%xmm4, %%xmm2              ;\n"
+               "por %%xmm5, %%xmm3              ;\n"
+
+               /* conditional swap based on sign */
+               "movl %3, %%ecx                  ;\n"
+               "movl %2, %%eax                  ;\n"
+               "xorl $1, %%ecx                  ;\n"
+               "movd %%ecx, %%xmm6              ;\n"
+               "pxor %%xmm7, %%xmm7             ;\n"
+               "pshufd $0x00, %%xmm6, %%xmm6    ;\n"
+               "pxor %%xmm0, %%xmm2             ;\n"
+               "pxor %%xmm1, %%xmm3             ;\n"
+               "pcmpeqd %%xmm6, %%xmm7          ;\n"
+               "movdqa %%xmm2, %%xmm4           ;\n"
+               "movdqa %%xmm3, %%xmm5           ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "pand %%xmm7, %%xmm5             ;\n"
+               "pxor %%xmm4, %%xmm0             ;\n"
+               "pxor %%xmm5, %%xmm1             ;\n"
+               "pxor %%xmm0, %%xmm2             ;\n"
+               "pxor %%xmm1, %%xmm3             ;\n"
+
+               /* store ysubx */
+               "movd %%xmm0, %%ecx              ;\n"
+               "movl %%ecx, %%edx               ;\n"
+               "pshufd $0x39, %%xmm0, %%xmm0    ;\n"
+               "andl $0x3ffffff, %%ecx          ;\n"
+               "movl %%ecx, 0(%%eax)            ;\n"
+               "movd %%xmm0, %%ecx              ;\n"
+               "pshufd $0x39, %%xmm0, %%xmm0    ;\n"
+               "shrdl $26, %%ecx, %%edx         ;\n"
+               "andl $0x1ffffff, %%edx          ;\n"
+               "movl %%edx, 4(%%eax)            ;\n"
+               "movd %%xmm0, %%edx              ;\n"
+               "pshufd $0x39, %%xmm0, %%xmm0    ;\n"
+               "shrdl $19, %%edx, %%ecx         ;\n"
+               "andl $0x3ffffff, %%ecx          ;\n"
+               "movl %%ecx, 8(%%eax)            ;\n"
+               "movd %%xmm0, %%ecx              ;\n"
+               "shrdl $13, %%ecx, %%edx         ;\n"
+               "andl $0x1ffffff, %%edx          ;\n"
+               "movl %%edx, 12(%%eax)           ;\n"
+               "movd %%xmm1, %%edx              ;\n"
+               "pshufd $0x39, %%xmm1, %%xmm1    ;\n"
+               "shrl $6, %%ecx                  ;\n"
+               "andl $0x3ffffff, %%ecx          ;\n"
+               "movl %%ecx, 16(%%eax)           ;\n"
+               "movl %%edx, %%ecx               ;\n"
+               "andl $0x1ffffff, %%edx          ;\n"
+               "movl %%edx, 20(%%eax)           ;\n"
+               "movd %%xmm1, %%edx              ;\n"
+               "pshufd $0x39, %%xmm1, %%xmm1    ;\n"
+               "shrdl $25, %%edx, %%ecx         ;\n"
+               "andl $0x3ffffff, %%ecx          ;\n"
+               "movl %%ecx, 24(%%eax)           ;\n"
+               "movd %%xmm1, %%ecx              ;\n"
+               "pshufd $0x39, %%xmm1, %%xmm1    ;\n"
+               "shrdl $19, %%ecx, %%edx         ;\n"
+               "andl $0x1ffffff, %%edx          ;\n"
+               "movl %%edx, 28(%%eax)           ;\n"
+               "movd %%xmm1, %%edx              ;\n"
+               "shrdl $12, %%edx, %%ecx         ;\n"
+               "andl $0x3ffffff, %%ecx          ;\n"
+               "movl %%ecx, 32(%%eax)           ;\n"
+               "shrl $6, %%edx                  ;\n"
+               "andl $0x1ffffff, %%edx          ;\n"
+               "xorl %%ecx, %%ecx               ;\n"
+               "movl %%edx, 36(%%eax)           ;\n"
+               "movl %%ecx, 40(%%eax)           ;\n"
+               "movl %%ecx, 44(%%eax)           ;\n"
+
+               /* store xaddy */
+               "addl $48, %%eax                 ;\n"
+               "movdqa %%xmm2, %%xmm0           ;\n"
+               "movdqa %%xmm3, %%xmm1           ;\n"
+               "movd %%xmm0, %%ecx              ;\n"
+               "movl %%ecx, %%edx               ;\n"
+               "pshufd $0x39, %%xmm0, %%xmm0    ;\n"
+               "andl $0x3ffffff, %%ecx          ;\n"
+               "movl %%ecx, 0(%%eax)            ;\n"
+               "movd %%xmm0, %%ecx              ;\n"
+               "pshufd $0x39, %%xmm0, %%xmm0    ;\n"
+               "shrdl $26, %%ecx, %%edx         ;\n"
+               "andl $0x1ffffff, %%edx          ;\n"
+               "movl %%edx, 4(%%eax)            ;\n"
+               "movd %%xmm0, %%edx              ;\n"
+               "pshufd $0x39, %%xmm0, %%xmm0    ;\n"
+               "shrdl $19, %%edx, %%ecx         ;\n"
+               "andl $0x3ffffff, %%ecx          ;\n"
+               "movl %%ecx, 8(%%eax)            ;\n"
+               "movd %%xmm0, %%ecx              ;\n"
+               "shrdl $13, %%ecx, %%edx         ;\n"
+               "andl $0x1ffffff, %%edx          ;\n"
+               "movl %%edx, 12(%%eax)           ;\n"
+               "movd %%xmm1, %%edx              ;\n"
+               "pshufd $0x39, %%xmm1, %%xmm1    ;\n"
+               "shrl $6, %%ecx                  ;\n"
+               "andl $0x3ffffff, %%ecx          ;\n"
+               "movl %%ecx, 16(%%eax)           ;\n"
+               "movl %%edx, %%ecx               ;\n"
+               "andl $0x1ffffff, %%edx          ;\n"
+               "movl %%edx, 20(%%eax)           ;\n"
+               "movd %%xmm1, %%edx              ;\n"
+               "pshufd $0x39, %%xmm1, %%xmm1    ;\n"
+               "shrdl $25, %%edx, %%ecx         ;\n"
+               "andl $0x3ffffff, %%ecx          ;\n"
+               "movl %%ecx, 24(%%eax)           ;\n"
+               "movd %%xmm1, %%ecx              ;\n"
+               "pshufd $0x39, %%xmm1, %%xmm1    ;\n"
+               "shrdl $19, %%ecx, %%edx         ;\n"
+               "andl $0x1ffffff, %%edx          ;\n"
+               "movl %%edx, 28(%%eax)           ;\n"
+               "movd %%xmm1, %%edx              ;\n"
+               "shrdl $12, %%edx, %%ecx         ;\n"
+               "andl $0x3ffffff, %%ecx          ;\n"
+               "movl %%ecx, 32(%%eax)           ;\n"
+               "shrl $6, %%edx                  ;\n"
+               "andl $0x1ffffff, %%edx          ;\n"
+               "xorl %%ecx, %%ecx               ;\n"
+               "movl %%edx, 36(%%eax)           ;\n"
+               "movl %%ecx, 40(%%eax)           ;\n"
+               "movl %%ecx, 44(%%eax)           ;\n"
+
+               /* t2d */
+               "movl %0, %%eax                  ;\n"
+               "movd %%eax, %%xmm6              ;\n"
+               "pshufd $0x00, %%xmm6, %%xmm6    ;\n"
+               "pxor %%xmm0, %%xmm0             ;\n"
+               "pxor %%xmm1, %%xmm1             ;\n"
+
+               /* 0 */
+               "movl $0, %%eax                  ;\n"
+               "movd %%eax, %%xmm7              ;\n"
+               "pshufd $0x00, %%xmm7, %%xmm7    ;\n"
+               "pcmpeqd %%xmm6, %%xmm7          ;\n"
+               "pxor %%xmm0, %%xmm0             ;\n"
+               "pxor %%xmm1, %%xmm1             ;\n"
+
+               /* 1 */
+               "movl $1, %%eax                  ;\n"
+               "movd %%eax, %%xmm7              ;\n"
+               "pshufd $0x00, %%xmm7, %%xmm7    ;\n"
+               "pcmpeqd %%xmm6, %%xmm7          ;\n"
+               "movdqa 64(%1), %%xmm3           ;\n"
+               "movdqa 80(%1), %%xmm4           ;\n"
+               "pand %%xmm7, %%xmm3             ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "por %%xmm3, %%xmm0              ;\n"
+               "por %%xmm4, %%xmm1              ;\n"
+
+               /* 2 */
+               "movl $2, %%eax                  ;\n"
+               "movd %%eax, %%xmm7              ;\n"
+               "pshufd $0x00, %%xmm7, %%xmm7    ;\n"
+               "pcmpeqd %%xmm6, %%xmm7          ;\n"
+               "movdqa 160(%1), %%xmm3          ;\n"
+               "movdqa 176(%1), %%xmm4          ;\n"
+               "pand %%xmm7, %%xmm3             ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "por %%xmm3, %%xmm0              ;\n"
+               "por %%xmm4, %%xmm1              ;\n"
+
+               /* 3 */
+               "movl $3, %%eax                  ;\n"
+               "movd %%eax, %%xmm7              ;\n"
+               "pshufd $0x00, %%xmm7, %%xmm7    ;\n"
+               "pcmpeqd %%xmm6, %%xmm7          ;\n"
+               "movdqa 256(%1), %%xmm3          ;\n"
+               "movdqa 272(%1), %%xmm4          ;\n"
+               "pand %%xmm7, %%xmm3             ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "por %%xmm3, %%xmm0              ;\n"
+               "por %%xmm4, %%xmm1              ;\n"
+
+               /* 4 */
+               "movl $4, %%eax                  ;\n"
+               "movd %%eax, %%xmm7              ;\n"
+               "pshufd $0x00, %%xmm7, %%xmm7    ;\n"
+               "pcmpeqd %%xmm6, %%xmm7          ;\n"
+               "movdqa 352(%1), %%xmm3          ;\n"
+               "movdqa 368(%1), %%xmm4          ;\n"
+               "pand %%xmm7, %%xmm3             ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "por %%xmm3, %%xmm0              ;\n"
+               "por %%xmm4, %%xmm1              ;\n"
+
+               /* 5 */
+               "movl $5, %%eax                  ;\n"
+               "movd %%eax, %%xmm7              ;\n"
+               "pshufd $0x00, %%xmm7, %%xmm7    ;\n"
+               "pcmpeqd %%xmm6, %%xmm7          ;\n"
+               "movdqa 448(%1), %%xmm3          ;\n"
+               "movdqa 464(%1), %%xmm4          ;\n"
+               "pand %%xmm7, %%xmm3             ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "por %%xmm3, %%xmm0              ;\n"
+               "por %%xmm4, %%xmm1              ;\n"
+
+               /* 6 */
+               "movl $6, %%eax                  ;\n"
+               "movd %%eax, %%xmm7              ;\n"
+               "pshufd $0x00, %%xmm7, %%xmm7    ;\n"
+               "pcmpeqd %%xmm6, %%xmm7          ;\n"
+               "movdqa 544(%1), %%xmm3          ;\n"
+               "movdqa 560(%1), %%xmm4          ;\n"
+               "pand %%xmm7, %%xmm3             ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "por %%xmm3, %%xmm0              ;\n"
+               "por %%xmm4, %%xmm1              ;\n"
+
+               /* 7 */
+               "movl $7, %%eax                  ;\n"
+               "movd %%eax, %%xmm7              ;\n"
+               "pshufd $0x00, %%xmm7, %%xmm7    ;\n"
+               "pcmpeqd %%xmm6, %%xmm7          ;\n"
+               "movdqa 640(%1), %%xmm3          ;\n"
+               "movdqa 656(%1), %%xmm4          ;\n"
+               "pand %%xmm7, %%xmm3             ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "por %%xmm3, %%xmm0              ;\n"
+               "por %%xmm4, %%xmm1              ;\n"
+
+               /* 8 */
+               "movl $8, %%eax                  ;\n"
+               "movd %%eax, %%xmm7              ;\n"
+               "pshufd $0x00, %%xmm7, %%xmm7    ;\n"
+               "pcmpeqd %%xmm6, %%xmm7          ;\n"
+               "movdqa 736(%1), %%xmm3          ;\n"
+               "movdqa 752(%1), %%xmm4          ;\n"
+               "pand %%xmm7, %%xmm3             ;\n"
+               "pand %%xmm7, %%xmm4             ;\n"
+               "por %%xmm3, %%xmm0              ;\n"
+               "por %%xmm4, %%xmm1              ;\n"
+
+               /* store t2d */
+               "movl %2, %%eax                  ;\n"
+               "addl $96, %%eax                 ;\n"
+               "movd %%xmm0, %%ecx              ;\n"
+               "movl %%ecx, %%edx               ;\n"
+               "pshufd $0x39, %%xmm0, %%xmm0    ;\n"
+               "andl $0x3ffffff, %%ecx          ;\n"
+               "movl %%ecx, 0(%%eax)            ;\n"
+               "movd %%xmm0, %%ecx              ;\n"
+               "pshufd $0x39, %%xmm0, %%xmm0    ;\n"
+               "shrdl $26, %%ecx, %%edx         ;\n"
+               "andl $0x1ffffff, %%edx          ;\n"
+               "movl %%edx, 4(%%eax)            ;\n"
+               "movd %%xmm0, %%edx              ;\n"
+               "pshufd $0x39, %%xmm0, %%xmm0    ;\n"
+               "shrdl $19, %%edx, %%ecx         ;\n"
+               "andl $0x3ffffff, %%ecx          ;\n"
+               "movl %%ecx, 8(%%eax)            ;\n"
+               "movd %%xmm0, %%ecx              ;\n"
+               "shrdl $13, %%ecx, %%edx         ;\n"
+               "andl $0x1ffffff, %%edx          ;\n"
+               "movl %%edx, 12(%%eax)           ;\n"
+               "movd %%xmm1, %%edx              ;\n"
+               "pshufd $0x39, %%xmm1, %%xmm1    ;\n"
+               "shrl $6, %%ecx                  ;\n"
+               "andl $0x3ffffff, %%ecx          ;\n"
+               "movl %%ecx, 16(%%eax)           ;\n"
+               "movl %%edx, %%ecx               ;\n"
+               "andl $0x1ffffff, %%edx          ;\n"
+               "movl %%edx, 20(%%eax)           ;\n"
+               "movd %%xmm1, %%edx              ;\n"
+               "pshufd $0x39, %%xmm1, %%xmm1    ;\n"
+               "shrdl $25, %%edx, %%ecx         ;\n"
+               "andl $0x3ffffff, %%ecx          ;\n"
+               "movl %%ecx, 24(%%eax)           ;\n"
+               "movd %%xmm1, %%ecx              ;\n"
+               "pshufd $0x39, %%xmm1, %%xmm1    ;\n"
+               "shrdl $19, %%ecx, %%edx         ;\n"
+               "andl $0x1ffffff, %%edx          ;\n"
+               "movl %%edx, 28(%%eax)           ;\n"
+               "movd %%xmm1, %%edx              ;\n"
+               "movd %%xmm1, %%edx              ;\n"
+               "shrdl $12, %%edx, %%ecx         ;\n"
+               "andl $0x3ffffff, %%ecx          ;\n"
+               "movl %%ecx, 32(%%eax)           ;\n"
+               "shrl $6, %%edx                  ;\n"
+               "andl $0x1ffffff, %%edx          ;\n"
+               "xorl %%ecx, %%ecx               ;\n"
+               "movl %%edx, 36(%%eax)           ;\n"
+               "movl %%ecx, 40(%%eax)           ;\n"
+               "movl %%ecx, 44(%%eax)           ;\n"
+               "movdqa 0(%%eax), %%xmm0         ;\n"
+               "movdqa 16(%%eax), %%xmm1        ;\n"
+               "movdqa 32(%%eax), %%xmm2        ;\n"
+
+               /* conditionally negate t2d */
+
+               /* set up 2p in to 3/4 */
+               "movl $0x7ffffda, %%ecx          ;\n"
+               "movl $0x3fffffe, %%edx          ;\n"
+               "movd %%ecx, %%xmm3              ;\n"
+               "movd %%edx, %%xmm5              ;\n"
+               "movl $0x7fffffe, %%ecx          ;\n"
+               "movd %%ecx, %%xmm4              ;\n"
+               "punpckldq %%xmm5, %%xmm3        ;\n"
+               "punpckldq %%xmm5, %%xmm4        ;\n"
+               "punpcklqdq %%xmm4, %%xmm3       ;\n"
+               "movdqa %%xmm4, %%xmm5           ;\n"
+               "punpcklqdq %%xmm4, %%xmm4       ;\n"
+
+               /* subtract and conditionally move */
+               "movl %3, %%ecx                  ;\n"
+               "sub $1, %%ecx                   ;\n"
+               "movd %%ecx, %%xmm6              ;\n"
+               "pshufd $0x00, %%xmm6, %%xmm6    ;\n"
+               "movdqa %%xmm6, %%xmm7           ;\n"
+               "psubd %%xmm0, %%xmm3            ;\n"
+               "psubd %%xmm1, %%xmm4            ;\n"
+               "psubd %%xmm2, %%xmm5            ;\n"
+               "pand %%xmm6, %%xmm0             ;\n"
+               "pand %%xmm6, %%xmm1             ;\n"
+               "pand %%xmm6, %%xmm2             ;\n"
+               "pandn %%xmm3, %%xmm6            ;\n"
+               "movdqa %%xmm7, %%xmm3           ;\n"
+               "pandn %%xmm4, %%xmm7            ;\n"
+               "pandn %%xmm5, %%xmm3            ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm3, %%xmm2              ;\n"
+
+               /* store */
+               "movdqa %%xmm0, 0(%%eax)         ;\n"
+               "movdqa %%xmm1, 16(%%eax)        ;\n"
+               "movdqa %%xmm2, 32(%%eax)        ;\n"
+               :
+               : "m"(u), "r"(&table[pos * 8]), "m"(t), "m"(sign) /* %0 = u, %1 = table, %2 = t, %3 = sign */
+               : "%eax", "%ecx", "%edx", "%xmm0", "%xmm1", "%xmm2", "%xmm3", "%xmm4", "%xmm5", "%xmm6", "%xmm7", "cc", "memory"
+       );
+}
+
+#endif /* defined(ED25519_GCC_32BIT_SSE_CHOOSE) */
+

diff --git a/crypto/ed25519-donna/src/ed25519-donna-32bit-tables.h b/crypto/ed25519-donna/src/ed25519-donna-32bit-tables.h
new file mode 100644 (file)
index 0000000..c977c26
--- /dev/null
+++ b/crypto/ed25519-donna/src/ed25519-donna-32bit-tables.h
@@ -0,0 +1,61 @@
+static const ge25519 ALIGN(16) ge25519_basepoint = {
+       {0x0325d51a,0x018b5823,0x00f6592a,0x0104a92d,0x01a4b31d,0x01d6dc5c,0x027118fe,0x007fd814,0x013cd6e5,0x0085a4db},
+       {0x02666658,0x01999999,0x00cccccc,0x01333333,0x01999999,0x00666666,0x03333333,0x00cccccc,0x02666666,0x01999999},
+       {0x00000001,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000,0x00000000},
+       {0x01b7dda3,0x01a2ace9,0x025eadbb,0x0003ba8a,0x0083c27e,0x00abe37d,0x01274732,0x00ccacdd,0x00fd78b7,0x019e1d7c}
+};
+
+/*
+       d
+*/
+
+static const bignum25519 ALIGN(16) ge25519_ecd = {
+       0x035978a3,0x00d37284,0x03156ebd,0x006a0a0e,0x0001c029,0x0179e898,0x03a03cbb,0x01ce7198,0x02e2b6ff,0x01480db3
+};
+
+static const bignum25519 ALIGN(16) ge25519_ec2d = {
+       0x02b2f159,0x01a6e509,0x022add7a,0x00d4141d,0x00038052,0x00f3d130,0x03407977,0x019ce331,0x01c56dff,0x00901b67
+};
+
+/*
+       sqrt(-1)
+*/
+
+static const bignum25519 ALIGN(16) ge25519_sqrtneg1 = {
+       0x020ea0b0,0x0186c9d2,0x008f189d,0x0035697f,0x00bd0c60,0x01fbd7a7,0x02804c9e,0x01e16569,0x0004fc1d,0x00ae0c92
+};
+
+static const ge25519_niels ALIGN(16) ge25519_niels_sliding_multiples[32] = {
+       {{0x0340913e,0x000e4175,0x03d673a2,0x002e8a05,0x03f4e67c,0x008f8a09,0x00c21a34,0x004cf4b8,0x01298f81,0x0113f4be},{0x018c3b85,0x0124f1bd,0x01c325f7,0x0037dc60,0x033e4cb7,0x003d42c2,0x01a44c32,0x014ca4e1,0x03a33d4b,0x001f3e74},{0x037aaa68,0x00448161,0x0093d579,0x011e6556,0x009b67a0,0x0143598c,0x01bee5ee,0x00b50b43,0x0289f0c6,0x01bc45ed}},
+       {{0x00fcd265,0x0047fa29,0x034faacc,0x01ef2e0d,0x00ef4d4f,0x014bd6bd,0x00f98d10,0x014c5026,0x007555bd,0x00aae456},{0x00ee9730,0x016c2a13,0x017155e4,0x01874432,0x00096a10,0x01016732,0x01a8014f,0x011e9823,0x01b9a80f,0x01e85938},{0x01d0d889,0x01a4cfc3,0x034c4295,0x0110e1ae,0x0162508c,0x00f2db4c,0x0072a2c6,0x0098da2e,0x02f12b9b,0x0168a09a}},
+       {{0x0047d6ba,0x0060b0e9,0x0136eff2,0x008a5939,0x03540053,0x0064a087,0x02788e5c,0x00be7c67,0x033eb1b5,0x005529f9},{0x00a5bb33,0x00af1102,0x01a05442,0x001e3af7,0x02354123,0x00bfec44,0x01f5862d,0x00dd7ba3,0x03146e20,0x00a51733},{0x012a8285,0x00f6fc60,0x023f9797,0x003e85ee,0x009c3820,0x01bda72d,0x01b3858d,0x00d35683,0x0296b3bb,0x010eaaf9}},
+       {{0x023221b1,0x01cb26aa,0x0074f74d,0x0099ddd1,0x01b28085,0x00192c3a,0x013b27c9,0x00fc13bd,0x01d2e531,0x0075bb75},{0x004ea3bf,0x00973425,0x001a4d63,0x01d59cee,0x01d1c0d4,0x00542e49,0x01294114,0x004fce36,0x029283c9,0x01186fa9},{0x01b8b3a2,0x00db7200,0x00935e30,0x003829f5,0x02cc0d7d,0x0077adf3,0x0220dd2c,0x0014ea53,0x01c6a0f9,0x01ea7eec}},
+       {{0x039d8064,0x01885f80,0x00337e6d,0x01b7a902,0x02628206,0x015eb044,0x01e30473,0x0191f2d9,0x011fadc9,0x01270169},{0x02a8632f,0x0199e2a9,0x00d8b365,0x017a8de2,0x02994279,0x0086f5b5,0x0119e4e3,0x01eb39d6,0x0338add7,0x00d2e7b4},{0x0045af1b,0x013a2fe4,0x0245e0d6,0x014538ce,0x038bfe0f,0x01d4cf16,0x037e14c9,0x0160d55e,0x0021b008,0x01cf05c8}},
+       {{0x01864348,0x01d6c092,0x0070262b,0x014bb844,0x00fb5acd,0x008deb95,0x003aaab5,0x00eff474,0x00029d5c,0x0062ad66},{0x02802ade,0x01c02122,0x01c4e5f7,0x00781181,0x039767fb,0x01703406,0x0342388b,0x01f5e227,0x022546d8,0x0109d6ab},{0x016089e9,0x00cb317f,0x00949b05,0x01099417,0x000c7ad2,0x011a8622,0x0088ccda,0x01290886,0x022b53df,0x00f71954}},
+       {{0x027fbf93,0x01c04ecc,0x01ed6a0d,0x004cdbbb,0x02bbf3af,0x00ad5968,0x01591955,0x0094f3a2,0x02d17602,0x00099e20},{0x02007f6d,0x003088a8,0x03db77ee,0x00d5ade6,0x02fe12ce,0x0107ba07,0x0107097d,0x00482a6f,0x02ec346f,0x008d3f5f},{0x032ea378,0x0028465c,0x028e2a6c,0x018efc6e,0x0090df9a,0x01a7e533,0x039bfc48,0x010c745d,0x03daa097,0x0125ee9b}},
+       {{0x028ccf0b,0x00f36191,0x021ac081,0x012154c8,0x034e0a6e,0x01b25192,0x00180403,0x01d7eea1,0x00218d05,0x010ed735},{0x03cfeaa0,0x01b300c4,0x008da499,0x0068c4e1,0x0219230a,0x01f2d4d0,0x02defd60,0x00e565b7,0x017f12de,0x018788a4},{0x03d0b516,0x009d8be6,0x03ddcbb3,0x0071b9fe,0x03ace2bd,0x01d64270,0x032d3ec9,0x01084065,0x0210ae4d,0x01447584}},
+       {{0x0020de87,0x00e19211,0x01b68102,0x00b5ac97,0x022873c0,0x01942d25,0x01271394,0x0102073f,0x02fe2482,0x01c69ff9},{0x010e9d81,0x019dbbe5,0x0089f258,0x006e06b8,0x02951883,0x018f1248,0x019b3237,0x00bc7553,0x024ddb85,0x01b4c964},{0x01c8c854,0x0060ae29,0x01406d8e,0x01cff2f9,0x00cff451,0x01778d0c,0x03ac8c41,0x01552e59,0x036559ee,0x011d1b12}},
+       {{0x00741147,0x0151b219,0x01092690,0x00e877e6,0x01f4d6bb,0x0072a332,0x01cd3b03,0x00dadff2,0x0097db5e,0x0086598d},{0x01c69a2b,0x01decf1b,0x02c2fa6e,0x013b7c4f,0x037beac8,0x013a16b5,0x028e7bda,0x01f6e8ac,0x01e34fe9,0x01726947},{0x01f10e67,0x003c73de,0x022b7ea2,0x010f32c2,0x03ff776a,0x00142277,0x01d38b88,0x00776138,0x03c60822,0x01201140}},
+       {{0x0236d175,0x0008748e,0x03c6476d,0x013f4cdc,0x02eed02a,0x00838a47,0x032e7210,0x018bcbb3,0x00858de4,0x01dc7826},{0x00a37fc7,0x0127b40b,0x01957884,0x011d30ad,0x02816683,0x016e0e23,0x00b76be4,0x012db115,0x02516506,0x0154ce62},{0x00451edf,0x00bd749e,0x03997342,0x01cc2c4c,0x00eb6975,0x01a59508,0x03a516cf,0x00c228ef,0x0168ff5a,0x01697b47}},
+       {{0x00527359,0x01783156,0x03afd75c,0x00ce56dc,0x00e4b970,0x001cabe9,0x029e0f6d,0x0188850c,0x0135fefd,0x00066d80},{0x02150e83,0x01448abf,0x02bb0232,0x012bf259,0x033c8268,0x00711e20,0x03fc148f,0x005e0e70,0x017d8bf9,0x0112b2e2},{0x02134b83,0x001a0517,0x0182c3cc,0x00792182,0x0313d799,0x001a3ed7,0x0344547e,0x01f24a0d,0x03de6ad2,0x00543127}},
+       {{0x00dca868,0x00618f27,0x015a1709,0x00ddc38a,0x0320fd13,0x0036168d,0x0371ab06,0x01783fc7,0x0391e05f,0x01e29b5d},{0x01471138,0x00fca542,0x00ca31cf,0x01ca7bad,0x0175bfbc,0x01a708ad,0x03bce212,0x01244215,0x0075bb99,0x01acad68},{0x03a0b976,0x01dc12d1,0x011aab17,0x00aba0ba,0x029806cd,0x0142f590,0x018fd8ea,0x01a01545,0x03c4ad55,0x01c971ff}},
+       {{0x00d098c0,0x000afdc7,0x006cd230,0x01276af3,0x03f905b2,0x0102994c,0x002eb8a4,0x015cfbeb,0x025f855f,0x01335518},{0x01cf99b2,0x0099c574,0x01a69c88,0x00881510,0x01cd4b54,0x0112109f,0x008abdc5,0x0074647a,0x0277cb1f,0x01e53324},{0x02ac5053,0x01b109b0,0x024b095e,0x016997b3,0x02f26bb6,0x00311021,0x00197885,0x01d0a55a,0x03b6fcc8,0x01c020d5}},
+       {{0x02584a34,0x00e7eee0,0x03257a03,0x011e95a3,0x011ead91,0x00536202,0x00b1ce24,0x008516c6,0x03669d6d,0x004ea4a8},{0x00773f01,0x0019c9ce,0x019f6171,0x01d4afde,0x02e33323,0x01ad29b6,0x02ead1dc,0x01ed51a5,0x01851ad0,0x001bbdfa},{0x00577de5,0x00ddc730,0x038b9952,0x00f281ae,0x01d50390,0x0002e071,0x000780ec,0x010d448d,0x01f8a2af,0x00f0a5b7}},
+       {{0x031f2541,0x00d34bae,0x0323ff9d,0x003a056d,0x02e25443,0x00a1ad05,0x00d1bee8,0x002f7f8e,0x03007477,0x002a24b1},{0x0114a713,0x01457e76,0x032255d5,0x01cc647f,0x02a4bdef,0x0153d730,0x00118bcf,0x00f755ff,0x013490c7,0x01ea674e},{0x02bda3e8,0x00bb490d,0x00f291ea,0x000abf40,0x01dea321,0x002f9ce0,0x00b2b193,0x00fa54b5,0x0128302f,0x00a19d8b}},
+       {{0x022ef5bd,0x01638af3,0x038c6f8a,0x01a33a3d,0x039261b2,0x01bb89b8,0x010bcf9d,0x00cf42a9,0x023d6f17,0x01da1bca},{0x00e35b25,0x000d824f,0x0152e9cf,0x00ed935d,0x020b8460,0x01c7b83f,0x00c969e5,0x01a74198,0x0046a9d9,0x00cbc768},{0x01597c6a,0x0144a99b,0x00a57551,0x0018269c,0x023c464c,0x0009b022,0x00ee39e1,0x0114c7f2,0x038a9ad2,0x01584c17}},
+       {{0x03b0c0d5,0x00b30a39,0x038a6ce4,0x01ded83a,0x01c277a6,0x01010a61,0x0346d3eb,0x018d995e,0x02f2c57c,0x000c286b},{0x0092aed1,0x0125e37b,0x027ca201,0x001a6b6b,0x03290f55,0x0047ba48,0x018d916c,0x01a59062,0x013e35d4,0x0002abb1},{0x003ad2aa,0x007ddcc0,0x00c10f76,0x0001590b,0x002cfca6,0x000ed23e,0x00ee4329,0x00900f04,0x01c24065,0x0082fa70}},
+       {{0x02025e60,0x003912b8,0x0327041c,0x017e5ee5,0x02c0ecec,0x015a0d1c,0x02b1ce7c,0x0062220b,0x0145067e,0x01a5d931},{0x009673a6,0x00e1f609,0x00927c2a,0x016faa37,0x01650ef0,0x016f63b5,0x03cd40e1,0x003bc38f,0x0361f0ac,0x01d42acc},{0x02f81037,0x008ca0e8,0x017e23d1,0x011debfe,0x01bcbb68,0x002e2563,0x03e8add6,0x000816e5,0x03fb7075,0x0153e5ac}},
+       {{0x02b11ecd,0x016bf185,0x008f22ef,0x00e7d2bb,0x0225d92e,0x00ece785,0x00508873,0x017e16f5,0x01fbe85d,0x01e39a0e},{0x01669279,0x017c810a,0x024941f5,0x0023ebeb,0x00eb7688,0x005760f1,0x02ca4146,0x0073cde7,0x0052bb75,0x00f5ffa7},{0x03b8856b,0x00cb7dcd,0x02f14e06,0x001820d0,0x01d74175,0x00e59e22,0x03fba550,0x00484641,0x03350088,0x01c3c9a3}},
+       {{0x00dcf355,0x0104481c,0x0022e464,0x01f73fe7,0x00e03325,0x0152b698,0x02ef769a,0x00973663,0x00039b8c,0x0101395b},{0x01805f47,0x019160ec,0x03832cd0,0x008b06eb,0x03d4d717,0x004cb006,0x03a75b8f,0x013b3d30,0x01cfad88,0x01f034d1},{0x0078338a,0x01c7d2e3,0x02bc2b23,0x018b3f05,0x0280d9aa,0x005f3d44,0x0220a95a,0x00eeeb97,0x0362aaec,0x00835d51}},
+       {{0x01b9f543,0x013fac4d,0x02ad93ae,0x018ef464,0x0212cdf7,0x01138ba9,0x011583ab,0x019c3d26,0x028790b4,0x00e2e2b6},{0x033bb758,0x01f0dbf1,0x03734bd1,0x0129b1e5,0x02b3950e,0x003bc922,0x01a53ec8,0x018c5532,0x006f3cee,0x00ae3c79},{0x0351f95d,0x0012a737,0x03d596b8,0x017658fe,0x00ace54a,0x008b66da,0x0036c599,0x012a63a2,0x032ceba1,0x00126bac}},
+       {{0x03dcfe7e,0x019f4f18,0x01c81aee,0x0044bc2b,0x00827165,0x014f7c13,0x03b430f0,0x00bf96cc,0x020c8d62,0x01471997},{0x01fc7931,0x001f42dd,0x00ba754a,0x005bd339,0x003fbe49,0x016b3930,0x012a159c,0x009f83b0,0x03530f67,0x01e57b85},{0x02ecbd81,0x0096c294,0x01fce4a9,0x017701a5,0x0175047d,0x00ee4a31,0x012686e5,0x008efcd4,0x0349dc54,0x01b3466f}},
+       {{0x02179ca3,0x01d86414,0x03f0afd0,0x00305964,0x015c7428,0x0099711e,0x015d5442,0x00c71014,0x01b40b2e,0x01d483cf},{0x01afc386,0x01984859,0x036203ff,0x0045c6a8,0x0020a8aa,0x00990baa,0x03313f10,0x007ceede,0x027429e4,0x017806ce},{0x039357a1,0x0142f8f4,0x0294a7b6,0x00eaccf4,0x0259edb3,0x01311e6e,0x004d326f,0x0130c346,0x01ccef3c,0x01c424b2}},
+       {{0x0364918c,0x00148fc0,0x01638a7b,0x01a1fd5b,0x028ad013,0x0081e5a4,0x01a54f33,0x0174e101,0x003d0257,0x003a856c},{0x00051dcf,0x00f62b1d,0x0143d0ad,0x0042adbd,0x000fda90,0x01743ceb,0x0173e5e4,0x017bc749,0x03b7137a,0x0105ce96},{0x00f9218a,0x015b8c7c,0x00e102f8,0x0158d7e2,0x0169a5b8,0x00b2f176,0x018b347a,0x014cfef2,0x0214a4e3,0x017f1595}},
+       {{0x006d7ae5,0x0195c371,0x0391e26d,0x0062a7c6,0x003f42ab,0x010dad86,0x024f8198,0x01542b2a,0x0014c454,0x0189c471},{0x0390988e,0x00b8799d,0x02e44912,0x0078e2e6,0x00075654,0x01923eed,0x0040cd72,0x00a37c76,0x0009d466,0x00c8531d},{0x02651770,0x00609d01,0x0286c265,0x0134513c,0x00ee9281,0x005d223c,0x035c760c,0x00679b36,0x0073ecb8,0x016faa50}},
+       {{0x02c89be4,0x016fc244,0x02f38c83,0x018beb72,0x02b3ce2c,0x0097b065,0x034f017b,0x01dd957f,0x00148f61,0x00eab357},{0x0343d2f8,0x003398fc,0x011e368e,0x00782a1f,0x00019eea,0x00117b6f,0x0128d0d1,0x01a5e6bb,0x01944f1b,0x012b41e1},{0x03318301,0x018ecd30,0x0104d0b1,0x0038398b,0x03726701,0x019da88c,0x002d9769,0x00a7a681,0x031d9028,0x00ebfc32}},
+       {{0x0220405e,0x0171face,0x02d930f8,0x017f6d6a,0x023b8c47,0x0129d5f9,0x02972456,0x00a3a524,0x006f4cd2,0x004439fa},{0x00c53505,0x0190c2fd,0x00507244,0x009930f9,0x01a39270,0x01d327c6,0x0399bc47,0x01cfe13d,0x0332bd99,0x00b33e7d},{0x0203f5e4,0x003627b5,0x00018af8,0x01478581,0x004a2218,0x002e3bb7,0x039384d0,0x0146ea62,0x020b9693,0x0017155f}},
+       {{0x03c97e6f,0x00738c47,0x03b5db1f,0x01808fcf,0x01e8fc98,0x01ed25dd,0x01bf5045,0x00eb5c2b,0x0178fe98,0x01b85530},{0x01c20eb0,0x01aeec22,0x030b9eee,0x01b7d07e,0x0187e16f,0x014421fb,0x009fa731,0x0040b6d7,0x00841861,0x00a27fbc},{0x02d69abf,0x0058cdbf,0x0129f9ec,0x013c19ae,0x026c5b93,0x013a7fe7,0x004bb2ba,0x0063226f,0x002a95ca,0x01abefd9}},
+       {{0x02f5d2c1,0x00378318,0x03734fb5,0x01258073,0x0263f0f6,0x01ad70e0,0x01b56d06,0x01188fbd,0x011b9503,0x0036d2e1},{0x0113a8cc,0x01541c3e,0x02ac2bbc,0x01d95867,0x01f47459,0x00ead489,0x00ab5b48,0x01db3b45,0x00edb801,0x004b024f},{0x00b8190f,0x011fe4c2,0x00621f82,0x010508d7,0x001a5a76,0x00c7d7fd,0x03aab96d,0x019cd9dc,0x019c6635,0x00ceaa1e}},
+       {{0x01085cf2,0x01fd47af,0x03e3f5e1,0x004b3e99,0x01e3d46a,0x0060033c,0x015ff0a8,0x0150cdd8,0x029e8e21,0x008cf1bc},{0x00156cb1,0x003d623f,0x01a4f069,0x00d8d053,0x01b68aea,0x01ca5ab6,0x0316ae43,0x0134dc44,0x001c8d58,0x0084b343},{0x0318c781,0x0135441f,0x03a51a5e,0x019293f4,0x0048bb37,0x013d3341,0x0143151e,0x019c74e1,0x00911914,0x0076ddde}},
+       {{0x006bc26f,0x00d48e5f,0x00227bbe,0x00629ea8,0x01ea5f8b,0x0179a330,0x027a1d5f,0x01bf8f8e,0x02d26e2a,0x00c6b65e},{0x01701ab6,0x0051da77,0x01b4b667,0x00a0ce7c,0x038ae37b,0x012ac852,0x03a0b0fe,0x0097c2bb,0x00a017d2,0x01eb8b2a},{0x0120b962,0x0005fb42,0x0353b6fd,0x0061f8ce,0x007a1463,0x01560a64,0x00e0a792,0x01907c92,0x013a6622,0x007b47f1}}
+};

diff --git a/crypto/ed25519-donna/src/ed25519-donna-64bit-sse2.h b/crypto/ed25519-donna/src/ed25519-donna-64bit-sse2.h
new file mode 100644 (file)
index 0000000..ca08651
--- /dev/null
+++ b/crypto/ed25519-donna/src/ed25519-donna-64bit-sse2.h
@@ -0,0 +1,436 @@
+#if defined(ED25519_GCC_64BIT_SSE_CHOOSE)
+
+#define HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS
+
+DONNA_NOINLINE static void
+ge25519_scalarmult_base_choose_niels(ge25519_niels *t, const uint8_t table[256][96], uint32_t pos, signed char b) {
+       int64_t breg = (int64_t)b;
+       uint64_t sign = (uint64_t)breg >> 63;
+       uint64_t mask = ~(sign - 1);
+       uint64_t u = (breg + mask) ^ mask;
+
+       __asm__ __volatile__ (
+               /* ysubx+xaddy+t2d */
+               "movq %0, %%rax                  ;\n"
+               "movd %%rax, %%xmm14             ;\n"
+               "pshufd $0x00, %%xmm14, %%xmm14  ;\n"
+               "pxor %%xmm0, %%xmm0             ;\n"
+               "pxor %%xmm1, %%xmm1             ;\n"
+               "pxor %%xmm2, %%xmm2             ;\n"
+               "pxor %%xmm3, %%xmm3             ;\n"
+               "pxor %%xmm4, %%xmm4             ;\n"
+               "pxor %%xmm5, %%xmm5             ;\n"
+
+               /* 0 */
+               "movq $0, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movq $1, %%rax                  ;\n"
+               "movd %%rax, %%xmm6              ;\n"
+               "pxor %%xmm7, %%xmm7             ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm6, %%xmm2              ;\n"
+               "por %%xmm7, %%xmm3              ;\n"
+
+               /* 1 */
+               "movq $1, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 0(%1), %%xmm6            ;\n"
+               "movdqa 16(%1), %%xmm7           ;\n"
+               "movdqa 32(%1), %%xmm8           ;\n"
+               "movdqa 48(%1), %%xmm9           ;\n"
+               "movdqa 64(%1), %%xmm10          ;\n"
+               "movdqa 80(%1), %%xmm11          ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* 2 */
+               "movq $2, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 96(%1), %%xmm6           ;\n"
+               "movdqa 112(%1), %%xmm7          ;\n"
+               "movdqa 128(%1), %%xmm8          ;\n"
+               "movdqa 144(%1), %%xmm9          ;\n"
+               "movdqa 160(%1), %%xmm10         ;\n"
+               "movdqa 176(%1), %%xmm11         ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* 3 */
+               "movq $3, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 192(%1), %%xmm6          ;\n"
+               "movdqa 208(%1), %%xmm7          ;\n"
+               "movdqa 224(%1), %%xmm8          ;\n"
+               "movdqa 240(%1), %%xmm9          ;\n"
+               "movdqa 256(%1), %%xmm10         ;\n"
+               "movdqa 272(%1), %%xmm11         ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* 4 */
+               "movq $4, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 288(%1), %%xmm6          ;\n"
+               "movdqa 304(%1), %%xmm7          ;\n"
+               "movdqa 320(%1), %%xmm8          ;\n"
+               "movdqa 336(%1), %%xmm9          ;\n"
+               "movdqa 352(%1), %%xmm10         ;\n"
+               "movdqa 368(%1), %%xmm11         ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* 5 */
+               "movq $5, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 384(%1), %%xmm6          ;\n"
+               "movdqa 400(%1), %%xmm7          ;\n"
+               "movdqa 416(%1), %%xmm8          ;\n"
+               "movdqa 432(%1), %%xmm9          ;\n"
+               "movdqa 448(%1), %%xmm10         ;\n"
+               "movdqa 464(%1), %%xmm11         ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* 6 */
+               "movq $6, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 480(%1), %%xmm6          ;\n"
+               "movdqa 496(%1), %%xmm7          ;\n"
+               "movdqa 512(%1), %%xmm8          ;\n"
+               "movdqa 528(%1), %%xmm9          ;\n"
+               "movdqa 544(%1), %%xmm10         ;\n"
+               "movdqa 560(%1), %%xmm11         ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* 7 */
+               "movq $7, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 576(%1), %%xmm6          ;\n"
+               "movdqa 592(%1), %%xmm7          ;\n"
+               "movdqa 608(%1), %%xmm8          ;\n"
+               "movdqa 624(%1), %%xmm9          ;\n"
+               "movdqa 640(%1), %%xmm10         ;\n"
+               "movdqa 656(%1), %%xmm11         ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* 8 */
+               "movq $8, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 672(%1), %%xmm6          ;\n"
+               "movdqa 688(%1), %%xmm7          ;\n"
+               "movdqa 704(%1), %%xmm8          ;\n"
+               "movdqa 720(%1), %%xmm9          ;\n"
+               "movdqa 736(%1), %%xmm10         ;\n"
+               "movdqa 752(%1), %%xmm11         ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* conditionally swap ysubx and xaddy */
+               "movq %3, %%rax                  ;\n"
+               "xorq $1, %%rax                  ;\n"
+               "movd %%rax, %%xmm14             ;\n"
+               "pxor %%xmm15, %%xmm15           ;\n"
+               "pshufd $0x00, %%xmm14, %%xmm14  ;\n"
+               "pxor %%xmm0, %%xmm2             ;\n"
+               "pxor %%xmm1, %%xmm3             ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa %%xmm2, %%xmm6           ;\n"
+               "movdqa %%xmm3, %%xmm7           ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pxor %%xmm6, %%xmm0             ;\n"
+               "pxor %%xmm7, %%xmm1             ;\n"
+               "pxor %%xmm0, %%xmm2             ;\n"
+               "pxor %%xmm1, %%xmm3             ;\n"
+
+               /* store ysubx */
+               "xorq %%rax, %%rax               ;\n"
+               "movd %%xmm0, %%rcx              ;\n"
+               "movd %%xmm0, %%r8               ;\n"
+               "movd %%xmm1, %%rsi              ;\n"
+               "pshufd $0xee, %%xmm0, %%xmm0    ;\n"
+               "pshufd $0xee, %%xmm1, %%xmm1    ;\n"
+               "movd %%xmm0, %%rdx              ;\n"
+               "movd %%xmm1, %%rdi              ;\n"
+               "shrdq $51, %%rdx, %%r8          ;\n"
+               "shrdq $38, %%rsi, %%rdx         ;\n"
+               "shrdq $25, %%rdi, %%rsi         ;\n"
+               "shrq $12, %%rdi                 ;\n"
+               "movq %%rcx, %%r9                ;\n"
+               "movq %%r8, %%r10                ;\n"
+               "movq %%rdx, %%r11               ;\n"
+               "movq %%rsi, %%r12               ;\n"
+               "movq %%rdi, %%r13               ;\n"
+               "shrq $26, %%r9                  ;\n"
+               "shrq $26, %%r10                 ;\n"
+               "shrq $26, %%r11                 ;\n"
+               "shrq $26, %%r12                 ;\n"
+               "shrq $26, %%r13                 ;\n"
+               "andl $0x3ffffff, %%ecx          ;\n"
+               "andl $0x1ffffff, %%r9d          ;\n"
+               "andl $0x3ffffff, %%r8d          ;\n"
+               "andl $0x1ffffff, %%r10d         ;\n"
+               "andl $0x3ffffff, %%edx          ;\n"
+               "andl $0x1ffffff, %%r11d         ;\n"
+               "andl $0x3ffffff, %%esi          ;\n"
+               "andl $0x1ffffff, %%r12d         ;\n"
+               "andl $0x3ffffff, %%edi          ;\n"
+               "andl $0x1ffffff, %%r13d         ;\n"
+               "movl %%ecx, 0(%2)               ;\n"
+               "movl %%r9d, 4(%2)               ;\n"
+               "movl %%r8d, 8(%2)               ;\n"
+               "movl %%r10d, 12(%2)             ;\n"
+               "movl %%edx, 16(%2)              ;\n"
+               "movl %%r11d, 20(%2)             ;\n"
+               "movl %%esi, 24(%2)              ;\n"
+               "movl %%r12d, 28(%2)             ;\n"
+               "movl %%edi, 32(%2)              ;\n"
+               "movl %%r13d, 36(%2)             ;\n"
+               "movq %%rax, 40(%2)              ;\n"
+
+               /* store xaddy */
+               "movd %%xmm2, %%rcx              ;\n"
+               "movd %%xmm2, %%r8               ;\n"
+               "movd %%xmm3, %%rsi              ;\n"
+               "pshufd $0xee, %%xmm2, %%xmm2    ;\n"
+               "pshufd $0xee, %%xmm3, %%xmm3    ;\n"
+               "movd %%xmm2, %%rdx              ;\n"
+               "movd %%xmm3, %%rdi              ;\n"
+               "shrdq $51, %%rdx, %%r8          ;\n"
+               "shrdq $38, %%rsi, %%rdx         ;\n"
+               "shrdq $25, %%rdi, %%rsi         ;\n"
+               "shrq $12, %%rdi                 ;\n"
+               "movq %%rcx, %%r9                ;\n"
+               "movq %%r8, %%r10                ;\n"
+               "movq %%rdx, %%r11               ;\n"
+               "movq %%rsi, %%r12               ;\n"
+               "movq %%rdi, %%r13               ;\n"
+               "shrq $26, %%r9                  ;\n"
+               "shrq $26, %%r10                 ;\n"
+               "shrq $26, %%r11                 ;\n"
+               "shrq $26, %%r12                 ;\n"
+               "shrq $26, %%r13                 ;\n"
+               "andl $0x3ffffff, %%ecx          ;\n"
+               "andl $0x1ffffff, %%r9d          ;\n"
+               "andl $0x3ffffff, %%r8d          ;\n"
+               "andl $0x1ffffff, %%r10d         ;\n"
+               "andl $0x3ffffff, %%edx          ;\n"
+               "andl $0x1ffffff, %%r11d         ;\n"
+               "andl $0x3ffffff, %%esi          ;\n"
+               "andl $0x1ffffff, %%r12d         ;\n"
+               "andl $0x3ffffff, %%edi          ;\n"
+               "andl $0x1ffffff, %%r13d         ;\n"
+               "movl %%ecx, 48(%2)              ;\n"
+               "movl %%r9d, 52(%2)              ;\n"
+               "movl %%r8d, 56(%2)              ;\n"
+               "movl %%r10d, 60(%2)             ;\n"
+               "movl %%edx, 64(%2)              ;\n"
+               "movl %%r11d, 68(%2)             ;\n"
+               "movl %%esi, 72(%2)              ;\n"
+               "movl %%r12d, 76(%2)             ;\n"
+               "movl %%edi, 80(%2)              ;\n"
+               "movl %%r13d, 84(%2)             ;\n"
+               "movq %%rax, 88(%2)              ;\n"
+
+               /* extract t2d */
+               "xorq %%rax, %%rax               ;\n"
+               "movd %%xmm4, %%rcx              ;\n"
+               "movd %%xmm4, %%r8               ;\n"
+               "movd %%xmm5, %%rsi              ;\n"
+               "pshufd $0xee, %%xmm4, %%xmm4    ;\n"
+               "pshufd $0xee, %%xmm5, %%xmm5    ;\n"
+               "movd %%xmm4, %%rdx              ;\n"
+               "movd %%xmm5, %%rdi              ;\n"
+               "shrdq $51, %%rdx, %%r8          ;\n"
+               "shrdq $38, %%rsi, %%rdx         ;\n"
+               "shrdq $25, %%rdi, %%rsi         ;\n"
+               "shrq $12, %%rdi                 ;\n"
+               "movq %%rcx, %%r9                ;\n"
+               "movq %%r8, %%r10                ;\n"
+               "movq %%rdx, %%r11               ;\n"
+               "movq %%rsi, %%r12               ;\n"
+               "movq %%rdi, %%r13               ;\n"
+               "shrq $26, %%r9                  ;\n"
+               "shrq $26, %%r10                 ;\n"
+               "shrq $26, %%r11                 ;\n"
+               "shrq $26, %%r12                 ;\n"
+               "shrq $26, %%r13                 ;\n"
+               "andl $0x3ffffff, %%ecx          ;\n"
+               "andl $0x1ffffff, %%r9d          ;\n"
+               "andl $0x3ffffff, %%r8d          ;\n"
+               "andl $0x1ffffff, %%r10d         ;\n"
+               "andl $0x3ffffff, %%edx          ;\n"
+               "andl $0x1ffffff, %%r11d         ;\n"
+               "andl $0x3ffffff, %%esi          ;\n"
+               "andl $0x1ffffff, %%r12d         ;\n"
+               "andl $0x3ffffff, %%edi          ;\n"
+               "andl $0x1ffffff, %%r13d         ;\n"
+               "movd %%ecx, %%xmm0              ;\n"
+               "movd %%r9d, %%xmm4              ;\n"
+               "movd %%r8d, %%xmm8              ;\n"
+               "movd %%r10d, %%xmm3             ;\n"
+               "movd %%edx, %%xmm1              ;\n"
+               "movd %%r11d, %%xmm5             ;\n"
+               "movd %%esi, %%xmm6              ;\n"
+               "movd %%r12d, %%xmm7             ;\n"
+               "movd %%edi, %%xmm2              ;\n"
+               "movd %%r13d, %%xmm9             ;\n"
+               "punpckldq %%xmm4, %%xmm0        ;\n"
+               "punpckldq %%xmm3, %%xmm8        ;\n"
+               "punpckldq %%xmm5, %%xmm1        ;\n"
+               "punpckldq %%xmm7, %%xmm6        ;\n"
+               "punpckldq %%xmm9, %%xmm2        ;\n"
+               "punpcklqdq %%xmm8, %%xmm0       ;\n"
+               "punpcklqdq %%xmm6, %%xmm1       ;\n"
+
+               /* set up 2p in to 3/4 */
+               "movl $0x7ffffda, %%ecx          ;\n"
+               "movl $0x3fffffe, %%edx          ;\n"
+               "movl $0x7fffffe, %%eax          ;\n"
+               "movd %%ecx, %%xmm3              ;\n"
+               "movd %%edx, %%xmm5              ;\n"
+               "movd %%eax, %%xmm4              ;\n"
+               "punpckldq %%xmm5, %%xmm3        ;\n"
+               "punpckldq %%xmm5, %%xmm4        ;\n"
+               "punpcklqdq %%xmm4, %%xmm3       ;\n"
+               "movdqa %%xmm4, %%xmm5           ;\n"
+               "punpcklqdq %%xmm4, %%xmm4       ;\n"
+
+               /* subtract and conditionally move */
+               "movl %3, %%ecx                  ;\n"
+               "sub $1, %%ecx                   ;\n"
+               "movd %%ecx, %%xmm6              ;\n"
+               "pshufd $0x00, %%xmm6, %%xmm6    ;\n"
+               "movdqa %%xmm6, %%xmm7           ;\n"
+               "psubd %%xmm0, %%xmm3            ;\n"
+               "psubd %%xmm1, %%xmm4            ;\n"
+               "psubd %%xmm2, %%xmm5            ;\n"
+               "pand %%xmm6, %%xmm0             ;\n"
+               "pand %%xmm6, %%xmm1             ;\n"
+               "pand %%xmm6, %%xmm2             ;\n"
+               "pandn %%xmm3, %%xmm6            ;\n"
+               "movdqa %%xmm7, %%xmm3           ;\n"
+               "pandn %%xmm4, %%xmm7            ;\n"
+               "pandn %%xmm5, %%xmm3            ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm3, %%xmm2              ;\n"
+
+               /* store t2d */
+               "movdqa %%xmm0, 96(%2)           ;\n"
+               "movdqa %%xmm1, 112(%2)          ;\n"
+               "movdqa %%xmm2, 128(%2)          ;\n"
+               :
+               : "m"(u), "r"(&table[pos * 8]), "r"(t), "m"(sign) /* %0 = u, %1 = table, %2 = t, %3 = sign */
+               :
+                       "%rax", "%rcx", "%rdx", "%rdi", "%rsi", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", 
+                       "%xmm0", "%xmm1", "%xmm2", "%xmm3", "%xmm4", "%xmm5", "%xmm6", "%xmm7", "%xmm8", "%xmm9", "%xmm10", "%xmm11", "%xmm14", "%xmm14",
+                       "cc", "memory"
+       );
+}
+
+#endif /* defined(ED25519_GCC_64BIT_SSE_CHOOSE) */
+

diff --git a/crypto/ed25519-donna/src/ed25519-donna-64bit-tables.h b/crypto/ed25519-donna/src/ed25519-donna-64bit-tables.h
new file mode 100644 (file)
index 0000000..4a6ff9e
--- /dev/null
+++ b/crypto/ed25519-donna/src/ed25519-donna-64bit-tables.h
@@ -0,0 +1,53 @@
+static const ge25519 ge25519_basepoint = {
+       {0x00062d608f25d51a,0x000412a4b4f6592a,0x00075b7171a4b31d,0x0001ff60527118fe,0x000216936d3cd6e5},
+       {0x0006666666666658,0x0004cccccccccccc,0x0001999999999999,0x0003333333333333,0x0006666666666666},
+       {0x0000000000000001,0x0000000000000000,0x0000000000000000,0x0000000000000000,0x0000000000000000},
+       {0x00068ab3a5b7dda3,0x00000eea2a5eadbb,0x0002af8df483c27e,0x000332b375274732,0x00067875f0fd78b7}
+};
+
+static const bignum25519 ge25519_ecd = {
+       0x00034dca135978a3,0x0001a8283b156ebd,0x0005e7a26001c029,0x000739c663a03cbb,0x00052036cee2b6ff
+};
+
+static const bignum25519 ge25519_ec2d = {
+       0x00069b9426b2f159,0x00035050762add7a,0x0003cf44c0038052,0x0006738cc7407977,0x0002406d9dc56dff
+};
+
+static const bignum25519 ge25519_sqrtneg1 = {
+       0x00061b274a0ea0b0,0x0000d5a5fc8f189d,0x0007ef5e9cbd0c60,0x00078595a6804c9e,0x0002b8324804fc1d
+};
+
+static const ge25519_niels ge25519_niels_sliding_multiples[32] = {
+       {{0x00003905d740913e,0x0000ba2817d673a2,0x00023e2827f4e67c,0x000133d2e0c21a34,0x00044fd2f9298f81},{0x000493c6f58c3b85,0x0000df7181c325f7,0x0000f50b0b3e4cb7,0x0005329385a44c32,0x00007cf9d3a33d4b},{0x00011205877aaa68,0x000479955893d579,0x00050d66309b67a0,0x0002d42d0dbee5ee,0x0006f117b689f0c6}},
+       {{0x00011fe8a4fcd265,0x0007bcb8374faacc,0x00052f5af4ef4d4f,0x0005314098f98d10,0x0002ab91587555bd},{0x0005b0a84cee9730,0x00061d10c97155e4,0x0004059cc8096a10,0x00047a608da8014f,0x0007a164e1b9a80f},{0x0006933f0dd0d889,0x00044386bb4c4295,0x0003cb6d3162508c,0x00026368b872a2c6,0x0005a2826af12b9b}},
+       {{0x000182c3a447d6ba,0x00022964e536eff2,0x000192821f540053,0x0002f9f19e788e5c,0x000154a7e73eb1b5},{0x0002bc4408a5bb33,0x000078ebdda05442,0x0002ffb112354123,0x000375ee8df5862d,0x0002945ccf146e20},{0x0003dbf1812a8285,0x0000fa17ba3f9797,0x0006f69cb49c3820,0x00034d5a0db3858d,0x00043aabe696b3bb}},
+       {{0x00072c9aaa3221b1,0x000267774474f74d,0x000064b0e9b28085,0x0003f04ef53b27c9,0x0001d6edd5d2e531},{0x00025cd0944ea3bf,0x00075673b81a4d63,0x000150b925d1c0d4,0x00013f38d9294114,0x000461bea69283c9},{0x00036dc801b8b3a2,0x0000e0a7d4935e30,0x0001deb7cecc0d7d,0x000053a94e20dd2c,0x0007a9fbb1c6a0f9}},
+       {{0x0006217e039d8064,0x0006dea408337e6d,0x00057ac112628206,0x000647cb65e30473,0x00049c05a51fadc9},{0x0006678aa6a8632f,0x0005ea3788d8b365,0x00021bd6d6994279,0x0007ace75919e4e3,0x00034b9ed338add7},{0x0004e8bf9045af1b,0x000514e33a45e0d6,0x0007533c5b8bfe0f,0x000583557b7e14c9,0x00073c172021b008}},
+       {{0x00075b0249864348,0x00052ee11070262b,0x000237ae54fb5acd,0x0003bfd1d03aaab5,0x00018ab598029d5c},{0x000700848a802ade,0x0001e04605c4e5f7,0x0005c0d01b9767fb,0x0007d7889f42388b,0x0004275aae2546d8},{0x00032cc5fd6089e9,0x000426505c949b05,0x00046a18880c7ad2,0x0004a4221888ccda,0x0003dc65522b53df}},
+       {{0x0007013b327fbf93,0x0001336eeded6a0d,0x0002b565a2bbf3af,0x000253ce89591955,0x0000267882d17602},{0x0000c222a2007f6d,0x000356b79bdb77ee,0x00041ee81efe12ce,0x000120a9bd07097d,0x000234fd7eec346f},{0x0000a119732ea378,0x00063bf1ba8e2a6c,0x00069f94cc90df9a,0x000431d1779bfc48,0x000497ba6fdaa097}},
+       {{0x0003cd86468ccf0b,0x00048553221ac081,0x0006c9464b4e0a6e,0x00075fba84180403,0x00043b5cd4218d05},{0x0006cc0313cfeaa0,0x0001a313848da499,0x0007cb534219230a,0x00039596dedefd60,0x00061e22917f12de},{0x0002762f9bd0b516,0x0001c6e7fbddcbb3,0x00075909c3ace2bd,0x00042101972d3ec9,0x000511d61210ae4d}},
+       {{0x000386484420de87,0x0002d6b25db68102,0x000650b4962873c0,0x0004081cfd271394,0x00071a7fe6fe2482},{0x000676ef950e9d81,0x0001b81ae089f258,0x00063c4922951883,0x0002f1d54d9b3237,0x0006d325924ddb85},{0x000182b8a5c8c854,0x00073fcbe5406d8e,0x0005de3430cff451,0x000554b967ac8c41,0x0004746c4b6559ee}},
+       {{0x000546c864741147,0x0003a1df99092690,0x0001ca8cc9f4d6bb,0x00036b7fc9cd3b03,0x000219663497db5e},{0x00077b3c6dc69a2b,0x0004edf13ec2fa6e,0x0004e85ad77beac8,0x0007dba2b28e7bda,0x0005c9a51de34fe9},{0x0000f1cf79f10e67,0x00043ccb0a2b7ea2,0x00005089dfff776a,0x0001dd84e1d38b88,0x0004804503c60822}},
+       {{0x000021d23a36d175,0x0004fd3373c6476d,0x00020e291eeed02a,0x00062f2ecf2e7210,0x000771e098858de4},{0x00049ed02ca37fc7,0x000474c2b5957884,0x0005b8388e816683,0x0004b6c454b76be4,0x000553398a516506},{0x0002f5d278451edf,0x000730b133997342,0x0006965420eb6975,0x000308a3bfa516cf,0x0005a5ed1d68ff5a}},
+       {{0x0005e0c558527359,0x0003395b73afd75c,0x000072afa4e4b970,0x00062214329e0f6d,0x000019b60135fefd},{0x0005122afe150e83,0x0004afc966bb0232,0x0001c478833c8268,0x00017839c3fc148f,0x00044acb897d8bf9},{0x000068145e134b83,0x0001e4860982c3cc,0x000068fb5f13d799,0x0007c9283744547e,0x000150c49fde6ad2}},
+       {{0x0001863c9cdca868,0x0003770e295a1709,0x0000d85a3720fd13,0x0005e0ff1f71ab06,0x00078a6d7791e05f},{0x0003f29509471138,0x000729eeb4ca31cf,0x00069c22b575bfbc,0x0004910857bce212,0x0006b2b5a075bb99},{0x0007704b47a0b976,0x0002ae82e91aab17,0x00050bd6429806cd,0x00068055158fd8ea,0x000725c7ffc4ad55}},
+       {{0x00002bf71cd098c0,0x00049dabcc6cd230,0x00040a6533f905b2,0x000573efac2eb8a4,0x0004cd54625f855f},{0x00026715d1cf99b2,0x0002205441a69c88,0x000448427dcd4b54,0x0001d191e88abdc5,0x000794cc9277cb1f},{0x0006c426c2ac5053,0x0005a65ece4b095e,0x0000c44086f26bb6,0x0007429568197885,0x0007008357b6fcc8}},
+       {{0x00039fbb82584a34,0x00047a568f257a03,0x00014d88091ead91,0x0002145b18b1ce24,0x00013a92a3669d6d},{0x0000672738773f01,0x000752bf799f6171,0x0006b4a6dae33323,0x0007b54696ead1dc,0x00006ef7e9851ad0},{0x0003771cc0577de5,0x0003ca06bb8b9952,0x00000b81c5d50390,0x00043512340780ec,0x0003c296ddf8a2af}},
+       {{0x00034d2ebb1f2541,0x0000e815b723ff9d,0x000286b416e25443,0x0000bdfe38d1bee8,0x0000a892c7007477},{0x000515f9d914a713,0x00073191ff2255d5,0x00054f5cc2a4bdef,0x0003dd57fc118bcf,0x0007a99d393490c7},{0x0002ed2436bda3e8,0x00002afd00f291ea,0x0000be7381dea321,0x0003e952d4b2b193,0x000286762d28302f}},
+       {{0x00058e2bce2ef5bd,0x00068ce8f78c6f8a,0x0006ee26e39261b2,0x00033d0aa50bcf9d,0x0007686f2a3d6f17},{0x000036093ce35b25,0x0003b64d7552e9cf,0x00071ee0fe0b8460,0x00069d0660c969e5,0x00032f1da046a9d9},{0x000512a66d597c6a,0x0000609a70a57551,0x000026c08a3c464c,0x0004531fc8ee39e1,0x000561305f8a9ad2}},
+       {{0x0002cc28e7b0c0d5,0x00077b60eb8a6ce4,0x0004042985c277a6,0x000636657b46d3eb,0x000030a1aef2c57c},{0x0004978dec92aed1,0x000069adae7ca201,0x00011ee923290f55,0x00069641898d916c,0x00000aaec53e35d4},{0x0001f773003ad2aa,0x000005642cc10f76,0x00003b48f82cfca6,0x0002403c10ee4329,0x00020be9c1c24065}},
+       {{0x0000e44ae2025e60,0x0005f97b9727041c,0x0005683472c0ecec,0x000188882eb1ce7c,0x00069764c545067e},{0x000387d8249673a6,0x0005bea8dc927c2a,0x0005bd8ed5650ef0,0x0000ef0e3fcd40e1,0x000750ab3361f0ac},{0x00023283a2f81037,0x000477aff97e23d1,0x0000b8958dbcbb68,0x0000205b97e8add6,0x00054f96b3fb7075}},
+       {{0x0005afc616b11ecd,0x00039f4aec8f22ef,0x0003b39e1625d92e,0x0005f85bd4508873,0x00078e6839fbe85d},{0x0005f20429669279,0x00008fafae4941f5,0x00015d83c4eb7688,0x0001cf379eca4146,0x0003d7fe9c52bb75},{0x00032df737b8856b,0x0000608342f14e06,0x0003967889d74175,0x0001211907fba550,0x00070f268f350088}},
+       {{0x0004112070dcf355,0x0007dcff9c22e464,0x00054ada60e03325,0x00025cd98eef769a,0x000404e56c039b8c},{0x00064583b1805f47,0x00022c1baf832cd0,0x000132c01bd4d717,0x0004ecf4c3a75b8f,0x0007c0d345cfad88},{0x00071f4b8c78338a,0x00062cfc16bc2b23,0x00017cf51280d9aa,0x0003bbae5e20a95a,0x00020d754762aaec}},
+       {{0x0004feb135b9f543,0x00063bd192ad93ae,0x00044e2ea612cdf7,0x000670f4991583ab,0x00038b8ada8790b4},{0x0007c36fc73bb758,0x0004a6c797734bd1,0x0000ef248ab3950e,0x00063154c9a53ec8,0x0002b8f1e46f3cee},{0x00004a9cdf51f95d,0x0005d963fbd596b8,0x00022d9b68ace54a,0x0004a98e8836c599,0x000049aeb32ceba1}},
+       {{0x00067d3c63dcfe7e,0x000112f0adc81aee,0x00053df04c827165,0x0002fe5b33b430f0,0x00051c665e0c8d62},{0x00007d0b75fc7931,0x00016f4ce4ba754a,0x0005ace4c03fbe49,0x00027e0ec12a159c,0x000795ee17530f67},{0x00025b0a52ecbd81,0x0005dc0695fce4a9,0x0003b928c575047d,0x00023bf3512686e5,0x0006cd19bf49dc54}},
+       {{0x0007619052179ca3,0x0000c16593f0afd0,0x000265c4795c7428,0x00031c40515d5442,0x0007520f3db40b2e},{0x0006612165afc386,0x0001171aa36203ff,0x0002642ea820a8aa,0x0001f3bb7b313f10,0x0005e01b3a7429e4},{0x00050be3d39357a1,0x0003ab33d294a7b6,0x0004c479ba59edb3,0x0004c30d184d326f,0x00071092c9ccef3c}},
+       {{0x0000523f0364918c,0x000687f56d638a7b,0x00020796928ad013,0x0005d38405a54f33,0x0000ea15b03d0257},{0x0003d8ac74051dcf,0x00010ab6f543d0ad,0x0005d0f3ac0fda90,0x0005ef1d2573e5e4,0x0004173a5bb7137a},{0x00056e31f0f9218a,0x0005635f88e102f8,0x0002cbc5d969a5b8,0x000533fbc98b347a,0x0005fc565614a4e3}},
+       {{0x0006570dc46d7ae5,0x00018a9f1b91e26d,0x000436b6183f42ab,0x000550acaa4f8198,0x00062711c414c454},{0x0002e1e67790988e,0x0001e38b9ae44912,0x000648fbb4075654,0x00028df1d840cd72,0x0003214c7409d466},{0x0001827406651770,0x0004d144f286c265,0x00017488f0ee9281,0x00019e6cdb5c760c,0x0005bea94073ecb8}},
+       {{0x0005bf0912c89be4,0x00062fadcaf38c83,0x00025ec196b3ce2c,0x00077655ff4f017b,0x0003aacd5c148f61},{0x0000ce63f343d2f8,0x0001e0a87d1e368e,0x000045edbc019eea,0x0006979aed28d0d1,0x0004ad0785944f1b},{0x00063b34c3318301,0x0000e0e62d04d0b1,0x000676a233726701,0x00029e9a042d9769,0x0003aff0cb1d9028}},
+       {{0x0005c7eb3a20405e,0x0005fdb5aad930f8,0x0004a757e63b8c47,0x00028e9492972456,0x000110e7e86f4cd2},{0x0006430bf4c53505,0x000264c3e4507244,0x00074c9f19a39270,0x00073f84f799bc47,0x0002ccf9f732bd99},{0x0000d89ed603f5e4,0x00051e1604018af8,0x0000b8eedc4a2218,0x00051ba98b9384d0,0x00005c557e0b9693}},
+       {{0x0001ce311fc97e6f,0x0006023f3fb5db1f,0x0007b49775e8fc98,0x0003ad70adbf5045,0x0006e154c178fe98},{0x0006bbb089c20eb0,0x0006df41fb0b9eee,0x00051087ed87e16f,0x000102db5c9fa731,0x000289fef0841861},{0x00016336fed69abf,0x0004f066b929f9ec,0x0004e9ff9e6c5b93,0x00018c89bc4bb2ba,0x0006afbf642a95ca}},
+       {{0x0000de0c62f5d2c1,0x00049601cf734fb5,0x0006b5c38263f0f6,0x0004623ef5b56d06,0x0000db4b851b9503},{0x00055070f913a8cc,0x000765619eac2bbc,0x0003ab5225f47459,0x00076ced14ab5b48,0x00012c093cedb801},{0x00047f9308b8190f,0x000414235c621f82,0x00031f5ff41a5a76,0x0006736773aab96d,0x00033aa8799c6635}},
+       {{0x0007f51ebd085cf2,0x00012cfa67e3f5e1,0x0001800cf1e3d46a,0x00054337615ff0a8,0x000233c6f29e8e21},{0x0000f588fc156cb1,0x000363414da4f069,0x0007296ad9b68aea,0x0004d3711316ae43,0x000212cd0c1c8d58},{0x0004d5107f18c781,0x00064a4fd3a51a5e,0x0004f4cd0448bb37,0x000671d38543151e,0x0001db7778911914}},
+       {{0x000352397c6bc26f,0x00018a7aa0227bbe,0x0005e68cc1ea5f8b,0x0006fe3e3a7a1d5f,0x00031ad97ad26e2a},{0x00014769dd701ab6,0x00028339f1b4b667,0x0004ab214b8ae37b,0x00025f0aefa0b0fe,0x0007ae2ca8a017d2},{0x000017ed0920b962,0x000187e33b53b6fd,0x00055829907a1463,0x000641f248e0a792,0x0001ed1fc53a6622}}
+};

diff --git a/crypto/ed25519-donna/src/ed25519-donna-64bit-x86-32bit.h b/crypto/ed25519-donna/src/ed25519-donna-64bit-x86-32bit.h
new file mode 100644 (file)
index 0000000..1ce109c
--- /dev/null
+++ b/crypto/ed25519-donna/src/ed25519-donna-64bit-x86-32bit.h
@@ -0,0 +1,435 @@
+#if defined(ED25519_GCC_64BIT_32BIT_CHOOSE)
+
+#define HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS
+
+DONNA_NOINLINE static void
+ge25519_scalarmult_base_choose_niels(ge25519_niels *t, const uint8_t table[256][96], uint32_t pos, signed char b) {
+       int64_t breg = (int64_t)b;
+       uint64_t sign = (uint64_t)breg >> 63;
+       uint64_t mask = ~(sign - 1);
+       uint64_t u = (breg + mask) ^ mask;
+
+       __asm__ __volatile__ (
+               /* ysubx+xaddy+t2d */
+               "movq %0, %%rax                  ;\n"
+               "movd %%rax, %%xmm14             ;\n"
+               "pshufd $0x00, %%xmm14, %%xmm14  ;\n"
+               "pxor %%xmm0, %%xmm0             ;\n"
+               "pxor %%xmm1, %%xmm1             ;\n"
+               "pxor %%xmm2, %%xmm2             ;\n"
+               "pxor %%xmm3, %%xmm3             ;\n"
+               "pxor %%xmm4, %%xmm4             ;\n"
+               "pxor %%xmm5, %%xmm5             ;\n"
+
+               /* 0 */
+               "movq $0, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movq $1, %%rax                  ;\n"
+               "movd %%rax, %%xmm6              ;\n"
+               "pxor %%xmm7, %%xmm7             ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm6, %%xmm2              ;\n"
+               "por %%xmm7, %%xmm3              ;\n"
+
+               /* 1 */
+               "movq $1, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 0(%1), %%xmm6            ;\n"
+               "movdqa 16(%1), %%xmm7           ;\n"
+               "movdqa 32(%1), %%xmm8           ;\n"
+               "movdqa 48(%1), %%xmm9           ;\n"
+               "movdqa 64(%1), %%xmm10          ;\n"
+               "movdqa 80(%1), %%xmm11          ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* 2 */
+               "movq $2, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 96(%1), %%xmm6           ;\n"
+               "movdqa 112(%1), %%xmm7          ;\n"
+               "movdqa 128(%1), %%xmm8          ;\n"
+               "movdqa 144(%1), %%xmm9          ;\n"
+               "movdqa 160(%1), %%xmm10         ;\n"
+               "movdqa 176(%1), %%xmm11         ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* 3 */
+               "movq $3, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 192(%1), %%xmm6          ;\n"
+               "movdqa 208(%1), %%xmm7          ;\n"
+               "movdqa 224(%1), %%xmm8          ;\n"
+               "movdqa 240(%1), %%xmm9          ;\n"
+               "movdqa 256(%1), %%xmm10         ;\n"
+               "movdqa 272(%1), %%xmm11         ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* 4 */
+               "movq $4, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 288(%1), %%xmm6          ;\n"
+               "movdqa 304(%1), %%xmm7          ;\n"
+               "movdqa 320(%1), %%xmm8          ;\n"
+               "movdqa 336(%1), %%xmm9          ;\n"
+               "movdqa 352(%1), %%xmm10         ;\n"
+               "movdqa 368(%1), %%xmm11         ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* 5 */
+               "movq $5, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 384(%1), %%xmm6          ;\n"
+               "movdqa 400(%1), %%xmm7          ;\n"
+               "movdqa 416(%1), %%xmm8          ;\n"
+               "movdqa 432(%1), %%xmm9          ;\n"
+               "movdqa 448(%1), %%xmm10         ;\n"
+               "movdqa 464(%1), %%xmm11         ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* 6 */
+               "movq $6, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 480(%1), %%xmm6          ;\n"
+               "movdqa 496(%1), %%xmm7          ;\n"
+               "movdqa 512(%1), %%xmm8          ;\n"
+               "movdqa 528(%1), %%xmm9          ;\n"
+               "movdqa 544(%1), %%xmm10         ;\n"
+               "movdqa 560(%1), %%xmm11         ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* 7 */
+               "movq $7, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 576(%1), %%xmm6          ;\n"
+               "movdqa 592(%1), %%xmm7          ;\n"
+               "movdqa 608(%1), %%xmm8          ;\n"
+               "movdqa 624(%1), %%xmm9          ;\n"
+               "movdqa 640(%1), %%xmm10         ;\n"
+               "movdqa 656(%1), %%xmm11         ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* 8 */
+               "movq $8, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 672(%1), %%xmm6          ;\n"
+               "movdqa 688(%1), %%xmm7          ;\n"
+               "movdqa 704(%1), %%xmm8          ;\n"
+               "movdqa 720(%1), %%xmm9          ;\n"
+               "movdqa 736(%1), %%xmm10         ;\n"
+               "movdqa 752(%1), %%xmm11         ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* conditionally swap ysubx and xaddy */
+               "movq %3, %%rax                  ;\n"
+               "xorq $1, %%rax                  ;\n"
+               "movd %%rax, %%xmm14             ;\n"
+               "pxor %%xmm15, %%xmm15           ;\n"
+               "pshufd $0x00, %%xmm14, %%xmm14  ;\n"
+               "pxor %%xmm0, %%xmm2             ;\n"
+               "pxor %%xmm1, %%xmm3             ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa %%xmm2, %%xmm6           ;\n"
+               "movdqa %%xmm3, %%xmm7           ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pxor %%xmm6, %%xmm0             ;\n"
+               "pxor %%xmm7, %%xmm1             ;\n"
+               "pxor %%xmm0, %%xmm2             ;\n"
+               "pxor %%xmm1, %%xmm3             ;\n"
+
+               /* store ysubx */
+               "xorq %%rax, %%rax               ;\n"
+               "movd %%xmm0, %%rcx              ;\n"
+               "movd %%xmm0, %%r8               ;\n"
+               "movd %%xmm1, %%rsi              ;\n"
+               "pshufd $0xee, %%xmm0, %%xmm0    ;\n"
+               "pshufd $0xee, %%xmm1, %%xmm1    ;\n"
+               "movd %%xmm0, %%rdx              ;\n"
+               "movd %%xmm1, %%rdi              ;\n"
+               "shrdq $51, %%rdx, %%r8          ;\n"
+               "shrdq $38, %%rsi, %%rdx         ;\n"
+               "shrdq $25, %%rdi, %%rsi         ;\n"
+               "shrq $12, %%rdi                 ;\n"
+               "movq %%rcx, %%r9                ;\n"
+               "movq %%r8, %%r10                ;\n"
+               "movq %%rdx, %%r11               ;\n"
+               "movq %%rsi, %%r12               ;\n"
+               "movq %%rdi, %%r13               ;\n"
+               "shrq $26, %%r9                  ;\n"
+               "shrq $26, %%r10                 ;\n"
+               "shrq $26, %%r11                 ;\n"
+               "shrq $26, %%r12                 ;\n"
+               "shrq $26, %%r13                 ;\n"
+               "andl $0x3ffffff, %%ecx          ;\n"
+               "andl $0x1ffffff, %%r9d          ;\n"
+               "andl $0x3ffffff, %%r8d          ;\n"
+               "andl $0x1ffffff, %%r10d         ;\n"
+               "andl $0x3ffffff, %%edx          ;\n"
+               "andl $0x1ffffff, %%r11d         ;\n"
+               "andl $0x3ffffff, %%esi          ;\n"
+               "andl $0x1ffffff, %%r12d         ;\n"
+               "andl $0x3ffffff, %%edi          ;\n"
+               "andl $0x1ffffff, %%r13d         ;\n"
+               "movl %%ecx, 0(%2)               ;\n"
+               "movl %%r9d, 4(%2)               ;\n"
+               "movl %%r8d, 8(%2)               ;\n"
+               "movl %%r10d, 12(%2)             ;\n"
+               "movl %%edx, 16(%2)              ;\n"
+               "movl %%r11d, 20(%2)             ;\n"
+               "movl %%esi, 24(%2)              ;\n"
+               "movl %%r12d, 28(%2)             ;\n"
+               "movl %%edi, 32(%2)              ;\n"
+               "movl %%r13d, 36(%2)             ;\n"
+
+               /* store xaddy */
+               "movd %%xmm2, %%rcx              ;\n"
+               "movd %%xmm2, %%r8               ;\n"
+               "movd %%xmm3, %%rsi              ;\n"
+               "pshufd $0xee, %%xmm2, %%xmm2    ;\n"
+               "pshufd $0xee, %%xmm3, %%xmm3    ;\n"
+               "movd %%xmm2, %%rdx              ;\n"
+               "movd %%xmm3, %%rdi              ;\n"
+               "shrdq $51, %%rdx, %%r8          ;\n"
+               "shrdq $38, %%rsi, %%rdx         ;\n"
+               "shrdq $25, %%rdi, %%rsi         ;\n"
+               "shrq $12, %%rdi                 ;\n"
+               "movq %%rcx, %%r9                ;\n"
+               "movq %%r8, %%r10                ;\n"
+               "movq %%rdx, %%r11               ;\n"
+               "movq %%rsi, %%r12               ;\n"
+               "movq %%rdi, %%r13               ;\n"
+               "shrq $26, %%r9                  ;\n"
+               "shrq $26, %%r10                 ;\n"
+               "shrq $26, %%r11                 ;\n"
+               "shrq $26, %%r12                 ;\n"
+               "shrq $26, %%r13                 ;\n"
+               "andl $0x3ffffff, %%ecx          ;\n"
+               "andl $0x1ffffff, %%r9d          ;\n"
+               "andl $0x3ffffff, %%r8d          ;\n"
+               "andl $0x1ffffff, %%r10d         ;\n"
+               "andl $0x3ffffff, %%edx          ;\n"
+               "andl $0x1ffffff, %%r11d         ;\n"
+               "andl $0x3ffffff, %%esi          ;\n"
+               "andl $0x1ffffff, %%r12d         ;\n"
+               "andl $0x3ffffff, %%edi          ;\n"
+               "andl $0x1ffffff, %%r13d         ;\n"
+               "movl %%ecx, 40(%2)              ;\n"
+               "movl %%r9d, 44(%2)              ;\n"
+               "movl %%r8d, 48(%2)              ;\n"
+               "movl %%r10d, 52(%2)             ;\n"
+               "movl %%edx, 56(%2)              ;\n"
+               "movl %%r11d, 60(%2)             ;\n"
+               "movl %%esi, 64(%2)              ;\n"
+               "movl %%r12d, 68(%2)             ;\n"
+               "movl %%edi, 72(%2)              ;\n"
+               "movl %%r13d, 76(%2)             ;\n"
+
+               /* extract t2d */
+               "xorq %%rax, %%rax               ;\n"
+               "movd %%xmm4, %%rcx              ;\n"
+               "movd %%xmm4, %%r8               ;\n"
+               "movd %%xmm5, %%rsi              ;\n"
+               "pshufd $0xee, %%xmm4, %%xmm4    ;\n"
+               "pshufd $0xee, %%xmm5, %%xmm5    ;\n"
+               "movd %%xmm4, %%rdx              ;\n"
+               "movd %%xmm5, %%rdi              ;\n"
+               "shrdq $51, %%rdx, %%r8          ;\n"
+               "shrdq $38, %%rsi, %%rdx         ;\n"
+               "shrdq $25, %%rdi, %%rsi         ;\n"
+               "shrq $12, %%rdi                 ;\n"
+               "movq %%rcx, %%r9                ;\n"
+               "movq %%r8, %%r10                ;\n"
+               "movq %%rdx, %%r11               ;\n"
+               "movq %%rsi, %%r12               ;\n"
+               "movq %%rdi, %%r13               ;\n"
+               "shrq $26, %%r9                  ;\n"
+               "shrq $26, %%r10                 ;\n"
+               "shrq $26, %%r11                 ;\n"
+               "shrq $26, %%r12                 ;\n"
+               "shrq $26, %%r13                 ;\n"
+               "andl $0x3ffffff, %%ecx          ;\n"
+               "andl $0x1ffffff, %%r9d          ;\n"
+               "andl $0x3ffffff, %%r8d          ;\n"
+               "andl $0x1ffffff, %%r10d         ;\n"
+               "andl $0x3ffffff, %%edx          ;\n"
+               "andl $0x1ffffff, %%r11d         ;\n"
+               "andl $0x3ffffff, %%esi          ;\n"
+               "andl $0x1ffffff, %%r12d         ;\n"
+               "andl $0x3ffffff, %%edi          ;\n"
+               "andl $0x1ffffff, %%r13d         ;\n"
+               "movd %%ecx, %%xmm0              ;\n"
+               "movd %%r9d, %%xmm4              ;\n"
+               "movd %%r8d, %%xmm8              ;\n"
+               "movd %%r10d, %%xmm3             ;\n"
+               "movd %%edx, %%xmm1              ;\n"
+               "movd %%r11d, %%xmm5             ;\n"
+               "movd %%esi, %%xmm6              ;\n"
+               "movd %%r12d, %%xmm7             ;\n"
+               "movd %%edi, %%xmm2              ;\n"
+               "movd %%r13d, %%xmm9             ;\n"
+               "punpckldq %%xmm4, %%xmm0        ;\n"
+               "punpckldq %%xmm3, %%xmm8        ;\n"
+               "punpckldq %%xmm5, %%xmm1        ;\n"
+               "punpckldq %%xmm7, %%xmm6        ;\n"
+               "punpckldq %%xmm9, %%xmm2        ;\n"
+               "punpcklqdq %%xmm8, %%xmm0       ;\n"
+               "punpcklqdq %%xmm6, %%xmm1       ;\n"
+
+               /* set up 2p in to 3/4 */
+               "movl $0x7ffffda, %%ecx          ;\n"
+               "movl $0x3fffffe, %%edx          ;\n"
+               "movl $0x7fffffe, %%eax          ;\n"
+               "movd %%ecx, %%xmm3              ;\n"
+               "movd %%edx, %%xmm5              ;\n"
+               "movd %%eax, %%xmm4              ;\n"
+               "punpckldq %%xmm5, %%xmm3        ;\n"
+               "punpckldq %%xmm5, %%xmm4        ;\n"
+               "punpcklqdq %%xmm4, %%xmm3       ;\n"
+               "movdqa %%xmm4, %%xmm5           ;\n"
+               "punpcklqdq %%xmm4, %%xmm4       ;\n"
+
+               /* subtract and conditionally move */
+               "movl %3, %%ecx                  ;\n"
+               "sub $1, %%ecx                   ;\n"
+               "movd %%ecx, %%xmm6              ;\n"
+               "pshufd $0x00, %%xmm6, %%xmm6    ;\n"
+               "movdqa %%xmm6, %%xmm7           ;\n"
+               "psubd %%xmm0, %%xmm3            ;\n"
+               "psubd %%xmm1, %%xmm4            ;\n"
+               "psubd %%xmm2, %%xmm5            ;\n"
+               "pand %%xmm6, %%xmm0             ;\n"
+               "pand %%xmm6, %%xmm1             ;\n"
+               "pand %%xmm6, %%xmm2             ;\n"
+               "pandn %%xmm3, %%xmm6            ;\n"
+               "movdqa %%xmm7, %%xmm3           ;\n"
+               "pandn %%xmm4, %%xmm7            ;\n"
+               "pandn %%xmm5, %%xmm3            ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm3, %%xmm2              ;\n"
+
+               /* store t2d */
+               "movdqa %%xmm0, 80(%2)           ;\n"
+               "movdqa %%xmm1, 96(%2)          ;\n"
+               "movd %%xmm2, %%rax              ;\n"
+               "movq %%rax, 112(%2)             ;\n"
+               :
+               : "m"(u), "r"(&table[pos * 8]), "r"(t), "m"(sign) /* %0 = u, %1 = table, %2 = t, %3 = sign */
+               :
+                       "%rax", "%rcx", "%rdx", "%rdi", "%rsi", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", 
+                       "%xmm0", "%xmm1", "%xmm2", "%xmm3", "%xmm4", "%xmm5", "%xmm6", "%xmm7", "%xmm8", "%xmm9", "%xmm10", "%xmm11", "%xmm14", "%xmm14",
+                       "cc", "memory"
+       );
+}
+
+#endif /* defined(ED25519_GCC_64BIT_32BIT_CHOOSE) */
+

diff --git a/crypto/ed25519-donna/src/ed25519-donna-64bit-x86.h b/crypto/ed25519-donna/src/ed25519-donna-64bit-x86.h
new file mode 100644 (file)
index 0000000..30bd472
--- /dev/null
+++ b/crypto/ed25519-donna/src/ed25519-donna-64bit-x86.h
@@ -0,0 +1,351 @@
+#if defined(ED25519_GCC_64BIT_X86_CHOOSE)
+
+#define HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS
+
+DONNA_NOINLINE static void
+ge25519_scalarmult_base_choose_niels(ge25519_niels *t, const uint8_t table[256][96], uint32_t pos, signed char b) {
+       int64_t breg = (int64_t)b;
+       uint64_t sign = (uint64_t)breg >> 63;
+       uint64_t mask = ~(sign - 1);
+       uint64_t u = (breg + mask) ^ mask;
+
+       __asm__ __volatile__ (
+               /* ysubx+xaddy+t2d */
+               "movq %0, %%rax                  ;\n"
+               "movd %%rax, %%xmm14             ;\n"
+               "pshufd $0x00, %%xmm14, %%xmm14  ;\n"
+               "pxor %%xmm0, %%xmm0             ;\n"
+               "pxor %%xmm1, %%xmm1             ;\n"
+               "pxor %%xmm2, %%xmm2             ;\n"
+               "pxor %%xmm3, %%xmm3             ;\n"
+               "pxor %%xmm4, %%xmm4             ;\n"
+               "pxor %%xmm5, %%xmm5             ;\n"
+
+               /* 0 */
+               "movq $0, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movq $1, %%rax                  ;\n"
+               "movd %%rax, %%xmm6              ;\n"
+               "pxor %%xmm7, %%xmm7             ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm6, %%xmm2              ;\n"
+               "por %%xmm7, %%xmm3              ;\n"
+
+               /* 1 */
+               "movq $1, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 0(%1), %%xmm6            ;\n"
+               "movdqa 16(%1), %%xmm7           ;\n"
+               "movdqa 32(%1), %%xmm8           ;\n"
+               "movdqa 48(%1), %%xmm9           ;\n"
+               "movdqa 64(%1), %%xmm10          ;\n"
+               "movdqa 80(%1), %%xmm11          ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* 2 */
+               "movq $2, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 96(%1), %%xmm6           ;\n"
+               "movdqa 112(%1), %%xmm7          ;\n"
+               "movdqa 128(%1), %%xmm8          ;\n"
+               "movdqa 144(%1), %%xmm9          ;\n"
+               "movdqa 160(%1), %%xmm10         ;\n"
+               "movdqa 176(%1), %%xmm11         ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* 3 */
+               "movq $3, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 192(%1), %%xmm6          ;\n"
+               "movdqa 208(%1), %%xmm7          ;\n"
+               "movdqa 224(%1), %%xmm8          ;\n"
+               "movdqa 240(%1), %%xmm9          ;\n"
+               "movdqa 256(%1), %%xmm10         ;\n"
+               "movdqa 272(%1), %%xmm11         ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* 4 */
+               "movq $4, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 288(%1), %%xmm6          ;\n"
+               "movdqa 304(%1), %%xmm7          ;\n"
+               "movdqa 320(%1), %%xmm8          ;\n"
+               "movdqa 336(%1), %%xmm9          ;\n"
+               "movdqa 352(%1), %%xmm10         ;\n"
+               "movdqa 368(%1), %%xmm11         ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* 5 */
+               "movq $5, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 384(%1), %%xmm6          ;\n"
+               "movdqa 400(%1), %%xmm7          ;\n"
+               "movdqa 416(%1), %%xmm8          ;\n"
+               "movdqa 432(%1), %%xmm9          ;\n"
+               "movdqa 448(%1), %%xmm10         ;\n"
+               "movdqa 464(%1), %%xmm11         ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* 6 */
+               "movq $6, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 480(%1), %%xmm6          ;\n"
+               "movdqa 496(%1), %%xmm7          ;\n"
+               "movdqa 512(%1), %%xmm8          ;\n"
+               "movdqa 528(%1), %%xmm9          ;\n"
+               "movdqa 544(%1), %%xmm10         ;\n"
+               "movdqa 560(%1), %%xmm11         ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* 7 */
+               "movq $7, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 576(%1), %%xmm6          ;\n"
+               "movdqa 592(%1), %%xmm7          ;\n"
+               "movdqa 608(%1), %%xmm8          ;\n"
+               "movdqa 624(%1), %%xmm9          ;\n"
+               "movdqa 640(%1), %%xmm10         ;\n"
+               "movdqa 656(%1), %%xmm11         ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* 8 */
+               "movq $8, %%rax                  ;\n"
+               "movd %%rax, %%xmm15             ;\n"
+               "pshufd $0x00, %%xmm15, %%xmm15  ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa 672(%1), %%xmm6          ;\n"
+               "movdqa 688(%1), %%xmm7          ;\n"
+               "movdqa 704(%1), %%xmm8          ;\n"
+               "movdqa 720(%1), %%xmm9          ;\n"
+               "movdqa 736(%1), %%xmm10         ;\n"
+               "movdqa 752(%1), %%xmm11         ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pand %%xmm15, %%xmm8            ;\n"
+               "pand %%xmm15, %%xmm9            ;\n"
+               "pand %%xmm15, %%xmm10           ;\n"
+               "pand %%xmm15, %%xmm11           ;\n"
+               "por %%xmm6, %%xmm0              ;\n"
+               "por %%xmm7, %%xmm1              ;\n"
+               "por %%xmm8, %%xmm2              ;\n"
+               "por %%xmm9, %%xmm3              ;\n"
+               "por %%xmm10, %%xmm4             ;\n"
+               "por %%xmm11, %%xmm5             ;\n"
+
+               /* conditionally swap ysubx and xaddy */
+               "movq %3, %%rax                  ;\n"
+               "xorq $1, %%rax                  ;\n"
+               "movd %%rax, %%xmm14             ;\n"
+               "pxor %%xmm15, %%xmm15           ;\n"
+               "pshufd $0x00, %%xmm14, %%xmm14  ;\n"
+               "pxor %%xmm0, %%xmm2             ;\n"
+               "pxor %%xmm1, %%xmm3             ;\n"
+               "pcmpeqd %%xmm14, %%xmm15        ;\n"
+               "movdqa %%xmm2, %%xmm6           ;\n"
+               "movdqa %%xmm3, %%xmm7           ;\n"
+               "pand %%xmm15, %%xmm6            ;\n"
+               "pand %%xmm15, %%xmm7            ;\n"
+               "pxor %%xmm6, %%xmm0             ;\n"
+               "pxor %%xmm7, %%xmm1             ;\n"
+               "pxor %%xmm0, %%xmm2             ;\n"
+               "pxor %%xmm1, %%xmm3             ;\n"
+
+               /* store ysubx */
+               "movq $0x7ffffffffffff, %%rax    ;\n"
+               "movd %%xmm0, %%rcx              ;\n"
+               "movd %%xmm0, %%r8               ;\n"
+               "movd %%xmm1, %%rsi              ;\n"
+               "pshufd $0xee, %%xmm0, %%xmm0    ;\n"
+               "pshufd $0xee, %%xmm1, %%xmm1    ;\n"
+               "movd %%xmm0, %%rdx              ;\n"
+               "movd %%xmm1, %%rdi              ;\n"
+               "shrdq $51, %%rdx, %%r8          ;\n"
+               "shrdq $38, %%rsi, %%rdx         ;\n"
+               "shrdq $25, %%rdi, %%rsi         ;\n"
+               "shrq $12, %%rdi                 ;\n"
+               "andq %%rax, %%rcx               ;\n"
+               "andq %%rax, %%r8                ;\n"
+               "andq %%rax, %%rdx               ;\n"
+               "andq %%rax, %%rsi               ;\n"
+               "andq %%rax, %%rdi               ;\n"
+               "movq %%rcx, 0(%2)               ;\n"
+               "movq %%r8, 8(%2)                ;\n"
+               "movq %%rdx, 16(%2)              ;\n"
+               "movq %%rsi, 24(%2)              ;\n"
+               "movq %%rdi, 32(%2)              ;\n"
+
+               /* store xaddy */
+               "movq $0x7ffffffffffff, %%rax    ;\n"
+               "movd %%xmm2, %%rcx              ;\n"
+               "movd %%xmm2, %%r8               ;\n"
+               "movd %%xmm3, %%rsi              ;\n"
+               "pshufd $0xee, %%xmm2, %%xmm2    ;\n"
+               "pshufd $0xee, %%xmm3, %%xmm3    ;\n"
+               "movd %%xmm2, %%rdx              ;\n"
+               "movd %%xmm3, %%rdi              ;\n"
+               "shrdq $51, %%rdx, %%r8          ;\n"
+               "shrdq $38, %%rsi, %%rdx         ;\n"
+               "shrdq $25, %%rdi, %%rsi         ;\n"
+               "shrq $12, %%rdi                 ;\n"
+               "andq %%rax, %%rcx               ;\n"
+               "andq %%rax, %%r8                ;\n"
+               "andq %%rax, %%rdx               ;\n"
+               "andq %%rax, %%rsi               ;\n"
+               "andq %%rax, %%rdi               ;\n"
+               "movq %%rcx, 40(%2)              ;\n"
+               "movq %%r8, 48(%2)               ;\n"
+               "movq %%rdx, 56(%2)              ;\n"
+               "movq %%rsi, 64(%2)              ;\n"
+               "movq %%rdi, 72(%2)              ;\n"
+
+               /* extract t2d */
+               "movq $0x7ffffffffffff, %%rax    ;\n"
+               "movd %%xmm4, %%rcx              ;\n"
+               "movd %%xmm4, %%r8               ;\n"
+               "movd %%xmm5, %%rsi              ;\n"
+               "pshufd $0xee, %%xmm4, %%xmm4    ;\n"
+               "pshufd $0xee, %%xmm5, %%xmm5    ;\n"
+               "movd %%xmm4, %%rdx              ;\n"
+               "movd %%xmm5, %%rdi              ;\n"
+               "shrdq $51, %%rdx, %%r8          ;\n"
+               "shrdq $38, %%rsi, %%rdx         ;\n"
+               "shrdq $25, %%rdi, %%rsi         ;\n"
+               "shrq $12, %%rdi                 ;\n"
+               "andq %%rax, %%rcx               ;\n"
+               "andq %%rax, %%r8                ;\n"
+               "andq %%rax, %%rdx               ;\n"
+               "andq %%rax, %%rsi               ;\n"
+               "andq %%rax, %%rdi               ;\n"
+
+               /* conditionally negate t2d */
+               "movq %3, %%rax                  ;\n"
+               "movq $0xfffffffffffda, %%r9     ;\n"
+               "movq $0xffffffffffffe, %%r10    ;\n"
+               "movq %%r10, %%r11               ;\n"
+               "movq %%r10, %%r12               ;\n"
+               "movq %%r10, %%r13               ;\n"
+               "subq %%rcx, %%r9                ;\n"
+               "subq %%r8, %%r10                ;\n"
+               "subq %%rdx, %%r11               ;\n"
+               "subq %%rsi, %%r12               ;\n"
+               "subq %%rdi, %%r13               ;\n"
+               "cmpq $1, %%rax                  ;\n"
+               "cmove %%r9, %%rcx               ;\n"
+               "cmove %%r10, %%r8               ;\n"
+               "cmove %%r11, %%rdx              ;\n"
+               "cmove %%r12, %%rsi              ;\n"
+               "cmove %%r13, %%rdi              ;\n"
+
+               /* store t2d */
+               "movq %%rcx, 80(%2)              ;\n"
+               "movq %%r8, 88(%2)               ;\n"
+               "movq %%rdx, 96(%2)              ;\n"
+               "movq %%rsi, 104(%2)             ;\n"
+               "movq %%rdi, 112(%2)             ;\n"
+               :
+               : "m"(u), "r"(&table[pos * 8]), "r"(t), "m"(sign) /* %0 = u, %1 = table, %2 = t, %3 = sign */
+               :
+                       "%rax", "%rcx", "%rdx", "%rdi", "%rsi", "%r8", "%r9", "%r10", "%r11", "%r12", "%r13", 
+                       "%xmm0", "%xmm1", "%xmm2", "%xmm3", "%xmm4", "%xmm5", "%xmm6", "%xmm7", "%xmm8", "%xmm9", "%xmm10", "%xmm11", "%xmm14", "%xmm14",
+                       "cc", "memory"
+       );
+}
+
+#endif /* defined(ED25519_GCC_64BIT_X86_CHOOSE) */
+

diff --git a/crypto/ed25519-donna/src/ed25519-donna-basepoint-table.h b/crypto/ed25519-donna/src/ed25519-donna-basepoint-table.h
new file mode 100644 (file)
index 0000000..41dcd52
--- /dev/null
+++ b/crypto/ed25519-donna/src/ed25519-donna-basepoint-table.h
@@ -0,0 +1,259 @@
+/* multiples of the base point in packed {ysubx, xaddy, t2d} form */
+static const uint8_t ALIGN(16) ge25519_niels_base_multiples[256][96] = {
+       {0x3e,0x91,0x40,0xd7,0x05,0x39,0x10,0x9d,0xb3,0xbe,0x40,0xd1,0x05,0x9f,0x39,0xfd,0x09,0x8a,0x8f,0x68,0x34,0x84,0xc1,0xa5,0x67,0x12,0xf8,0x98,0x92,0x2f,0xfd,0x44,0x85,0x3b,0x8c,0xf5,0xc6,0x93,0xbc,0x2f,0x19,0x0e,0x8c,0xfb,0xc6,0x2d,0x93,0xcf,0xc2,0x42,0x3d,0x64,0x98,0x48,0x0b,0x27,0x65,0xba,0xd4,0x33,0x3a,0x9d,0xcf,0x07,0x59,0xbb,0x6f,0x4b,0x67,0x15,0xbd,0xdb,0xea,0xa5,0xa2,0xee,0x00,0x3f,0xe1,0x41,0xfa,0xc6,0x57,0xc9,0x1c,0x9d,0xd4,0xcd,0xca,0xec,0x16,0xaf,0x1f,0xbe,0x0e,0x4f},
+       {0xa8,0xd5,0xb4,0x42,0x60,0xa5,0x99,0x8a,0xf6,0xac,0x60,0x4e,0x0c,0x81,0x2b,0x8f,0xaa,0x37,0x6e,0xb1,0x6b,0x23,0x9e,0xe0,0x55,0x25,0xc9,0x69,0xa6,0x95,0xb5,0x6b,0xd7,0x71,0x3c,0x93,0xfc,0xe7,0x24,0x92,0xb5,0xf5,0x0f,0x7a,0x96,0x9d,0x46,0x9f,0x02,0x07,0xd6,0xe1,0x65,0x9a,0xa6,0x5a,0x2e,0x2e,0x7d,0xa8,0x3f,0x06,0x0c,0x59,0x02,0x68,0xd3,0xda,0xaa,0x7e,0x34,0x6e,0x05,0x48,0xee,0x83,0x93,0x59,0xf3,0xba,0x26,0x68,0x07,0xe6,0x10,0xbe,0xca,0x3b,0xb8,0xd1,0x5e,0x16,0x0a,0x4f,0x31,0x49},
+       {0x65,0xd2,0xfc,0xa4,0xe8,0x1f,0x61,0x56,0x7d,0xba,0xc1,0xe5,0xfd,0x53,0xd3,0x3b,0xbd,0xd6,0x4b,0x21,0x1a,0xf3,0x31,0x81,0x62,0xda,0x5b,0x55,0x87,0x15,0xb9,0x2a,0x30,0x97,0xee,0x4c,0xa8,0xb0,0x25,0xaf,0x8a,0x4b,0x86,0xe8,0x30,0x84,0x5a,0x02,0x32,0x67,0x01,0x9f,0x02,0x50,0x1b,0xc1,0xf4,0xf8,0x80,0x9a,0x1b,0x4e,0x16,0x7a,0x34,0x48,0x67,0xf1,0xf4,0x11,0xf2,0x9b,0x95,0xf8,0x2d,0xf6,0x17,0x6b,0x4e,0xb8,0x4e,0x2a,0x72,0x5b,0x07,0x6f,0xde,0xd7,0x21,0x2a,0xbb,0x63,0xb9,0x04,0x9a,0x54},
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+       {0xee,0x8a,0x94,0x08,0x4d,0x86,0xf4,0xb0,0x6f,0x1c,0xba,0x91,0xee,0x19,0xdc,0x07,0x58,0xa1,0xac,0xa6,0xae,0xcd,0x75,0x79,0xbb,0xd4,0x62,0x42,0x13,0x61,0x0b,0x33,0x72,0x42,0xcb,0xf9,0x93,0xbc,0x68,0xc1,0x98,0xdb,0xce,0xc7,0x1f,0x71,0xb8,0xae,0x7a,0x8d,0xac,0x34,0xaa,0x52,0x0e,0x7f,0xbb,0x55,0x7d,0x7e,0x09,0xc1,0xce,0x41,0x8a,0x80,0x6d,0xa2,0xd7,0x19,0x96,0xf7,0x6d,0x15,0x9e,0x1d,0x9e,0xd4,0x1f,0xbb,0x27,0xdf,0xa1,0xdb,0x6c,0xc3,0xd7,0x73,0x7d,0x77,0x28,0x1f,0xd9,0x4c,0xb4,0x26},
+       {0x75,0x74,0x38,0x8f,0x47,0x48,0xf0,0x51,0x3c,0xcb,0xbe,0x9c,0xf4,0xbc,0x5d,0xb2,0x55,0x20,0x9f,0xd9,0x44,0x12,0xab,0x9a,0xd6,0xa5,0x10,0x1c,0x6c,0x9e,0x70,0x2c,0x83,0x03,0x73,0x62,0x93,0xf2,0xb7,0xe1,0x2c,0x8a,0xca,0xeb,0xff,0x79,0x52,0x4b,0x14,0x13,0xd4,0xbf,0x8a,0x77,0xfc,0xda,0x0f,0x61,0x72,0x9c,0x14,0x10,0xeb,0x7d,0x7a,0xee,0x66,0x87,0x6a,0xaf,0x62,0xcb,0x0e,0xcd,0x53,0x55,0x04,0xec,0xcb,0x66,0xb5,0xe4,0x0b,0x0f,0x38,0x01,0x80,0x58,0xea,0xe2,0x2c,0xf6,0x9f,0x8e,0xe6,0x08},
+       {0xad,0x30,0xc1,0x4b,0x0a,0x50,0xad,0x34,0x9c,0xd4,0x0b,0x3d,0x49,0xdb,0x38,0x8d,0xbe,0x89,0x0a,0x50,0x98,0x3d,0x5c,0xa2,0x09,0x3b,0xba,0xee,0x87,0x3f,0x1f,0x2f,0xf9,0xf2,0xb8,0x0a,0xd5,0x09,0x2d,0x2f,0xdf,0x23,0x59,0xc5,0x8d,0x21,0xb9,0xac,0xb9,0x6c,0x76,0x73,0x26,0x34,0x8f,0x4a,0xf5,0x19,0xf7,0x38,0xd7,0x3b,0xb1,0x4c,0x4a,0xb6,0x15,0xe5,0x75,0x8c,0x84,0xf7,0x38,0x90,0x4a,0xdb,0xba,0x01,0x95,0xa5,0x50,0x1b,0x75,0x3f,0x3f,0x31,0x0d,0xc2,0xe8,0x2e,0xae,0xc0,0x53,0xe3,0xa1,0x19},
+       {0xc3,0x05,0xfa,0xba,0x60,0x75,0x1c,0x7d,0x61,0x5e,0xe5,0xc6,0xa0,0xa0,0xe1,0xb3,0x73,0x64,0xd6,0xc0,0x18,0x97,0x52,0xe3,0x86,0x34,0x0c,0xc2,0x11,0x6b,0x54,0x41,0xbd,0xbd,0x96,0xd5,0xcd,0x72,0x21,0xb4,0x40,0xfc,0xee,0x98,0x43,0x45,0xe0,0x93,0xb5,0x09,0x41,0xb4,0x47,0x53,0xb1,0x9f,0x34,0xae,0x66,0x02,0x99,0xd3,0x6b,0x73,0xb4,0xb3,0x34,0x93,0x50,0x2d,0x53,0x85,0x73,0x65,0x81,0x60,0x4b,0x11,0xfd,0x46,0x75,0x83,0x5c,0x42,0x30,0x5f,0x5f,0xcc,0x5c,0xab,0x7f,0xb8,0xa2,0x95,0x22,0x41},
+       {0xe9,0xd6,0x7e,0xf5,0x88,0x9b,0xc9,0x19,0x25,0xc8,0xf8,0x6d,0x26,0xcb,0x93,0x53,0x73,0xd2,0x0a,0xb3,0x13,0x32,0xee,0x5c,0x34,0x2e,0x2d,0xb5,0xeb,0x53,0xe1,0x14,0xc6,0xea,0x93,0xe2,0x61,0x52,0x65,0x2e,0xdb,0xac,0x33,0x21,0x03,0x92,0x5a,0x84,0x6b,0x99,0x00,0x79,0xcb,0x75,0x09,0x46,0x80,0xdd,0x5a,0x19,0x8d,0xbb,0x60,0x07,0x8a,0x81,0xe6,0xcd,0x17,0x1a,0x3e,0x41,0x84,0xa0,0x69,0xed,0xa9,0x6d,0x15,0x57,0xb1,0xcc,0xca,0x46,0x8f,0x26,0xbf,0x2c,0xf2,0xc5,0x3a,0xc3,0x9b,0xbe,0x34,0x6b},
+       {0xb2,0xc0,0x78,0x3a,0x64,0x2f,0xdf,0xf3,0x7c,0x02,0x2e,0xf2,0x1e,0x97,0x3e,0x4c,0xa3,0xb5,0xc1,0x49,0x5e,0x1c,0x7d,0xec,0x2d,0xdd,0x22,0x09,0x8f,0xc1,0x12,0x20,0xd3,0xf2,0x71,0x65,0x65,0x69,0xfc,0x11,0x7a,0x73,0x0e,0x53,0x45,0xe8,0xc9,0xc6,0x35,0x50,0xfe,0xd4,0xa2,0xe7,0x3a,0xe3,0x0b,0xd3,0x6d,0x2e,0xb6,0xc7,0xb9,0x01,0x29,0x9d,0xc8,0x5a,0xe5,0x55,0x0b,0x88,0x63,0xa7,0xa0,0x45,0x1f,0x24,0x83,0x14,0x1f,0x6c,0xe7,0xc2,0xdf,0xef,0x36,0x3d,0xe8,0xad,0x4b,0x4e,0x78,0x5b,0xaf,0x08},
+       {0x33,0x25,0x1f,0x88,0xdc,0x99,0x34,0x28,0xb6,0x23,0x93,0x77,0xda,0x25,0x05,0x9d,0xf4,0x41,0x34,0x67,0xfb,0xdd,0x7a,0x89,0x8d,0x16,0x3a,0x16,0x71,0x9d,0xb7,0x32,0x4b,0x2c,0xcc,0x89,0xd2,0x14,0x73,0xe2,0x8d,0x17,0x87,0xa2,0x11,0xbd,0xe4,0x4b,0xce,0x64,0x33,0xfa,0xd6,0x28,0xd5,0x18,0x6e,0x82,0xd9,0xaf,0xd5,0xc1,0x23,0x64,0x6a,0xb3,0xfc,0xed,0xd9,0xf8,0x85,0xcc,0xf9,0xe5,0x46,0x37,0x8f,0xc2,0xbc,0x22,0xcd,0xd3,0xe5,0xf9,0x38,0xe3,0x9d,0xe4,0xcc,0x2d,0x3e,0xc1,0xfb,0x5e,0x0a,0x48},
+       {0x71,0x20,0x62,0x01,0x0b,0xe7,0x51,0x0b,0xc5,0xaf,0x1d,0x8b,0xcf,0x05,0xb5,0x06,0xcd,0xab,0x5a,0xef,0x61,0xb0,0x6b,0x2c,0x31,0xbf,0xb7,0x0c,0x60,0x27,0xaa,0x47,0x1f,0x22,0xce,0x42,0xe4,0x4c,0x61,0xb6,0x28,0x39,0x05,0x4c,0xcc,0x9d,0x19,0x6e,0x03,0xbe,0x1c,0xdc,0xa4,0xb4,0x3f,0x66,0x06,0x8e,0x1c,0x69,0x47,0x1d,0xb3,0x24,0xc3,0xf8,0x15,0xc0,0xed,0x1e,0x54,0x2a,0x7c,0x3f,0x69,0x7c,0x7e,0xfe,0xa4,0x11,0xd6,0x78,0xa2,0x4e,0x13,0x66,0xaf,0xf0,0x94,0xa0,0xdd,0x14,0x5d,0x58,0x5b,0x54},
+       {0x0f,0x3a,0xd4,0xa0,0x5e,0x27,0xbf,0x67,0xbe,0xee,0x9b,0x08,0x34,0x8e,0xe6,0xad,0x2e,0xe7,0x79,0xd4,0x4c,0x13,0x89,0x42,0x54,0x54,0xba,0x32,0xc3,0xf9,0x62,0x0f,0xe1,0x21,0xb3,0xe3,0xd0,0xe4,0x04,0x62,0x95,0x1e,0xff,0x28,0x7a,0x63,0xaa,0x3b,0x9e,0xbd,0x99,0x5b,0xfd,0xcf,0x0c,0x0b,0x71,0xd0,0xc8,0x64,0x3e,0xdc,0x22,0x4d,0x39,0x5f,0x3b,0xd6,0x89,0x65,0xb4,0xfc,0x61,0xcf,0xcb,0x57,0x3f,0x6a,0xae,0x5c,0x05,0xfa,0x3a,0x95,0xd2,0xc2,0xba,0xfe,0x36,0x14,0x37,0x36,0x1a,0xa0,0x0f,0x1c},
+       {0xff,0x3d,0x94,0x22,0xb6,0x04,0xc6,0xd2,0xa0,0xb3,0xcf,0x44,0xce,0xbe,0x8c,0xbc,0x78,0x86,0x80,0x97,0xf3,0x4f,0x25,0x5d,0xbf,0xa6,0x1c,0x3b,0x4f,0x61,0xa3,0x0f,0x50,0x6a,0x93,0x8c,0x0e,0x2b,0x08,0x69,0xb6,0xc5,0xda,0xc1,0x35,0xa0,0xc9,0xf9,0x34,0xb6,0xdf,0xc4,0x54,0x3e,0xb7,0x6f,0x40,0xc1,0x2b,0x1d,0x9b,0x41,0x05,0x40,0xf0,0x82,0xbe,0xb9,0xbd,0xfe,0x03,0xa0,0x90,0xac,0x44,0x3a,0xaf,0xc1,0x89,0x20,0x8e,0xfa,0x54,0x19,0x91,0x9f,0x49,0xf8,0x42,0xab,0x40,0xef,0x8a,0x21,0xba,0x1f},
+       {0x3e,0xf5,0xc8,0xfa,0x48,0x94,0x54,0xab,0x41,0x37,0xa6,0x7b,0x9a,0xe8,0xf6,0x81,0x01,0x5e,0x2b,0x6c,0x7d,0x6c,0xfd,0x74,0x42,0x6e,0xc8,0xa8,0xca,0x3a,0x2e,0x39,0x94,0x01,0x7b,0x3e,0x04,0x57,0x3e,0x4f,0x7f,0xaf,0xda,0x08,0xee,0x3e,0x1d,0xa8,0xf1,0xde,0xdc,0x99,0xab,0xc6,0x39,0xc8,0xd5,0x61,0x77,0xff,0x13,0x5d,0x53,0x6c,0xaf,0x35,0x8a,0x3e,0xe9,0x34,0xbd,0x4c,0x16,0xe8,0x87,0x58,0x44,0x81,0x07,0x2e,0xab,0xb0,0x9a,0xf2,0x76,0x9c,0x31,0x19,0x3b,0xc1,0x0a,0xd5,0xe4,0x7f,0xe1,0x25},
+       {0x76,0xf6,0x04,0x1e,0xd7,0x9b,0x28,0x0a,0x95,0x0f,0x42,0xd6,0x52,0x1c,0x8e,0x20,0xab,0x1f,0x69,0x34,0xb0,0xd8,0x86,0x51,0x51,0xb3,0x9f,0x2a,0x44,0x51,0x57,0x25,0xa7,0x21,0xf1,0x76,0xf5,0x7f,0x5f,0x91,0xe3,0x87,0xcd,0x2f,0x27,0x32,0x4a,0xc3,0x26,0xe5,0x1b,0x4d,0xde,0x2f,0xba,0xcc,0x9b,0x89,0x69,0x89,0x8f,0x82,0xba,0x6b,0x01,0x39,0xfe,0x90,0x66,0xbc,0xd1,0xe2,0xd5,0x7a,0x99,0xa0,0x18,0x4a,0xb5,0x4c,0xd4,0x60,0x84,0xaf,0x14,0x69,0x1d,0x97,0xe4,0x7b,0x6b,0x7f,0x4f,0x50,0x9d,0x55},
+       {0xd5,0x54,0xeb,0xb3,0x78,0x83,0x73,0xa7,0x7c,0x3c,0x55,0xa5,0x66,0xd3,0x69,0x1d,0xba,0x00,0x28,0xf9,0x62,0xcf,0x26,0x0a,0x17,0x32,0x7e,0x80,0xd5,0x12,0xab,0x01,0xfd,0x66,0xd2,0xf6,0xe7,0x91,0x48,0x9c,0x1b,0x78,0x07,0x03,0x9b,0xa1,0x44,0x07,0x3b,0xe2,0x61,0x60,0x1d,0x8f,0x38,0x88,0x0e,0xd5,0x4b,0x35,0xa3,0xa6,0x3e,0x12,0x96,0x2d,0xe3,0x41,0x90,0x18,0x8d,0x11,0x48,0x58,0x31,0xd8,0xc2,0xe3,0xed,0xb9,0xd9,0x45,0x32,0xd8,0x71,0x42,0xab,0x1e,0x54,0xa1,0x18,0xc9,0xe2,0x61,0x39,0x4a},
+       {0xa0,0xbb,0xe6,0xf8,0xe0,0x3b,0xdc,0x71,0x0a,0xe3,0xff,0x7e,0x34,0xf8,0xce,0xd6,0x6a,0x47,0x3a,0xe1,0x5f,0x42,0x92,0xa9,0x63,0xb7,0x1d,0xfb,0xe3,0xbc,0xd6,0x2c,0x1e,0x3f,0x23,0xf3,0x44,0xd6,0x27,0x03,0x16,0xf0,0xfc,0x34,0x0e,0x26,0x9a,0x49,0x79,0xb9,0xda,0xf2,0x16,0xa7,0xb5,0x83,0x1f,0x11,0xd4,0x9b,0xad,0xee,0xac,0x68,0x10,0xc2,0xd7,0xf3,0x0e,0xc9,0xb4,0x38,0x0c,0x04,0xad,0xb7,0x24,0x6e,0x8e,0x30,0x23,0x3e,0xe7,0xb7,0xf1,0xd9,0x60,0x38,0x97,0xf5,0x08,0xb5,0xd5,0x60,0x57,0x59},
+       {0x97,0x63,0xaa,0x04,0xe1,0xbf,0x29,0x61,0xcb,0xfc,0xa7,0xa4,0x08,0x00,0x96,0x8f,0x58,0x94,0x90,0x7d,0x89,0xc0,0x8b,0x3f,0xa9,0x91,0xb2,0xdc,0x3e,0xa4,0x9f,0x70,0x90,0x27,0x02,0xfd,0xeb,0xcb,0x2a,0x88,0x60,0x57,0x11,0xc4,0x05,0x33,0xaf,0x89,0xf4,0x73,0x34,0x7d,0xe3,0x92,0xf4,0x65,0x2b,0x5a,0x51,0x54,0xdf,0xc5,0xb2,0x2c,0xca,0x2a,0xfd,0x63,0x8c,0x5d,0x0a,0xeb,0xff,0x4e,0x69,0x2e,0x66,0xc1,0x2b,0xd2,0x3a,0xb0,0xcb,0xf8,0x6e,0xf3,0x23,0x27,0x1f,0x13,0xc8,0xf0,0xec,0x29,0xf0,0x70},
+       {0x33,0x3e,0xed,0x2e,0xb3,0x07,0x13,0x46,0xe7,0x81,0x55,0xa4,0x33,0x2f,0x04,0xae,0x66,0x03,0x5f,0x19,0xd3,0x49,0x44,0xc9,0x58,0x48,0x31,0x6c,0x8a,0x5d,0x7d,0x0b,0xb9,0xb0,0x10,0x5e,0xaa,0xaf,0x6a,0x2a,0xa9,0x1a,0x04,0xef,0x70,0xa3,0xf0,0x78,0x1f,0xd6,0x3a,0xaa,0x77,0xfb,0x3e,0x77,0xe1,0xd9,0x4b,0xa7,0xa2,0xa5,0xec,0x44,0x43,0xd5,0x95,0x7b,0x32,0x48,0xd4,0x25,0x1d,0x0f,0x34,0xa3,0x00,0x83,0xd3,0x70,0x2b,0xc5,0xe1,0x60,0x1c,0x53,0x1c,0xde,0xe4,0xe9,0x7d,0x2c,0x51,0x24,0x22,0x27},
+       {0x2e,0x34,0xc5,0x49,0xaf,0x92,0xbc,0x1a,0xd0,0xfa,0xe6,0xb2,0x11,0xd8,0xee,0xff,0x29,0x4e,0xc8,0xfc,0x8d,0x8c,0xa2,0xef,0x43,0xc5,0x4c,0xa4,0x18,0xdf,0xb5,0x11,0xfc,0x75,0xa9,0x42,0x8a,0xbb,0x7b,0xbf,0x58,0xa3,0xad,0x96,0x77,0x39,0x5c,0x8c,0x48,0xaa,0xed,0xcd,0x6f,0xc7,0x7f,0xe2,0xa6,0x20,0xbc,0xf6,0xd7,0x5f,0x73,0x19,0x66,0x42,0xc8,0x42,0xd0,0x90,0xab,0xe3,0x7e,0x54,0x19,0x7f,0x0f,0x8e,0x84,0xeb,0xb9,0x97,0xa4,0x65,0xd0,0xa1,0x03,0x25,0x5f,0x89,0xdf,0x91,0x11,0x91,0xef,0x0f}
+};

diff --git a/crypto/ed25519-donna/src/ed25519-donna-batchverify.h b/crypto/ed25519-donna/src/ed25519-donna-batchverify.h
new file mode 100644 (file)
index 0000000..43c4923
--- /dev/null
+++ b/crypto/ed25519-donna/src/ed25519-donna-batchverify.h
@@ -0,0 +1,275 @@
+/*
+       Ed25519 batch verification
+*/
+
+#define max_batch_size 64
+#define heap_batch_size ((max_batch_size * 2) + 1)
+
+/* which limb is the 128th bit in? */
+static const size_t limb128bits = (128 + bignum256modm_bits_per_limb - 1) / bignum256modm_bits_per_limb;
+
+typedef size_t heap_index_t;
+
+typedef struct batch_heap_t {
+       unsigned char r[heap_batch_size][16]; /* 128 bit random values */
+       ge25519 points[heap_batch_size];
+       bignum256modm scalars[heap_batch_size];
+       heap_index_t heap[heap_batch_size];
+       size_t size;
+} batch_heap;
+
+/* swap two values in the heap */
+static void
+heap_swap(heap_index_t *heap, size_t a, size_t b) {
+       heap_index_t temp;
+       temp = heap[a];
+       heap[a] = heap[b];
+       heap[b] = temp;
+}
+
+/* add the scalar at the end of the list to the heap */
+static void
+heap_insert_next(batch_heap *heap) {
+       size_t node = heap->size, parent;
+       heap_index_t *pheap = heap->heap;
+       bignum256modm *scalars = heap->scalars;
+
+       /* insert at the bottom */
+       pheap[node] = (heap_index_t)node;
+
+       /* sift node up to its sorted spot */
+       parent = (node - 1) / 2;
+       while (node && lt256_modm_batch(scalars[pheap[parent]], scalars[pheap[node]], bignum256modm_limb_size - 1)) {
+               heap_swap(pheap, parent, node);
+               node = parent;
+               parent = (node - 1) / 2;
+       }
+       heap->size++;
+}
+
+/* update the heap when the root element is updated */
+static void
+heap_updated_root(batch_heap *heap, size_t limbsize) {
+       size_t node, parent, childr, childl;
+       heap_index_t *pheap = heap->heap;
+       bignum256modm *scalars = heap->scalars;
+
+       /* sift root to the bottom */
+       parent = 0;
+       node = 1;
+       childl = 1;
+       childr = 2;
+       while ((childr < heap->size)) {
+               node = lt256_modm_batch(scalars[pheap[childl]], scalars[pheap[childr]], limbsize) ? childr : childl;
+               heap_swap(pheap, parent, node);
+               parent = node;
+               childl = (parent * 2) + 1;
+               childr = childl + 1;
+       }
+
+       /* sift root back up to its sorted spot */
+       parent = (node - 1) / 2;
+       while (node && lte256_modm_batch(scalars[pheap[parent]], scalars[pheap[node]], limbsize)) {
+               heap_swap(pheap, parent, node);
+               node = parent;
+               parent = (node - 1) / 2;
+       }
+}
+
+/* build the heap with count elements, count must be >= 3 */
+static void
+heap_build(batch_heap *heap, size_t count) {
+       heap->heap[0] = 0;
+       heap->size = 0;
+       while (heap->size < count)
+               heap_insert_next(heap);
+}
+
+/* extend the heap to contain new_count elements */
+static void
+heap_extend(batch_heap *heap, size_t new_count) {
+       while (heap->size < new_count)
+               heap_insert_next(heap);
+}
+
+/* get the top 2 elements of the heap */
+static void
+heap_get_top2(batch_heap *heap, heap_index_t *max1, heap_index_t *max2, size_t limbsize) {
+       heap_index_t h0 = heap->heap[0], h1 = heap->heap[1], h2 = heap->heap[2];
+       if (lt256_modm_batch(heap->scalars[h1], heap->scalars[h2], limbsize))
+               h1 = h2;
+       *max1 = h0;
+       *max2 = h1;
+}
+
+/* */
+static void
+ge25519_multi_scalarmult_vartime_final(ge25519 *r, ge25519 *point, bignum256modm scalar) {
+       const bignum256modm_element_t topbit = ((bignum256modm_element_t)1 << (bignum256modm_bits_per_limb - 1));
+       size_t limb = limb128bits;
+       bignum256modm_element_t flag;
+
+       if (isone256_modm_batch(scalar)) {
+               /* this will happen most of the time after bos-carter */
+               *r = *point;
+               return;
+       } else if (iszero256_modm_batch(scalar)) {
+               /* this will only happen if all scalars == 0 */
+               memset(r, 0, sizeof(*r));
+               r->y[0] = 1;
+               r->z[0] = 1;
+               return;
+       }
+
+       *r = *point;
+
+       /* find the limb where first bit is set */
+       while (!scalar[limb])
+               limb--;
+
+       /* find the first bit */
+       flag = topbit;
+       while ((scalar[limb] & flag) == 0)
+               flag >>= 1;
+
+       /* exponentiate */
+       for (;;) {
+               ge25519_double(r, r);
+               if (scalar[limb] & flag)
+                       ge25519_add(r, r, point);
+
+               flag >>= 1;
+               if (!flag) {
+                       if (!limb--)
+                               break;
+                       flag = topbit;
+               }
+       }
+}
+
+/* count must be >= 5 */
+static void
+ge25519_multi_scalarmult_vartime(ge25519 *r, batch_heap *heap, size_t count) {
+       heap_index_t max1, max2;
+
+       /* start with the full limb size */
+       size_t limbsize = bignum256modm_limb_size - 1;
+
+       /* whether the heap has been extended to include the 128 bit scalars */
+       int extended = 0;
+
+       /* grab an odd number of scalars to build the heap, unknown limb sizes */
+       heap_build(heap, ((count + 1) / 2) | 1);
+
+       for (;;) {
+               heap_get_top2(heap, &max1, &max2, limbsize);
+
+               /* only one scalar remaining, we're done */
+               if (iszero256_modm_batch(heap->scalars[max2]))
+                       break;
+
+               /* exhausted another limb? */
+               if (!heap->scalars[max1][limbsize])
+                       limbsize -= 1;
+
+               /* can we extend to the 128 bit scalars? */
+               if (!extended && isatmost128bits256_modm_batch(heap->scalars[max1])) {
+                       heap_extend(heap, count);
+                       heap_get_top2(heap, &max1, &max2, limbsize);
+                       extended = 1;
+               }
+
+               sub256_modm_batch(heap->scalars[max1], heap->scalars[max1], heap->scalars[max2], limbsize);
+               ge25519_add(&heap->points[max2], &heap->points[max2], &heap->points[max1]);
+               heap_updated_root(heap, limbsize);
+       }
+
+       ge25519_multi_scalarmult_vartime_final(r, &heap->points[max1], heap->scalars[max1]);
+}
+
+/* not actually used for anything other than testing */
+unsigned char batch_point_buffer[3][32];
+
+static int
+ge25519_is_neutral_vartime(const ge25519 *p) {
+       static const unsigned char zero[32] = {0};
+       unsigned char point_buffer[3][32];
+       curve25519_contract(point_buffer[0], p->x);
+       curve25519_contract(point_buffer[1], p->y);
+       curve25519_contract(point_buffer[2], p->z);
+       memcpy(batch_point_buffer[1], point_buffer[1], 32);
+       return (memcmp(point_buffer[0], zero, 32) == 0) && (memcmp(point_buffer[1], point_buffer[2], 32) == 0);
+}
+
+int
+ED25519_FN(ed25519_sign_open_batch) (const unsigned char **m, size_t *mlen, const unsigned char **pk, const unsigned char **RS, size_t num, int *valid) {
+       batch_heap ALIGN(16) batch;
+       ge25519 ALIGN(16) p;
+       bignum256modm *r_scalars;
+       size_t i, batchsize;
+       unsigned char hram[64];
+       int ret = 0;
+
+       for (i = 0; i < num; i++)
+               valid[i] = 1;
+
+       while (num > 3) {
+               batchsize = (num > max_batch_size) ? max_batch_size : num;
+
+               /* generate r (scalars[batchsize+1]..scalars[2*batchsize] */
+               ED25519_FN(ed25519_randombytes_unsafe) (batch.r, batchsize * 16);
+               r_scalars = &batch.scalars[batchsize + 1];
+               for (i = 0; i < batchsize; i++)
+                       expand256_modm(r_scalars[i], batch.r[i], 16);
+
+               /* compute scalars[0] = ((r1s1 + r2s2 + ...)) */
+               for (i = 0; i < batchsize; i++) {
+                       expand256_modm(batch.scalars[i], RS[i] + 32, 32);
+                       mul256_modm(batch.scalars[i], batch.scalars[i], r_scalars[i]);
+               }
+               for (i = 1; i < batchsize; i++)
+                       add256_modm(batch.scalars[0], batch.scalars[0], batch.scalars[i]);
+
+               /* compute scalars[1]..scalars[batchsize] as r[i]*H(R[i],A[i],m[i]) */
+               for (i = 0; i < batchsize; i++) {
+                       ed25519_hram(hram, RS[i], pk[i], m[i], mlen[i]);
+                       expand256_modm(batch.scalars[i+1], hram, 64);
+                       mul256_modm(batch.scalars[i+1], batch.scalars[i+1], r_scalars[i]);
+               }
+
+               /* compute points */
+               batch.points[0] = ge25519_basepoint;
+               for (i = 0; i < batchsize; i++)
+                       if (!ge25519_unpack_negative_vartime(&batch.points[i+1], pk[i]))
+                               goto fallback;
+               for (i = 0; i < batchsize; i++)
+                       if (!ge25519_unpack_negative_vartime(&batch.points[batchsize+i+1], RS[i]))
+                               goto fallback;
+
+               ge25519_multi_scalarmult_vartime(&p, &batch, (batchsize * 2) + 1);
+               if (!ge25519_is_neutral_vartime(&p)) {
+                       ret |= 2;
+
+                       fallback:
+                       for (i = 0; i < batchsize; i++) {
+                               valid[i] = ED25519_FN(ed25519_sign_open) (m[i], mlen[i], pk[i], RS[i]) ? 0 : 1;
+                               ret |= (valid[i] ^ 1);
+                       }
+               }
+
+               m += batchsize;
+               mlen += batchsize;
+               pk += batchsize;
+               RS += batchsize;
+               num -= batchsize;
+               valid += batchsize;
+       }
+
+       for (i = 0; i < num; i++) {
+               valid[i] = ED25519_FN(ed25519_sign_open) (m[i], mlen[i], pk[i], RS[i]) ? 0 : 1;
+               ret |= (valid[i] ^ 1);
+       }
+
+       return ret;
+}
+

diff --git a/crypto/ed25519-donna/src/ed25519-donna-impl-base.h b/crypto/ed25519-donna/src/ed25519-donna-impl-base.h
new file mode 100644 (file)
index 0000000..48913ed
--- /dev/null
+++ b/crypto/ed25519-donna/src/ed25519-donna-impl-base.h
@@ -0,0 +1,364 @@
+/*
+       conversions
+*/
+
+DONNA_INLINE static void
+ge25519_p1p1_to_partial(ge25519 *r, const ge25519_p1p1 *p) {
+       curve25519_mul(r->x, p->x, p->t);
+       curve25519_mul(r->y, p->y, p->z);
+       curve25519_mul(r->z, p->z, p->t); 
+}
+
+DONNA_INLINE static void
+ge25519_p1p1_to_full(ge25519 *r, const ge25519_p1p1 *p) {
+       curve25519_mul(r->x, p->x, p->t);
+       curve25519_mul(r->y, p->y, p->z);
+       curve25519_mul(r->z, p->z, p->t); 
+       curve25519_mul(r->t, p->x, p->y); 
+}
+
+static void
+ge25519_full_to_pniels(ge25519_pniels *p, const ge25519 *r) {
+       curve25519_sub(p->ysubx, r->y, r->x);
+       curve25519_add(p->xaddy, r->y, r->x);
+       curve25519_copy(p->z, r->z);
+       curve25519_mul(p->t2d, r->t, ge25519_ec2d);
+}
+
+/*
+       adding & doubling
+*/
+
+static void
+ge25519_add_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519 *q) {
+       bignum25519 a,b,c,d,t,u;
+
+       curve25519_sub(a, p->y, p->x);
+       curve25519_add(b, p->y, p->x);
+       curve25519_sub(t, q->y, q->x);
+       curve25519_add(u, q->y, q->x);
+       curve25519_mul(a, a, t);
+       curve25519_mul(b, b, u);
+       curve25519_mul(c, p->t, q->t);
+       curve25519_mul(c, c, ge25519_ec2d);
+       curve25519_mul(d, p->z, q->z);
+       curve25519_add(d, d, d);
+       curve25519_sub(r->x, b, a);
+       curve25519_add(r->y, b, a);
+       curve25519_add_after_basic(r->z, d, c);
+       curve25519_sub_after_basic(r->t, d, c);
+}
+
+
+static void
+ge25519_double_p1p1(ge25519_p1p1 *r, const ge25519 *p) {
+       bignum25519 a,b,c;
+
+       curve25519_square(a, p->x);
+       curve25519_square(b, p->y);
+       curve25519_square(c, p->z);
+       curve25519_add_reduce(c, c, c);
+       curve25519_add(r->x, p->x, p->y);
+       curve25519_square(r->x, r->x);
+       curve25519_add(r->y, b, a);
+       curve25519_sub(r->z, b, a);
+       curve25519_sub_after_basic(r->x, r->x, r->y);
+       curve25519_sub_after_basic(r->t, c, r->z);
+}
+
+static void
+ge25519_nielsadd2_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519_niels *q, unsigned char signbit) {
+       const bignum25519 *qb = (const bignum25519 *)q;
+       bignum25519 *rb = (bignum25519 *)r;
+       bignum25519 a,b,c;
+
+       curve25519_sub(a, p->y, p->x);
+       curve25519_add(b, p->y, p->x);
+       curve25519_mul(a, a, qb[signbit]); /* x for +, y for - */
+       curve25519_mul(r->x, b, qb[signbit^1]); /* y for +, x for - */
+       curve25519_add(r->y, r->x, a);
+       curve25519_sub(r->x, r->x, a);
+       curve25519_mul(c, p->t, q->t2d);
+       curve25519_add_reduce(r->t, p->z, p->z);
+       curve25519_copy(r->z, r->t);
+       curve25519_add(rb[2+signbit], rb[2+signbit], c); /* z for +, t for - */
+       curve25519_sub(rb[2+(signbit^1)], rb[2+(signbit^1)], c); /* t for +, z for - */
+}
+
+static void
+ge25519_pnielsadd_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519_pniels *q, unsigned char signbit) {
+       const bignum25519 *qb = (const bignum25519 *)q;
+       bignum25519 *rb = (bignum25519 *)r;
+       bignum25519 a,b,c;
+
+       curve25519_sub(a, p->y, p->x);
+       curve25519_add(b, p->y, p->x);
+       curve25519_mul(a, a, qb[signbit]); /* ysubx for +, xaddy for - */
+       curve25519_mul(r->x, b, qb[signbit^1]); /* xaddy for +, ysubx for - */
+       curve25519_add(r->y, r->x, a);
+       curve25519_sub(r->x, r->x, a);
+       curve25519_mul(c, p->t, q->t2d);
+       curve25519_mul(r->t, p->z, q->z);
+       curve25519_add_reduce(r->t, r->t, r->t);
+       curve25519_copy(r->z, r->t);
+       curve25519_add(rb[2+signbit], rb[2+signbit], c); /* z for +, t for - */
+       curve25519_sub(rb[2+(signbit^1)], rb[2+(signbit^1)], c); /* t for +, z for - */
+}
+
+static void
+ge25519_double_partial(ge25519 *r, const ge25519 *p) {
+       ge25519_p1p1 t;
+       ge25519_double_p1p1(&t, p);
+       ge25519_p1p1_to_partial(r, &t);
+}
+
+static void
+ge25519_double(ge25519 *r, const ge25519 *p) {
+       ge25519_p1p1 t;
+       ge25519_double_p1p1(&t, p);
+       ge25519_p1p1_to_full(r, &t);
+}
+
+static void
+ge25519_add(ge25519 *r, const ge25519 *p,  const ge25519 *q) {
+       ge25519_p1p1 t;
+       ge25519_add_p1p1(&t, p, q);
+       ge25519_p1p1_to_full(r, &t);
+}
+
+static void
+ge25519_nielsadd2(ge25519 *r, const ge25519_niels *q) {
+       bignum25519 a,b,c,e,f,g,h;
+
+       curve25519_sub(a, r->y, r->x);
+       curve25519_add(b, r->y, r->x);
+       curve25519_mul(a, a, q->ysubx);
+       curve25519_mul(e, b, q->xaddy);
+       curve25519_add(h, e, a);
+       curve25519_sub(e, e, a);
+       curve25519_mul(c, r->t, q->t2d);
+       curve25519_add(f, r->z, r->z);
+       curve25519_add_after_basic(g, f, c);
+       curve25519_sub_after_basic(f, f, c);
+       curve25519_mul(r->x, e, f);
+       curve25519_mul(r->y, h, g);
+       curve25519_mul(r->z, g, f);
+       curve25519_mul(r->t, e, h);
+}
+
+static void
+ge25519_pnielsadd(ge25519_pniels *r, const ge25519 *p, const ge25519_pniels *q) {
+       bignum25519 a,b,c,x,y,z,t;
+
+       curve25519_sub(a, p->y, p->x);
+       curve25519_add(b, p->y, p->x);
+       curve25519_mul(a, a, q->ysubx);
+       curve25519_mul(x, b, q->xaddy);
+       curve25519_add(y, x, a);
+       curve25519_sub(x, x, a);
+       curve25519_mul(c, p->t, q->t2d);
+       curve25519_mul(t, p->z, q->z);
+       curve25519_add(t, t, t);
+       curve25519_add_after_basic(z, t, c);
+       curve25519_sub_after_basic(t, t, c);
+       curve25519_mul(r->xaddy, x, t);
+       curve25519_mul(r->ysubx, y, z);
+       curve25519_mul(r->z, z, t);
+       curve25519_mul(r->t2d, x, y);
+       curve25519_copy(y, r->ysubx);
+       curve25519_sub(r->ysubx, r->ysubx, r->xaddy);
+       curve25519_add(r->xaddy, r->xaddy, y);
+       curve25519_mul(r->t2d, r->t2d, ge25519_ec2d);
+}
+
+
+/*
+       pack & unpack
+*/
+
+static void
+ge25519_pack(unsigned char r[32], const ge25519 *p) {
+       bignum25519 tx, ty, zi;
+       unsigned char parity[32];
+       curve25519_recip(zi, p->z);
+       curve25519_mul(tx, p->x, zi);
+       curve25519_mul(ty, p->y, zi);
+       curve25519_contract(r, ty);
+       curve25519_contract(parity, tx);
+       r[31] ^= ((parity[0] & 1) << 7);
+}
+
+static int
+ge25519_unpack_negative_vartime(ge25519 *r, const unsigned char p[32]) {
+       static const unsigned char zero[32] = {0};
+       static const bignum25519 one = {1};
+       unsigned char parity = p[31] >> 7;
+       unsigned char check[32];
+       bignum25519 t, root, num, den, d3;
+
+       curve25519_expand(r->y, p);
+       curve25519_copy(r->z, one);
+       curve25519_square(num, r->y); /* x = y^2 */
+       curve25519_mul(den, num, ge25519_ecd); /* den = dy^2 */
+       curve25519_sub_reduce(num, num, r->z); /* x = y^1 - 1 */
+       curve25519_add(den, den, r->z); /* den = dy^2 + 1 */
+
+       /* Computation of sqrt(num/den) */
+       /* 1.: computation of num^((p-5)/8)*den^((7p-35)/8) = (num*den^7)^((p-5)/8) */
+       curve25519_square(t, den);
+       curve25519_mul(d3, t, den);
+       curve25519_square(r->x, d3);
+       curve25519_mul(r->x, r->x, den);
+       curve25519_mul(r->x, r->x, num);
+       curve25519_pow_two252m3(r->x, r->x);
+
+       /* 2. computation of r->x = num * den^3 * (num*den^7)^((p-5)/8) */
+       curve25519_mul(r->x, r->x, d3);
+       curve25519_mul(r->x, r->x, num);
+
+       /* 3. Check if either of the roots works: */
+       curve25519_square(t, r->x);
+       curve25519_mul(t, t, den);
+       curve25519_sub_reduce(root, t, num);
+       curve25519_contract(check, root);
+       if (!ed25519_verify(check, zero, 32)) {
+               curve25519_add_reduce(t, t, num);
+               curve25519_contract(check, t);
+               if (!ed25519_verify(check, zero, 32))
+                       return 0;
+               curve25519_mul(r->x, r->x, ge25519_sqrtneg1);
+       }
+
+       curve25519_contract(check, r->x);
+       if ((check[0] & 1) == parity) {
+               curve25519_copy(t, r->x);
+               curve25519_neg(r->x, t);
+       }
+       curve25519_mul(r->t, r->x, r->y);
+       return 1;
+}
+
+
+/*
+       scalarmults
+*/
+
+#define S1_SWINDOWSIZE 5
+#define S1_TABLE_SIZE (1<<(S1_SWINDOWSIZE-2))
+#define S2_SWINDOWSIZE 7
+#define S2_TABLE_SIZE (1<<(S2_SWINDOWSIZE-2))
+
+/* computes [s1]p1 + [s2]basepoint */
+static void 
+ge25519_double_scalarmult_vartime(ge25519 *r, const ge25519 *p1, const bignum256modm s1, const bignum256modm s2) {
+       signed char slide1[256], slide2[256];
+       ge25519_pniels pre1[S1_TABLE_SIZE];
+       ge25519 d1;
+       ge25519_p1p1 t;
+       int32_t i;
+
+       contract256_slidingwindow_modm(slide1, s1, S1_SWINDOWSIZE);
+       contract256_slidingwindow_modm(slide2, s2, S2_SWINDOWSIZE);
+
+       ge25519_double(&d1, p1);
+       ge25519_full_to_pniels(pre1, p1);
+       for (i = 0; i < S1_TABLE_SIZE - 1; i++)
+               ge25519_pnielsadd(&pre1[i+1], &d1, &pre1[i]);
+
+       /* set neutral */
+       memset(r, 0, sizeof(ge25519));
+       r->y[0] = 1;
+       r->z[0] = 1;
+
+       i = 255;
+       while ((i >= 0) && !(slide1[i] | slide2[i]))
+               i--;
+
+       for (; i >= 0; i--) {
+               ge25519_double_p1p1(&t, r);
+
+               if (slide1[i]) {
+                       ge25519_p1p1_to_full(r, &t);
+                       ge25519_pnielsadd_p1p1(&t, r, &pre1[abs(slide1[i]) / 2], (unsigned char)slide1[i] >> 7);
+               }
+
+               if (slide2[i]) {
+                       ge25519_p1p1_to_full(r, &t);
+                       ge25519_nielsadd2_p1p1(&t, r, &ge25519_niels_sliding_multiples[abs(slide2[i]) / 2], (unsigned char)slide2[i] >> 7);
+               }
+
+               ge25519_p1p1_to_partial(r, &t);
+       }
+}
+
+
+
+#if !defined(HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS)
+
+static uint32_t
+ge25519_windowb_equal(uint32_t b, uint32_t c) {
+       return ((b ^ c) - 1) >> 31;
+}
+
+static void
+ge25519_scalarmult_base_choose_niels(ge25519_niels *t, const uint8_t table[256][96], uint32_t pos, signed char b) {
+       bignum25519 neg;
+       uint32_t sign = (uint32_t)((unsigned char)b >> 7);
+       uint32_t mask = ~(sign - 1);
+       uint32_t u = (b + mask) ^ mask;
+       uint32_t i;
+
+       /* ysubx, xaddy, t2d in packed form. initialize to ysubx = 1, xaddy = 1, t2d = 0 */
+       uint8_t packed[96] = {0};
+       packed[0] = 1;
+       packed[32] = 1;
+
+       for (i = 0; i < 8; i++)
+               curve25519_move_conditional_bytes(packed, table[(pos * 8) + i], ge25519_windowb_equal(u, i + 1));
+
+       /* expand in to t */
+       curve25519_expand(t->ysubx, packed +  0);
+       curve25519_expand(t->xaddy, packed + 32);
+       curve25519_expand(t->t2d  , packed + 64);
+
+       /* adjust for sign */
+       curve25519_swap_conditional(t->ysubx, t->xaddy, sign);
+       curve25519_neg(neg, t->t2d);
+       curve25519_swap_conditional(t->t2d, neg, sign);
+}
+
+#endif /* HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS */
+
+
+/* computes [s]basepoint */
+static void
+ge25519_scalarmult_base_niels(ge25519 *r, const uint8_t basepoint_table[256][96], const bignum256modm s) {
+       signed char b[64];
+       uint32_t i;
+       ge25519_niels t;
+
+       contract256_window4_modm(b, s);
+
+       ge25519_scalarmult_base_choose_niels(&t, basepoint_table, 0, b[1]);
+       curve25519_sub_reduce(r->x, t.xaddy, t.ysubx);
+       curve25519_add_reduce(r->y, t.xaddy, t.ysubx);
+       memset(r->z, 0, sizeof(bignum25519));
+       curve25519_copy(r->t, t.t2d);
+       r->z[0] = 2;    
+       for (i = 3; i < 64; i += 2) {
+               ge25519_scalarmult_base_choose_niels(&t, basepoint_table, i / 2, b[i]);
+               ge25519_nielsadd2(r, &t);
+       }
+       ge25519_double_partial(r, r);
+       ge25519_double_partial(r, r);
+       ge25519_double_partial(r, r);
+       ge25519_double(r, r);
+       ge25519_scalarmult_base_choose_niels(&t, basepoint_table, 0, b[0]);
+       curve25519_mul(t.t2d, t.t2d, ge25519_ecd);
+       ge25519_nielsadd2(r, &t);
+       for(i = 2; i < 64; i += 2) {
+               ge25519_scalarmult_base_choose_niels(&t, basepoint_table, i / 2, b[i]);
+               ge25519_nielsadd2(r, &t);
+       }
+}
+

diff --git a/crypto/ed25519-donna/src/ed25519-donna-impl-sse2.h b/crypto/ed25519-donna/src/ed25519-donna-impl-sse2.h
new file mode 100644 (file)
index 0000000..5fe3416
--- /dev/null
+++ b/crypto/ed25519-donna/src/ed25519-donna-impl-sse2.h
@@ -0,0 +1,390 @@
+/*
+       conversions
+*/
+
+static void
+ge25519_p1p1_to_partial(ge25519 *r, const ge25519_p1p1 *p) {
+       packed64bignum25519 ALIGN(16) xz, tt, xzout;
+       curve25519_mul(r->y, p->y, p->z);
+       curve25519_tangle64(xz, p->x, p->z);
+       curve25519_tangleone64(tt, p->t);
+       curve25519_mul_packed64(xzout, xz, tt);
+       curve25519_untangle64(r->x, r->z, xzout);
+}
+
+static void 
+ge25519_p1p1_to_full(ge25519 *r, const ge25519_p1p1 *p) {
+       packed64bignum25519 ALIGN(16) zy, xt, xx, zz, ty;
+       curve25519_tangle64(ty, p->t, p->y);
+       curve25519_tangleone64(xx, p->x);
+       curve25519_mul_packed64(xt, xx, ty);
+       curve25519_untangle64(r->x, r->t, xt);
+       curve25519_tangleone64(zz, p->z);
+       curve25519_mul_packed64(zy, zz, ty);
+       curve25519_untangle64(r->z, r->y, zy);
+}
+
+static void
+ge25519_full_to_pniels(ge25519_pniels *p, const ge25519 *r) {
+       curve25519_sub(p->ysubx, r->y, r->x);
+       curve25519_add(p->xaddy, r->x, r->y);
+       curve25519_copy(p->z, r->z);
+       curve25519_mul(p->t2d, r->t, ge25519_ec2d);
+}
+
+/*
+       adding & doubling
+*/
+
+static void
+ge25519_add_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519 *q) {
+       bignum25519 ALIGN(16) a,b,c,d;
+       packed32bignum25519 ALIGN(16) xx, yy, yypxx, yymxx, bd, ac, bdmac, bdpac;
+       packed64bignum25519 ALIGN(16) at, bu, atbu, ptz, qtz, cd;
+
+       curve25519_tangle32(yy, p->y, q->y);
+       curve25519_tangle32(xx, p->x, q->x);
+       curve25519_add_packed32(yypxx, yy, xx);
+       curve25519_sub_packed32(yymxx, yy, xx);
+       curve25519_tangle64_from32(at, bu, yymxx, yypxx);
+       curve25519_mul_packed64(atbu, at, bu);
+       curve25519_untangle64(a, b, atbu);
+       curve25519_tangle64(ptz, p->t, p->z);
+       curve25519_tangle64(qtz, q->t, q->z);
+       curve25519_mul_packed64(cd, ptz, qtz);
+       curve25519_untangle64(c, d, cd);
+       curve25519_mul(c, c, ge25519_ec2d);
+       curve25519_add_reduce(d, d, d);
+       /* reduce, so no after_basic is needed later */
+       curve25519_tangle32(bd, b, d);
+       curve25519_tangle32(ac, a, c);
+       curve25519_sub_packed32(bdmac, bd, ac);
+       curve25519_add_packed32(bdpac, bd, ac);
+       curve25519_untangle32(r->x, r->t, bdmac);
+       curve25519_untangle32(r->y, r->z, bdpac);
+}
+
+
+static void
+ge25519_double_p1p1(ge25519_p1p1 *r, const ge25519 *p) {
+       bignum25519 ALIGN(16) a,b,c,x;
+       packed64bignum25519 ALIGN(16) xy, zx, ab, cx;
+       packed32bignum25519 ALIGN(16) xc, yz, xt, yc, ac, bc;
+
+       curve25519_add(x, p->x, p->y);
+       curve25519_tangle64(xy, p->x, p->y);
+       curve25519_square_packed64(ab, xy);
+       curve25519_untangle64(a, b, ab);
+       curve25519_tangle64(zx, p->z, x);
+       curve25519_square_packed64(cx, zx);
+       curve25519_untangle64(c, x, cx);
+       curve25519_tangle32(bc, b, c);
+       curve25519_tangle32(ac, a, c);
+       curve25519_add_reduce_packed32(yc, bc, ac);
+       curve25519_untangle32(r->y, c, yc);
+       curve25519_sub(r->z, b, a);
+       curve25519_tangle32(yz, r->y, r->z);
+       curve25519_tangle32(xc, x, c);
+       curve25519_sub_after_basic_packed32(xt, xc, yz);
+       curve25519_untangle32(r->x, r->t, xt);
+}
+
+static void
+ge25519_nielsadd2_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519_niels *q, unsigned char signbit) {
+       const bignum25519 *qb = (const bignum25519 *)q;
+       bignum25519 *rb = (bignum25519 *)r;
+       bignum25519 ALIGN(16) a,b,c;
+       packed64bignum25519 ALIGN(16) ab, yx, aybx;
+       packed32bignum25519 ALIGN(16) bd, ac, bdac;
+
+       curve25519_sub(a, p->y, p->x);
+       curve25519_add(b, p->y, p->x);
+       curve25519_tangle64(ab, a, b);
+       curve25519_tangle64(yx, qb[signbit], qb[signbit^1]);
+       curve25519_mul_packed64(aybx, ab, yx);
+       curve25519_untangle64(a, b, aybx);
+       curve25519_add(r->y, b, a);
+       curve25519_add_reduce(r->t, p->z, p->z);
+       curve25519_mul(c, p->t, q->t2d);
+       curve25519_copy(r->z, r->t);
+       curve25519_add(rb[2+signbit], rb[2+signbit], c);
+       curve25519_tangle32(bd, b, rb[2+(signbit^1)]);
+       curve25519_tangle32(ac, a, c);
+       curve25519_sub_packed32(bdac, bd, ac);
+       curve25519_untangle32(r->x, rb[2+(signbit^1)], bdac);
+}
+
+static void
+ge25519_pnielsadd_p1p1(ge25519_p1p1 *r, const ge25519 *p, const ge25519_pniels *q, unsigned char signbit) {
+       const bignum25519 *qb = (const bignum25519 *)q;
+       bignum25519 *rb = (bignum25519 *)r;
+       bignum25519 ALIGN(16) a,b,c;
+       packed64bignum25519 ALIGN(16) ab, yx, aybx, zt, zt2d, tc;
+       packed32bignum25519 ALIGN(16) bd, ac, bdac;
+
+       curve25519_sub(a, p->y, p->x);
+       curve25519_add(b, p->y, p->x);
+       curve25519_tangle64(ab, a, b);
+       curve25519_tangle64(yx, qb[signbit], qb[signbit^1]);
+       curve25519_mul_packed64(aybx, ab, yx);
+       curve25519_untangle64(a, b, aybx);
+       curve25519_add(r->y, b, a);
+       curve25519_tangle64(zt, p->z, p->t);
+       curve25519_tangle64(zt2d, q->z, q->t2d);
+       curve25519_mul_packed64(tc, zt, zt2d);
+       curve25519_untangle64(r->t, c, tc);
+       curve25519_add_reduce(r->t, r->t, r->t);
+       curve25519_copy(r->z, r->t);
+       curve25519_add(rb[2+signbit], rb[2+signbit], c);
+       curve25519_tangle32(bd, b, rb[2+(signbit^1)]);
+       curve25519_tangle32(ac, a, c);
+       curve25519_sub_packed32(bdac, bd, ac);
+       curve25519_untangle32(r->x, rb[2+(signbit^1)], bdac);
+}
+
+static void
+ge25519_double(ge25519 *r, const ge25519 *p) {
+       ge25519_p1p1 ALIGN(16) t;
+       ge25519_double_p1p1(&t, p);
+       ge25519_p1p1_to_full(r, &t);
+}
+
+static void
+ge25519_add(ge25519 *r, const ge25519 *p, const ge25519 *q) {
+       ge25519_p1p1 ALIGN(16) t;
+       ge25519_add_p1p1(&t, p, q);
+       ge25519_p1p1_to_full(r, &t);
+}
+
+static void
+ge25519_double_partial(ge25519 *r, const ge25519 *p) {
+       ge25519_p1p1 ALIGN(16) t;
+       ge25519_double_p1p1(&t, p);
+       ge25519_p1p1_to_partial(r, &t);
+}
+
+static void
+ge25519_nielsadd2(ge25519 *r, const ge25519_niels *q) {
+       packed64bignum25519 ALIGN(16) ab, yx, aybx, eg, ff, hh, xz, ty;
+       packed32bignum25519 ALIGN(16) bd, ac, bdac;
+       bignum25519 ALIGN(16) a,b,c,d,e,f,g,h;
+
+       curve25519_sub(a, r->y, r->x);
+       curve25519_add(b, r->y, r->x);
+       curve25519_tangle64(ab, a, b);
+       curve25519_tangle64(yx, q->ysubx, q->xaddy);
+       curve25519_mul_packed64(aybx, ab, yx);
+       curve25519_untangle64(a, b, aybx);
+       curve25519_add(h, b, a);
+       curve25519_add_reduce(d, r->z, r->z);
+       curve25519_mul(c, r->t, q->t2d);
+       curve25519_add(g, d, c); /* d is reduced, so no need for after_basic */
+       curve25519_tangle32(bd, b, d);
+       curve25519_tangle32(ac, a, c);
+       curve25519_sub_packed32(bdac, bd, ac); /* d is reduced, so no need for after_basic */
+       curve25519_untangle32(e, f, bdac);
+       curve25519_tangle64(eg, e, g);
+       curve25519_tangleone64(ff, f);
+       curve25519_mul_packed64(xz, eg, ff);
+       curve25519_untangle64(r->x, r->z, xz);
+       curve25519_tangleone64(hh, h);
+       curve25519_mul_packed64(ty, eg, hh);
+       curve25519_untangle64(r->t, r->y, ty);
+}
+
+static void
+ge25519_pnielsadd(ge25519_pniels *r, const ge25519 *p, const ge25519_pniels *q) {
+       ge25519_p1p1 ALIGN(16) t;
+       ge25519 ALIGN(16) f;
+       ge25519_pnielsadd_p1p1(&t, p, q, 0);
+       ge25519_p1p1_to_full(&f, &t);
+       ge25519_full_to_pniels(r, &f);
+}
+
+/*
+       pack & unpack
+*/
+
+static void
+ge25519_pack(unsigned char r[32], const ge25519 *p) {
+       bignum25519 ALIGN(16) tx, ty, zi;
+       unsigned char parity[32];
+       curve25519_recip(zi, p->z);
+       curve25519_mul(tx, p->x, zi);
+       curve25519_mul(ty, p->y, zi);
+       curve25519_contract(r, ty);
+       curve25519_contract(parity, tx);
+       r[31] ^= ((parity[0] & 1) << 7);
+}
+
+
+static int
+ge25519_unpack_negative_vartime(ge25519 *r, const unsigned char p[32]) {
+       static const bignum25519 ALIGN(16) one = {1};
+       static const unsigned char zero[32] = {0};
+       unsigned char parity = p[31] >> 7;
+       unsigned char check[32];
+       bignum25519 ALIGN(16) t, root, num, den, d3;
+
+       curve25519_expand(r->y, p);
+       curve25519_copy(r->z, one);
+       curve25519_square_times(num, r->y, 1); /* x = y^2 */
+       curve25519_mul(den, num, ge25519_ecd); /* den = dy^2 */
+       curve25519_sub_reduce(num,  num, r->z); /* x = y^2 - 1 */
+       curve25519_add(den, den, r->z); /* den = dy^2 + 1 */
+
+       /* Computation of sqrt(num/den) */
+       /* 1.: computation of num^((p-5)/8)*den^((7p-35)/8) = (num*den^7)^((p-5)/8) */
+       curve25519_square_times(t, den, 1);
+       curve25519_mul(d3, t, den);
+       curve25519_square_times(r->x, d3, 1);
+       curve25519_mul(r->x, r->x, den);
+       curve25519_mul(r->x, r->x, num);
+       curve25519_pow_two252m3(r->x, r->x);
+
+       /* 2. computation of r->x = t * num * den^3 */
+       curve25519_mul(r->x, r->x, d3);
+       curve25519_mul(r->x, r->x, num);
+
+       /* 3. Check if either of the roots works: */
+       curve25519_square_times(t, r->x, 1);
+       curve25519_mul(t, t, den);
+       curve25519_copy(root, t);
+       curve25519_sub_reduce(root,  root, num);
+       curve25519_contract(check, root);
+       if (!ed25519_verify(check, zero, 32)) {
+               curve25519_add_reduce(t, t, num);
+               curve25519_contract(check, t);
+               if (!ed25519_verify(check, zero, 32))
+                       return 0;
+               curve25519_mul(r->x, r->x, ge25519_sqrtneg1);
+       }
+
+       curve25519_contract(check, r->x);
+       if ((check[0] & 1) == parity) {
+               curve25519_copy(t, r->x);
+               curve25519_neg(r->x, t);
+       }
+       curve25519_mul(r->t, r->x, r->y);
+       return 1;
+}
+
+
+
+/*
+       scalarmults
+*/
+
+#define S1_SWINDOWSIZE 5
+#define S1_TABLE_SIZE (1<<(S1_SWINDOWSIZE-2))
+#define S2_SWINDOWSIZE 7
+#define S2_TABLE_SIZE (1<<(S2_SWINDOWSIZE-2))
+
+static void
+ge25519_double_scalarmult_vartime(ge25519 *r, const ge25519 *p1, const bignum256modm s1, const bignum256modm s2) {
+       signed char slide1[256], slide2[256];
+       ge25519_pniels ALIGN(16) pre1[S1_TABLE_SIZE];
+       ge25519 ALIGN(16) d1;
+       ge25519_p1p1 ALIGN(16) t;
+       int32_t i;
+
+       contract256_slidingwindow_modm(slide1, s1, S1_SWINDOWSIZE);
+       contract256_slidingwindow_modm(slide2, s2, S2_SWINDOWSIZE);
+
+       ge25519_double(&d1, p1);
+       ge25519_full_to_pniels(pre1, p1);
+       for (i = 0; i < S1_TABLE_SIZE - 1; i++)
+               ge25519_pnielsadd(&pre1[i+1], &d1, &pre1[i]);
+
+       /* set neutral */
+       memset(r, 0, sizeof(ge25519));
+       r->y[0] = 1;
+       r->z[0] = 1;
+
+       i = 255;
+       while ((i >= 0) && !(slide1[i] | slide2[i]))
+               i--;
+
+       for (; i >= 0; i--) {
+               ge25519_double_p1p1(&t, r);
+
+               if (slide1[i]) {
+                       ge25519_p1p1_to_full(r, &t);
+                       ge25519_pnielsadd_p1p1(&t, r, &pre1[abs(slide1[i]) / 2], (unsigned char)slide1[i] >> 7);
+               }
+
+               if (slide2[i]) {
+                       ge25519_p1p1_to_full(r, &t);
+                       ge25519_nielsadd2_p1p1(&t, r, &ge25519_niels_sliding_multiples[abs(slide2[i]) / 2], (unsigned char)slide2[i] >> 7);
+               }
+
+               ge25519_p1p1_to_partial(r, &t);
+       }
+}
+
+#if !defined(HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS)
+
+static uint32_t
+ge25519_windowb_equal(uint32_t b, uint32_t c) {
+       return ((b ^ c) - 1) >> 31;
+}
+
+static void
+ge25519_scalarmult_base_choose_niels(ge25519_niels *t, const uint8_t table[256][96], uint32_t pos, signed char b) {
+       bignum25519 ALIGN(16) neg;
+       uint32_t sign = (uint32_t)((unsigned char)b >> 7);
+       uint32_t mask = ~(sign - 1);
+       uint32_t u = (b + mask) ^ mask;
+       uint32_t i;
+
+       /* ysubx, xaddy, t2d in packed form. initialize to ysubx = 1, xaddy = 1, t2d = 0 */
+       uint8_t ALIGN(16) packed[96] = {0};
+       packed[0] = 1;
+       packed[32] = 1;
+
+       for (i = 0; i < 8; i++)
+               curve25519_move_conditional_bytes(packed, table[(pos * 8) + i], ge25519_windowb_equal(u, i + 1));
+
+       /* expand in to t */
+       curve25519_expand(t->ysubx, packed +  0);
+       curve25519_expand(t->xaddy, packed + 32);
+       curve25519_expand(t->t2d  , packed + 64);
+
+       /* adjust for sign */
+       curve25519_swap_conditional(t->ysubx, t->xaddy, sign);
+       curve25519_neg(neg, t->t2d);
+       curve25519_swap_conditional(t->t2d, neg, sign);
+}
+
+#endif /* HAVE_GE25519_SCALARMULT_BASE_CHOOSE_NIELS */
+
+static void
+ge25519_scalarmult_base_niels(ge25519 *r, const uint8_t table[256][96], const bignum256modm s) {
+       signed char b[64];
+       uint32_t i;
+       ge25519_niels ALIGN(16) t;
+
+       contract256_window4_modm(b, s);
+
+       ge25519_scalarmult_base_choose_niels(&t, table, 0, b[1]);
+       curve25519_sub_reduce(r->x, t.xaddy, t.ysubx);
+       curve25519_add_reduce(r->y, t.xaddy, t.ysubx);
+       memset(r->z, 0, sizeof(bignum25519)); 
+       r->z[0] = 2;
+       curve25519_copy(r->t, t.t2d);
+       for (i = 3; i < 64; i += 2) {
+               ge25519_scalarmult_base_choose_niels(&t, table, i / 2, b[i]);
+               ge25519_nielsadd2(r, &t);
+       }
+       ge25519_double_partial(r, r);
+       ge25519_double_partial(r, r);
+       ge25519_double_partial(r, r);
+       ge25519_double(r, r);
+       ge25519_scalarmult_base_choose_niels(&t, table, 0, b[0]);
+       curve25519_mul(t.t2d, t.t2d, ge25519_ecd);
+       ge25519_nielsadd2(r, &t);
+       for(i = 2; i < 64; i += 2) {
+               ge25519_scalarmult_base_choose_niels(&t, table, i / 2, b[i]);
+               ge25519_nielsadd2(r, &t);
+       }
+}

diff --git a/crypto/ed25519-donna/src/ed25519-donna-portable-identify.h b/crypto/ed25519-donna/src/ed25519-donna-portable-identify.h
new file mode 100644 (file)
index 0000000..26a264c
--- /dev/null
+++ b/crypto/ed25519-donna/src/ed25519-donna-portable-identify.h
@@ -0,0 +1,103 @@
+/* os */
+#if defined(_WIN32)    || defined(_WIN64) || defined(__TOS_WIN__) || defined(__WINDOWS__)
+       #define OS_WINDOWS
+#elif defined(sun) || defined(__sun) || defined(__SVR4) || defined(__svr4__)
+       #define OS_SOLARIS
+#else
+       #include <sys/param.h> /* need this to define BSD */
+       #define OS_NIX
+       #if defined(__linux__)
+               #define OS_LINUX
+       #elif defined(BSD)
+               #define OS_BSD
+               #if defined(MACOS_X) || (defined(__APPLE__) & defined(__MACH__))
+                       #define OS_OSX
+               #elif defined(macintosh) || defined(Macintosh)
+                       #define OS_MAC
+               #elif defined(__OpenBSD__)
+                       #define OS_OPENBSD
+               #endif
+       #endif
+#endif
+
+
+/* compiler */
+#if defined(_MSC_VER)
+       #define COMPILER_MSVC
+#endif
+#if defined(__ICC)
+       #define COMPILER_INTEL
+#endif
+#if defined(__GNUC__)
+       #if (__GNUC__ >= 3)
+               #define COMPILER_GCC ((__GNUC__ * 10000) + (__GNUC_MINOR__ * 100) + (__GNUC_PATCHLEVEL__))
+       #else
+               #define COMPILER_GCC ((__GNUC__ * 10000) + (__GNUC_MINOR__ * 100)                        )
+       #endif
+#endif
+#if defined(__PATHCC__)
+       #define COMPILER_PATHCC
+#endif
+#if defined(__clang__)
+       #define COMPILER_CLANG ((__clang_major__ * 10000) + (__clang_minor__ * 100) + (__clang_patchlevel__))
+#endif
+
+
+
+/* cpu */
+#if defined(__amd64__) || defined(__amd64) || defined(__x86_64__ ) || defined(_M_X64)
+       #define CPU_X86_64
+#elif defined(__i586__) || defined(__i686__) || (defined(_M_IX86) && (_M_IX86 >= 500))
+       #define CPU_X86 500
+#elif defined(__i486__) || (defined(_M_IX86) && (_M_IX86 >= 400))
+       #define CPU_X86 400
+#elif defined(__i386__) || (defined(_M_IX86) && (_M_IX86 >= 300)) || defined(__X86__) || defined(_X86_) || defined(__I86__)
+       #define CPU_X86 300
+#elif defined(__ia64__) || defined(_IA64) || defined(__IA64__) || defined(_M_IA64) || defined(__ia64)
+       #define CPU_IA64
+#endif
+
+#if defined(__sparc__) || defined(__sparc) || defined(__sparcv9)
+       #define CPU_SPARC
+       #if defined(__sparcv9)
+               #define CPU_SPARC64
+       #endif
+#endif
+
+#if defined(powerpc) || defined(__PPC__) || defined(__ppc__) || defined(_ARCH_PPC) || defined(__powerpc__) || defined(__powerpc) || defined(POWERPC) || defined(_M_PPC)
+       #define CPU_PPC
+       #if defined(_ARCH_PWR7)
+               #define CPU_POWER7
+       #elif defined(__64BIT__)
+               #define CPU_PPC64
+       #else
+               #define CPU_PPC32
+       #endif
+#endif
+
+#if defined(__hppa__) || defined(__hppa)
+       #define CPU_HPPA
+#endif
+
+#if defined(__alpha__) || defined(__alpha) || defined(_M_ALPHA)
+       #define CPU_ALPHA
+#endif
+
+/* 64 bit cpu */
+#if defined(CPU_X86_64) || defined(CPU_IA64) || defined(CPU_SPARC64) || defined(__64BIT__) || defined(__LP64__) || defined(_LP64) || (defined(_MIPS_SZLONG) && (_MIPS_SZLONG == 64))
+       #define CPU_64BITS
+#endif
+
+#if defined(COMPILER_MSVC)
+       typedef signed char int8_t;
+       typedef unsigned char uint8_t;
+       typedef signed short int16_t;
+       typedef unsigned short uint16_t;
+       typedef signed int int32_t;
+       typedef unsigned int uint32_t;
+       typedef signed __int64 int64_t;
+       typedef unsigned __int64 uint64_t;
+#else
+       #include <stdint.h>
+#endif
+

diff --git a/crypto/ed25519-donna/src/ed25519-donna-portable.h b/crypto/ed25519-donna/src/ed25519-donna-portable.h
new file mode 100644 (file)
index 0000000..0a0f7fc
--- /dev/null
+++ b/crypto/ed25519-donna/src/ed25519-donna-portable.h
@@ -0,0 +1,135 @@
+#include "ed25519-donna-portable-identify.h"
+
+#define mul32x32_64(a,b) (((uint64_t)(a))*(b))
+
+/* platform */
+#if defined(COMPILER_MSVC)
+       #include <intrin.h>
+       #if !defined(_DEBUG)
+               #undef mul32x32_64              
+               #define mul32x32_64(a,b) __emulu(a,b)
+       #endif
+       #undef inline
+       #define inline __forceinline
+       #define DONNA_INLINE __forceinline
+       #define DONNA_NOINLINE __declspec(noinline)
+       #define ALIGN(x) __declspec(align(x))
+       #define ROTL32(a,b) _rotl(a,b)
+       #define ROTR32(a,b) _rotr(a,b)
+#else
+       #include <sys/param.h>
+       #define DONNA_INLINE inline __attribute__((always_inline))
+       #define DONNA_NOINLINE __attribute__((noinline))
+       #define ALIGN(x) __attribute__((aligned(x)))
+       #define ROTL32(a,b) (((a) << (b)) | ((a) >> (32 - b)))
+       #define ROTR32(a,b) (((a) >> (b)) | ((a) << (32 - b)))
+#endif
+
+/* uint128_t */
+#if defined(CPU_64BITS) && !defined(ED25519_FORCE_32BIT)
+       #if defined(COMPILER_CLANG) && (COMPILER_CLANG >= 30100)
+               #define HAVE_NATIVE_UINT128
+               typedef unsigned __int128 uint128_t;
+       #elif defined(COMPILER_MSVC)
+               #define HAVE_UINT128
+               typedef struct uint128_t {
+                       uint64_t lo, hi;
+               } uint128_t;
+               #define mul64x64_128(out,a,b) out.lo = _umul128(a,b,&out.hi);
+               #define shr128_pair(out,hi,lo,shift) out = __shiftright128(lo, hi, shift);
+               #define shl128_pair(out,hi,lo,shift) out = __shiftleft128(lo, hi, shift);
+               #define shr128(out,in,shift) shr128_pair(out, in.hi, in.lo, shift)
+               #define shl128(out,in,shift) shl128_pair(out, in.hi, in.lo, shift)
+               #define add128(a,b) { uint64_t p = a.lo; a.lo += b.lo; a.hi += b.hi + (a.lo < p); }
+               #define add128_64(a,b) { uint64_t p = a.lo; a.lo += b; a.hi += (a.lo < p); }
+               #define lo128(a) (a.lo)
+               #define hi128(a) (a.hi)
+       #elif defined(COMPILER_GCC) && !defined(HAVE_NATIVE_UINT128)
+               #if defined(__SIZEOF_INT128__)
+                       #define HAVE_NATIVE_UINT128
+                       typedef unsigned __int128 uint128_t;
+               #elif (COMPILER_GCC >= 40400)
+                       #define HAVE_NATIVE_UINT128
+                       typedef unsigned uint128_t __attribute__((mode(TI)));
+               #elif defined(CPU_X86_64)
+                       #define HAVE_UINT128
+                       typedef struct uint128_t {
+                               uint64_t lo, hi;
+                       } uint128_t;
+                       #define mul64x64_128(out,a,b) __asm__ ("mulq %3" : "=a" (out.lo), "=d" (out.hi) : "a" (a), "rm" (b));
+                       #define shr128_pair(out,hi,lo,shift) __asm__ ("shrdq %2,%1,%0" : "+r" (lo) : "r" (hi), "J" (shift)); out = lo;
+                       #define shl128_pair(out,hi,lo,shift) __asm__ ("shldq %2,%1,%0" : "+r" (hi) : "r" (lo), "J" (shift)); out = hi;
+                       #define shr128(out,in,shift) shr128_pair(out,in.hi, in.lo, shift)
+                       #define shl128(out,in,shift) shl128_pair(out,in.hi, in.lo, shift)
+                       #define add128(a,b) __asm__ ("addq %4,%2; adcq %5,%3" : "=r" (a.hi), "=r" (a.lo) : "1" (a.lo), "0" (a.hi), "rm" (b.lo), "rm" (b.hi) : "cc");
+                       #define add128_64(a,b) __asm__ ("addq %4,%2; adcq $0,%3" : "=r" (a.hi), "=r" (a.lo) : "1" (a.lo), "0" (a.hi), "rm" (b) : "cc");
+                       #define lo128(a) (a.lo)
+                       #define hi128(a) (a.hi)
+               #endif
+       #endif
+
+       #if defined(HAVE_NATIVE_UINT128)
+               #define HAVE_UINT128
+               #define mul64x64_128(out,a,b) out = (uint128_t)a * b;
+               #define shr128_pair(out,hi,lo,shift) out = (uint64_t)((((uint128_t)hi << 64) | lo) >> (shift));
+               #define shl128_pair(out,hi,lo,shift) out = (uint64_t)(((((uint128_t)hi << 64) | lo) << (shift)) >> 64);
+               #define shr128(out,in,shift) out = (uint64_t)(in >> (shift));
+               #define shl128(out,in,shift) out = (uint64_t)((in << shift) >> 64);
+               #define add128(a,b) a += b;
+               #define add128_64(a,b) a += (uint64_t)b;
+               #define lo128(a) ((uint64_t)a)
+               #define hi128(a) ((uint64_t)(a >> 64))
+       #endif
+
+       #if !defined(HAVE_UINT128)
+               #error Need a uint128_t implementation!
+       #endif
+#endif
+
+/* endian */
+#if !defined(ED25519_OPENSSLRNG)
+static inline void U32TO8_LE(unsigned char *p, const uint32_t v) {
+       p[0] = (unsigned char)(v      );
+       p[1] = (unsigned char)(v >>  8);
+       p[2] = (unsigned char)(v >> 16);
+       p[3] = (unsigned char)(v >> 24);
+}
+#endif
+
+#if !defined(HAVE_UINT128)
+static inline uint32_t U8TO32_LE(const unsigned char *p) {
+       return
+       (((uint32_t)(p[0])      ) | 
+        ((uint32_t)(p[1]) <<  8) |
+        ((uint32_t)(p[2]) << 16) |
+        ((uint32_t)(p[3]) << 24));
+}
+#else
+static inline uint64_t U8TO64_LE(const unsigned char *p) {
+       return
+       (((uint64_t)(p[0])      ) |
+        ((uint64_t)(p[1]) <<  8) |
+        ((uint64_t)(p[2]) << 16) |
+        ((uint64_t)(p[3]) << 24) |
+        ((uint64_t)(p[4]) << 32) |
+        ((uint64_t)(p[5]) << 40) |
+        ((uint64_t)(p[6]) << 48) |
+        ((uint64_t)(p[7]) << 56));
+}
+
+static inline void U64TO8_LE(unsigned char *p, const uint64_t v) {
+       p[0] = (unsigned char)(v      );
+       p[1] = (unsigned char)(v >>  8);
+       p[2] = (unsigned char)(v >> 16);
+       p[3] = (unsigned char)(v >> 24);
+       p[4] = (unsigned char)(v >> 32);
+       p[5] = (unsigned char)(v >> 40);
+       p[6] = (unsigned char)(v >> 48);
+       p[7] = (unsigned char)(v >> 56);
+}
+#endif
+
+#include <stdlib.h>
+#include <string.h>
+
+

diff --git a/crypto/ed25519-donna/src/ed25519-donna.h b/crypto/ed25519-donna/src/ed25519-donna.h
new file mode 100644 (file)
index 0000000..de1120f
--- /dev/null
+++ b/crypto/ed25519-donna/src/ed25519-donna.h
@@ -0,0 +1,115 @@
+/*
+       Public domain by Andrew M. <liquidsun@gmail.com>
+       Modified from the amd64-51-30k implementation by
+               Daniel J. Bernstein
+               Niels Duif
+               Tanja Lange
+               Peter Schwabe
+               Bo-Yin Yang
+*/
+
+
+#include "ed25519-donna-portable.h"
+
+#if defined(ED25519_SSE2)
+#else
+       #if defined(HAVE_UINT128) && !defined(ED25519_FORCE_32BIT)
+               #define ED25519_64BIT
+       #else
+               #define ED25519_32BIT
+       #endif
+#endif
+
+#if !defined(ED25519_NO_INLINE_ASM)
+       /* detect extra features first so un-needed functions can be disabled throughout */
+       #if defined(ED25519_SSE2)
+               #if defined(COMPILER_GCC) && defined(CPU_X86)
+                       #define ED25519_GCC_32BIT_SSE_CHOOSE
+               #elif defined(COMPILER_GCC) && defined(CPU_X86_64)
+                       #define ED25519_GCC_64BIT_SSE_CHOOSE
+               #endif
+       #else
+               #if defined(CPU_X86_64)
+                       #if defined(COMPILER_GCC) 
+                               #if defined(ED25519_64BIT)
+                                       #define ED25519_GCC_64BIT_X86_CHOOSE
+                               #else
+                                       #define ED25519_GCC_64BIT_32BIT_CHOOSE
+                               #endif
+                       #endif
+               #endif
+       #endif
+#endif
+
+#if defined(ED25519_SSE2)
+       #include "curve25519-donna-sse2.h"
+#elif defined(ED25519_64BIT)
+       #include "curve25519-donna-64bit.h"
+#else
+       #include "curve25519-donna-32bit.h"
+#endif
+
+#include "curve25519-donna-helpers.h"
+
+/* separate uint128 check for 64 bit sse2 */
+#if defined(HAVE_UINT128) && !defined(ED25519_FORCE_32BIT)
+       #include "modm-donna-64bit.h"
+#else
+       #include "modm-donna-32bit.h"
+#endif
+
+typedef unsigned char hash_512bits[64];
+
+/*
+       Timing safe memory compare
+*/
+static int
+ed25519_verify(const unsigned char *x, const unsigned char *y, size_t len) {
+       size_t differentbits = 0;
+       while (len--)
+               differentbits |= (*x++ ^ *y++);
+       return (int) (1 & ((differentbits - 1) >> 8));
+}
+
+
+/*
+ * Arithmetic on the twisted Edwards curve -x^2 + y^2 = 1 + dx^2y^2
+ * with d = -(121665/121666) = 37095705934669439343138083508754565189542113879843219016388785533085940283555
+ * Base point: (15112221349535400772501151409588531511454012693041857206046113283949847762202,46316835694926478169428394003475163141307993866256225615783033603165251855960);
+ */
+
+typedef struct ge25519_t {
+       bignum25519 x, y, z, t;
+} ge25519;
+
+typedef struct ge25519_p1p1_t {
+       bignum25519 x, y, z, t;
+} ge25519_p1p1;
+
+typedef struct ge25519_niels_t {
+       bignum25519 ysubx, xaddy, t2d;
+} ge25519_niels;
+
+typedef struct ge25519_pniels_t {
+       bignum25519 ysubx, xaddy, z, t2d;
+} ge25519_pniels;
+
+#include "ed25519-donna-basepoint-table.h"
+
+#if defined(ED25519_64BIT)
+       #include "ed25519-donna-64bit-tables.h"
+       #include "ed25519-donna-64bit-x86.h"
+#else
+       #include "ed25519-donna-32bit-tables.h"
+       #include "ed25519-donna-64bit-x86-32bit.h"
+#endif
+
+
+#if defined(ED25519_SSE2)
+       #include "ed25519-donna-32bit-sse2.h"
+       #include "ed25519-donna-64bit-sse2.h"
+       #include "ed25519-donna-impl-sse2.h"
+#else
+       #include "ed25519-donna-impl-base.h"
+#endif
+

diff --git a/crypto/ed25519-donna/src/ed25519-hash-custom.h b/crypto/ed25519-donna/src/ed25519-hash-custom.h
new file mode 100644 (file)
index 0000000..7dc2491
--- /dev/null
+++ b/crypto/ed25519-donna/src/ed25519-hash-custom.h
@@ -0,0 +1,11 @@
+/*
+       a custom hash must have a 512bit digest and implement:
+
+       struct ed25519_hash_context;
+
+       void ed25519_hash_init(ed25519_hash_context *ctx);
+       void ed25519_hash_update(ed25519_hash_context *ctx, const uint8_t *in, size_t inlen);
+       void ed25519_hash_final(ed25519_hash_context *ctx, uint8_t *hash);
+       void ed25519_hash(uint8_t *hash, const uint8_t *in, size_t inlen);
+*/
+

diff --git a/crypto/ed25519-donna/src/ed25519-hash.h b/crypto/ed25519-donna/src/ed25519-hash.h
new file mode 100644 (file)
index 0000000..6ba8f52
--- /dev/null
+++ b/crypto/ed25519-donna/src/ed25519-hash.h
@@ -0,0 +1,219 @@
+#if defined(ED25519_REFHASH)
+
+/* reference/slow SHA-512. really, do not use this */
+
+#define HASH_BLOCK_SIZE 128
+#define HASH_DIGEST_SIZE 64
+
+typedef struct sha512_state_t {
+       uint64_t H[8];
+       uint64_t T[2];
+       uint32_t leftover;
+       uint8_t buffer[HASH_BLOCK_SIZE];
+} sha512_state;
+
+typedef sha512_state ed25519_hash_context;
+
+static const uint64_t sha512_constants[80] = {
+       0x428a2f98d728ae22ull, 0x7137449123ef65cdull, 0xb5c0fbcfec4d3b2full, 0xe9b5dba58189dbbcull,
+       0x3956c25bf348b538ull, 0x59f111f1b605d019ull, 0x923f82a4af194f9bull, 0xab1c5ed5da6d8118ull,
+       0xd807aa98a3030242ull, 0x12835b0145706fbeull, 0x243185be4ee4b28cull, 0x550c7dc3d5ffb4e2ull,
+       0x72be5d74f27b896full, 0x80deb1fe3b1696b1ull, 0x9bdc06a725c71235ull, 0xc19bf174cf692694ull,
+       0xe49b69c19ef14ad2ull, 0xefbe4786384f25e3ull, 0x0fc19dc68b8cd5b5ull, 0x240ca1cc77ac9c65ull,
+       0x2de92c6f592b0275ull, 0x4a7484aa6ea6e483ull, 0x5cb0a9dcbd41fbd4ull, 0x76f988da831153b5ull,
+       0x983e5152ee66dfabull, 0xa831c66d2db43210ull, 0xb00327c898fb213full, 0xbf597fc7beef0ee4ull,
+       0xc6e00bf33da88fc2ull, 0xd5a79147930aa725ull, 0x06ca6351e003826full, 0x142929670a0e6e70ull,
+       0x27b70a8546d22ffcull, 0x2e1b21385c26c926ull, 0x4d2c6dfc5ac42aedull, 0x53380d139d95b3dfull,
+       0x650a73548baf63deull, 0x766a0abb3c77b2a8ull, 0x81c2c92e47edaee6ull, 0x92722c851482353bull,
+       0xa2bfe8a14cf10364ull, 0xa81a664bbc423001ull, 0xc24b8b70d0f89791ull, 0xc76c51a30654be30ull,
+       0xd192e819d6ef5218ull, 0xd69906245565a910ull, 0xf40e35855771202aull, 0x106aa07032bbd1b8ull,
+       0x19a4c116b8d2d0c8ull, 0x1e376c085141ab53ull, 0x2748774cdf8eeb99ull, 0x34b0bcb5e19b48a8ull,
+       0x391c0cb3c5c95a63ull, 0x4ed8aa4ae3418acbull, 0x5b9cca4f7763e373ull, 0x682e6ff3d6b2b8a3ull,
+       0x748f82ee5defb2fcull, 0x78a5636f43172f60ull, 0x84c87814a1f0ab72ull, 0x8cc702081a6439ecull,
+       0x90befffa23631e28ull, 0xa4506cebde82bde9ull, 0xbef9a3f7b2c67915ull, 0xc67178f2e372532bull,
+       0xca273eceea26619cull, 0xd186b8c721c0c207ull, 0xeada7dd6cde0eb1eull, 0xf57d4f7fee6ed178ull,
+       0x06f067aa72176fbaull, 0x0a637dc5a2c898a6ull, 0x113f9804bef90daeull, 0x1b710b35131c471bull,
+       0x28db77f523047d84ull, 0x32caab7b40c72493ull, 0x3c9ebe0a15c9bebcull, 0x431d67c49c100d4cull,
+       0x4cc5d4becb3e42b6ull, 0x597f299cfc657e2aull, 0x5fcb6fab3ad6faecull, 0x6c44198c4a475817ull
+};
+
+static uint64_t
+sha512_ROTR64(uint64_t x, int k) {
+       return (x >> k) | (x << (64 - k));
+}
+
+static uint64_t
+sha512_LOAD64_BE(const uint8_t *p) {
+       return 
+               ((uint64_t)p[0] << 56) |
+               ((uint64_t)p[1] << 48) |
+               ((uint64_t)p[2] << 40) |
+               ((uint64_t)p[3] << 32) |
+               ((uint64_t)p[4] << 24) |
+               ((uint64_t)p[5] << 16) |
+               ((uint64_t)p[6] <<  8) |
+               ((uint64_t)p[7]      );
+}
+
+static void
+sha512_STORE64_BE(uint8_t *p, uint64_t v) {
+       p[0] = (uint8_t)(v >> 56);
+       p[1] = (uint8_t)(v >> 48);
+       p[2] = (uint8_t)(v >> 40);
+       p[3] = (uint8_t)(v >> 32);
+       p[4] = (uint8_t)(v >> 24);
+       p[5] = (uint8_t)(v >> 16);
+       p[6] = (uint8_t)(v >>  8);
+       p[7] = (uint8_t)(v      );
+}
+
+#define Ch(x,y,z)  (z ^ (x & (y ^ z)))
+#define Maj(x,y,z) (((x | y) & z) | (x & y))
+#define S0(x)      (sha512_ROTR64(x, 28) ^ sha512_ROTR64(x, 34) ^ sha512_ROTR64(x, 39))
+#define S1(x)      (sha512_ROTR64(x, 14) ^ sha512_ROTR64(x, 18) ^ sha512_ROTR64(x, 41))
+#define G0(x)      (sha512_ROTR64(x,  1) ^ sha512_ROTR64(x,  8) ^ (x >>  7))
+#define G1(x)      (sha512_ROTR64(x, 19) ^ sha512_ROTR64(x, 61) ^ (x >>  6))
+#define W0(in,i)   (sha512_LOAD64_BE(&in[i * 8]))
+#define W1(i)      (G1(w[i - 2]) + w[i - 7] + G0(w[i - 15]) + w[i - 16])
+#define STEP(i) \
+       t1 = S0(r[0]) + Maj(r[0], r[1], r[2]); \
+       t0 = r[7] + S1(r[4]) + Ch(r[4], r[5], r[6]) + sha512_constants[i] + w[i]; \
+       r[7] = r[6]; \
+       r[6] = r[5]; \
+       r[5] = r[4]; \
+       r[4] = r[3] + t0; \
+       r[3] = r[2]; \
+       r[2] = r[1]; \
+       r[1] = r[0]; \
+       r[0] = t0 + t1;
+
+static void
+sha512_blocks(sha512_state *S, const uint8_t *in, size_t blocks) {
+       uint64_t r[8], w[80], t0, t1;
+       size_t i;
+
+       for (i = 0; i < 8; i++) r[i] = S->H[i];
+
+       while (blocks--) {
+               for (i =  0; i < 16; i++) { w[i] = W0(in, i); }
+               for (i = 16; i < 80; i++) { w[i] = W1(i); }
+               for (i =  0; i < 80; i++) { STEP(i); }
+               for (i =  0; i <  8; i++) { r[i] += S->H[i]; S->H[i] = r[i]; }
+               S->T[0] += HASH_BLOCK_SIZE * 8;
+               S->T[1] += (!S->T[0]) ? 1 : 0;
+               in += HASH_BLOCK_SIZE;
+       }
+}
+
+static void
+ed25519_hash_init(sha512_state *S) {
+       S->H[0] = 0x6a09e667f3bcc908ull;
+       S->H[1] = 0xbb67ae8584caa73bull;
+       S->H[2] = 0x3c6ef372fe94f82bull;
+       S->H[3] = 0xa54ff53a5f1d36f1ull;
+       S->H[4] = 0x510e527fade682d1ull;
+       S->H[5] = 0x9b05688c2b3e6c1full;
+       S->H[6] = 0x1f83d9abfb41bd6bull;
+       S->H[7] = 0x5be0cd19137e2179ull;
+       S->T[0] = 0;
+       S->T[1] = 0;
+       S->leftover = 0;
+}
+
+static void
+ed25519_hash_update(sha512_state *S, const uint8_t *in, size_t inlen) {
+       size_t blocks, want;
+
+       /* handle the previous data */
+       if (S->leftover) {
+               want = (HASH_BLOCK_SIZE - S->leftover);
+               want = (want < inlen) ? want : inlen;
+               memcpy(S->buffer + S->leftover, in, want);
+               S->leftover += (uint32_t)want;
+               if (S->leftover < HASH_BLOCK_SIZE)
+                       return;
+               in += want;
+               inlen -= want;
+               sha512_blocks(S, S->buffer, 1);
+       }
+
+       /* handle the current data */
+       blocks = (inlen & ~(HASH_BLOCK_SIZE - 1));
+       S->leftover = (uint32_t)(inlen - blocks);
+       if (blocks) {
+               sha512_blocks(S, in, blocks / HASH_BLOCK_SIZE);
+               in += blocks;
+       }
+
+       /* handle leftover data */
+       if (S->leftover)
+               memcpy(S->buffer, in, S->leftover);
+}
+
+static void
+ed25519_hash_final(sha512_state *S, uint8_t *hash) {
+       uint64_t t0 = S->T[0] + (S->leftover * 8), t1 = S->T[1];
+
+       S->buffer[S->leftover] = 0x80;
+       if (S->leftover <= 111) {
+               memset(S->buffer + S->leftover + 1, 0, 111 - S->leftover);
+       } else {
+               memset(S->buffer + S->leftover + 1, 0, 127 - S->leftover);
+               sha512_blocks(S, S->buffer, 1);
+               memset(S->buffer, 0, 112);
+       }
+
+       sha512_STORE64_BE(S->buffer + 112, t1);
+       sha512_STORE64_BE(S->buffer + 120, t0);
+       sha512_blocks(S, S->buffer, 1);
+
+       sha512_STORE64_BE(&hash[ 0], S->H[0]);
+       sha512_STORE64_BE(&hash[ 8], S->H[1]);
+       sha512_STORE64_BE(&hash[16], S->H[2]);
+       sha512_STORE64_BE(&hash[24], S->H[3]);
+       sha512_STORE64_BE(&hash[32], S->H[4]);
+       sha512_STORE64_BE(&hash[40], S->H[5]);
+       sha512_STORE64_BE(&hash[48], S->H[6]);
+       sha512_STORE64_BE(&hash[56], S->H[7]);
+}
+
+static void
+ed25519_hash(uint8_t *hash, const uint8_t *in, size_t inlen) {
+       ed25519_hash_context ctx;
+       ed25519_hash_init(&ctx);
+       ed25519_hash_update(&ctx, in, inlen);
+       ed25519_hash_final(&ctx, hash);
+}
+
+#elif defined(ED25519_CUSTOMHASH)
+
+#include "ed25519-hash-custom.h"
+
+#else
+
+#include <openssl/sha.h>
+
+typedef SHA512_CTX ed25519_hash_context;
+
+static void
+ed25519_hash_init(ed25519_hash_context *ctx) {
+       SHA512_Init(ctx);
+}
+
+static void
+ed25519_hash_update(ed25519_hash_context *ctx, const uint8_t *in, size_t inlen) {
+       SHA512_Update(ctx, in, inlen);
+}
+
+static void
+ed25519_hash_final(ed25519_hash_context *ctx, uint8_t *hash) {
+       SHA512_Final(hash, ctx);
+}
+
+static void
+ed25519_hash(uint8_t *hash, const uint8_t *in, size_t inlen) {
+       SHA512(in, inlen, hash);
+}
+
+#endif
+

diff --git a/crypto/ed25519-donna/src/ed25519-randombytes-custom.h b/crypto/ed25519-donna/src/ed25519-randombytes-custom.h
new file mode 100644 (file)
index 0000000..9f51063
--- /dev/null
+++ b/crypto/ed25519-donna/src/ed25519-randombytes-custom.h
@@ -0,0 +1,8 @@
+/*
+       a custom randombytes must implement:
+
+       void ED25519_FN(ed25519_randombytes_unsafe) (void *p, size_t len);
+
+       ed25519_randombytes_unsafe is used by the batch verification function
+       to create random scalars
+*/

diff --git a/crypto/ed25519-donna/src/ed25519-randombytes.h b/crypto/ed25519-donna/src/ed25519-randombytes.h
new file mode 100644 (file)
index 0000000..1dc6290
--- /dev/null
+++ b/crypto/ed25519-donna/src/ed25519-randombytes.h
@@ -0,0 +1,91 @@
+#if defined(ED25519_TEST)
+/*
+       ISAAC+ "variant", the paper is not clear on operator precedence and other
+       things. This is the "first in, first out" option!
+
+       Not threadsafe or securely initialized, only for deterministic testing
+*/
+typedef struct isaacp_state_t {
+       uint32_t state[256];
+       unsigned char buffer[1024];
+       uint32_t a, b, c;
+       size_t left;
+} isaacp_state;
+
+#define isaacp_step(offset, mix) \
+       x = mm[i + offset]; \
+       a = (a ^ (mix)) + (mm[(i + offset + 128) & 0xff]); \
+       y = (a ^ b) + mm[(x >> 2) & 0xff]; \
+       mm[i + offset] = y; \
+       b = (x + a) ^ mm[(y >> 10) & 0xff]; \
+       U32TO8_LE(out + (i + offset) * 4, b);
+
+static void
+isaacp_mix(isaacp_state *st) {
+       uint32_t i, x, y;
+       uint32_t a = st->a, b = st->b, c = st->c;
+       uint32_t *mm = st->state;
+       unsigned char *out = st->buffer;
+
+       c = c + 1;
+       b = b + c;
+
+       for (i = 0; i < 256; i += 4) {
+               isaacp_step(0, ROTL32(a,13))
+               isaacp_step(1, ROTR32(a, 6))
+               isaacp_step(2, ROTL32(a, 2))
+               isaacp_step(3, ROTR32(a,16))
+       }
+
+       st->a = a;
+       st->b = b;
+       st->c = c;
+       st->left = 1024;
+}
+
+static void
+isaacp_random(isaacp_state *st, void *p, size_t len) {
+       size_t use;
+       unsigned char *c = (unsigned char *)p;
+       while (len) {
+               use = (len > st->left) ? st->left : len;
+               memcpy(c, st->buffer + (sizeof(st->buffer) - st->left), use);
+
+               st->left -= use;
+               c += use;
+               len -= use;
+
+               if (!st->left)
+                       isaacp_mix(st);
+       }
+}
+
+void
+ED25519_FN(ed25519_randombytes_unsafe) (void *p, size_t len) {
+       static int initialized = 0;
+       static isaacp_state rng;
+
+       if (!initialized) {
+               memset(&rng, 0, sizeof(rng));
+               isaacp_mix(&rng);
+               isaacp_mix(&rng);
+               initialized = 1;
+       }
+
+       isaacp_random(&rng, p, len);
+}
+#elif defined(ED25519_CUSTOMRANDOM)
+
+#include "ed25519-randombytes-custom.h"
+
+#else
+
+#include <openssl/rand.h>
+
+void
+ED25519_FN(ed25519_randombytes_unsafe) (void *p, size_t len) {
+
+  RAND_bytes(p, (int) len);
+
+}
+#endif

diff --git a/crypto/ed25519-donna/src/ed25519.c b/crypto/ed25519-donna/src/ed25519.c
new file mode 100644 (file)
index 0000000..58a755b
--- /dev/null
+++ b/crypto/ed25519-donna/src/ed25519.c
@@ -0,0 +1,150 @@
+/*
+       Public domain by Andrew M. <liquidsun@gmail.com>
+
+       Ed25519 reference implementation using Ed25519-donna
+*/
+
+
+/* define ED25519_SUFFIX to have it appended to the end of each public function */
+#if !defined(ED25519_SUFFIX)
+#define ED25519_SUFFIX 
+#endif
+
+#define ED25519_FN3(fn,suffix) fn##suffix
+#define ED25519_FN2(fn,suffix) ED25519_FN3(fn,suffix)
+#define ED25519_FN(fn)         ED25519_FN2(fn,ED25519_SUFFIX)
+
+#include "ed25519-donna.h"
+#include "ed25519.h"
+#include "ed25519-randombytes.h"
+#include "ed25519-hash.h"
+
+/*
+       Generates a (extsk[0..31]) and aExt (extsk[32..63])
+*/
+
+DONNA_INLINE static void
+ed25519_extsk(hash_512bits extsk, const ed25519_secret_key sk) {
+       ed25519_hash(extsk, sk, 32);
+       extsk[0] &= 248;
+       extsk[31] &= 127;
+       extsk[31] |= 64;
+}
+
+static void
+ed25519_hram(hash_512bits hram, const ed25519_signature RS, const ed25519_public_key pk, const unsigned char *m, size_t mlen) {
+       ed25519_hash_context ctx;
+       ed25519_hash_init(&ctx);
+       ed25519_hash_update(&ctx, RS, 32);
+       ed25519_hash_update(&ctx, pk, 32);
+       ed25519_hash_update(&ctx, m, mlen);
+       ed25519_hash_final(&ctx, hram);
+}
+
+void
+ED25519_FN(ed25519_publickey) (const ed25519_secret_key sk, ed25519_public_key pk) {
+       bignum256modm a;
+       ge25519 ALIGN(16) A;
+       hash_512bits extsk;
+
+       /* A = aB */
+       ed25519_extsk(extsk, sk);
+       expand256_modm(a, extsk, 32);
+       ge25519_scalarmult_base_niels(&A, ge25519_niels_base_multiples, a);
+       ge25519_pack(pk, &A);
+}
+
+
+void
+ED25519_FN(ed25519_sign) (const unsigned char *m, size_t mlen, const ed25519_secret_key sk, const ed25519_public_key pk, ed25519_signature RS) {
+       ed25519_hash_context ctx;
+       bignum256modm r, S, a;
+       ge25519 ALIGN(16) R;
+       hash_512bits extsk, hashr, hram;
+
+       ed25519_extsk(extsk, sk);
+
+       /* r = H(aExt[32..64], m) */
+       ed25519_hash_init(&ctx);
+       ed25519_hash_update(&ctx, extsk + 32, 32);
+       ed25519_hash_update(&ctx, m, mlen);
+       ed25519_hash_final(&ctx, hashr);
+       expand256_modm(r, hashr, 64);
+
+       /* R = rB */
+       ge25519_scalarmult_base_niels(&R, ge25519_niels_base_multiples, r);
+       ge25519_pack(RS, &R);
+
+       /* S = H(R,A,m).. */
+       ed25519_hram(hram, RS, pk, m, mlen);
+       expand256_modm(S, hram, 64);
+
+       /* S = H(R,A,m)a */
+       expand256_modm(a, extsk, 32);
+       mul256_modm(S, S, a);
+
+       /* S = (r + H(R,A,m)a) */
+       add256_modm(S, S, r);
+
+       /* S = (r + H(R,A,m)a) mod L */ 
+       contract256_modm(RS + 32, S);
+}
+
+int
+ED25519_FN(ed25519_sign_open) (const unsigned char *m, size_t mlen, const ed25519_public_key pk, const ed25519_signature RS) {
+       ge25519 ALIGN(16) R, A;
+       hash_512bits hash;
+       bignum256modm hram, S;
+       unsigned char checkR[32];
+
+       if ((RS[63] & 224) || !ge25519_unpack_negative_vartime(&A, pk))
+               return -1;
+
+       /* hram = H(R,A,m) */
+       ed25519_hram(hash, RS, pk, m, mlen);
+       expand256_modm(hram, hash, 64);
+
+       /* S */
+       expand256_modm(S, RS + 32, 32);
+
+       /* SB - H(R,A,m)A */
+       ge25519_double_scalarmult_vartime(&R, &A, hram, S);
+       ge25519_pack(checkR, &R);
+
+       /* check that R = SB - H(R,A,m)A */
+       return ed25519_verify(RS, checkR, 32) ? 0 : -1;
+}
+
+#include "ed25519-donna-batchverify.h"
+
+/*
+       Fast Curve25519 basepoint scalar multiplication
+*/
+
+void
+ED25519_FN(curved25519_scalarmult_basepoint) (curved25519_key pk, const curved25519_key e) {
+       curved25519_key ec;
+       bignum256modm s;
+       bignum25519 ALIGN(16) yplusz, zminusy;
+       ge25519 ALIGN(16) p;
+       size_t i;
+
+       /* clamp */
+       for (i = 0; i < 32; i++) ec[i] = e[i];
+       ec[0] &= 248;
+       ec[31] &= 127;
+       ec[31] |= 64;
+
+       expand_raw256_modm(s, ec);
+
+       /* scalar * basepoint */
+       ge25519_scalarmult_base_niels(&p, ge25519_niels_base_multiples, s);
+
+       /* u = (y + z) / (z - y) */
+       curve25519_add(yplusz, p.y, p.z);
+       curve25519_sub(zminusy, p.z, p.y);
+       curve25519_recip(zminusy, zminusy);
+       curve25519_mul(yplusz, yplusz, zminusy);
+       curve25519_contract(pk, yplusz);
+}
+

diff --git a/crypto/ed25519-donna/src/ed25519.h b/crypto/ed25519-donna/src/ed25519.h
new file mode 100644 (file)
index 0000000..dc86675
--- /dev/null
+++ b/crypto/ed25519-donna/src/ed25519.h
@@ -0,0 +1,30 @@
+#ifndef ED25519_H
+#define ED25519_H
+
+#include <stdlib.h>
+
+#if defined(__cplusplus)
+extern "C" {
+#endif
+
+typedef unsigned char ed25519_signature[64];
+typedef unsigned char ed25519_public_key[32];
+typedef unsigned char ed25519_secret_key[32];
+
+typedef unsigned char curved25519_key[32];
+
+void ed25519_publickey(const ed25519_secret_key sk, ed25519_public_key pk);
+int ed25519_sign_open(const unsigned char *m, size_t mlen, const ed25519_public_key pk, const ed25519_signature RS);
+void ed25519_sign(const unsigned char *m, size_t mlen, const ed25519_secret_key sk, const ed25519_public_key pk, ed25519_signature RS);
+
+int ed25519_sign_open_batch(const unsigned char **m, size_t *mlen, const unsigned char **pk, const unsigned char **RS, size_t num, int *valid);
+
+void ed25519_randombytes_unsafe(void *out, size_t count);
+
+void curved25519_scalarmult_basepoint(curved25519_key pk, const curved25519_key e);
+
+#if defined(__cplusplus)
+}
+#endif
+
+#endif // ED25519_H

diff --git a/crypto/ed25519-donna/src/fuzz/README.md b/crypto/ed25519-donna/src/fuzz/README.md
new file mode 100644 (file)
index 0000000..306ddfe
--- /dev/null
+++ b/crypto/ed25519-donna/src/fuzz/README.md
@@ -0,0 +1,173 @@
+This code fuzzes ed25519-donna (and optionally ed25519-donna-sse2) against the ref10 implementations of
+[curve25519](https://github.com/floodyberry/supercop/tree/master/crypto_scalarmult/curve25519/ref10) and 
+[ed25519](https://github.com/floodyberry/supercop/tree/master/crypto_sign/ed25519/ref10).
+
+Curve25519 tests that generating a public key from a secret key
+
+# Building
+
+## *nix + PHP
+
+`php build-nix.php (required parameters) (optional parameters)`
+
+Required parameters:
+
+* `--function=[curve25519,ed25519]`
+* `--bits=[32,64]`
+
+Optional parameters:
+
+* `--with-sse2`
+
+    Also fuzz against ed25519-donna-sse2
+* `--with-openssl`
+
+    Build with OpenSSL's SHA-512.
+
+    Default: Reference SHA-512 implementation (slow!)
+
+* `--compiler=[gcc,clang,icc]`
+
+    Default: gcc
+
+* `--no-asm`
+
+    Do not use platform specific assembler
+
+
+example:
+    
+    php build-nix.php --bits=64 --function=ed25519 --with-sse2 --compiler=icc 
+
+## Windows
+
+Create a project with access to the ed25519 files.
+
+If you are not using OpenSSL, add the `ED25519_REFHASH` define to the projects 
+"Properties/Preprocessor/Preprocessor Definitions" option
+
+Add the following files to the project:
+
+* `fuzz/curve25519-ref10.c`
+* `fuzz/ed25519-ref10.c`
+* `fuzz/ed25519-donna.c`
+* `fuzz/ed25519-donna-sse2.c` (optional)
+* `fuzz-[curve25519/ed25519].c` (depending on which you want to fuzz)
+
+If you are also fuzzing against ed25519-donna-sse2, add the `ED25519_SSE2` define for `fuzz-[curve25519/ed25519].c` under 
+its "Properties/Preprocessor/Preprocessor Definitions" option.
+
+# Running
+
+If everything agrees, the program will only output occasional status dots (every 0x1000 passes) 
+and a 64bit progress count (every 0x20000 passes):
+
+    fuzzing:  ref10 curved25519 curved25519-sse2
+    
+    ................................ [0000000000020000]
+    ................................ [0000000000040000]
+    ................................ [0000000000060000]
+    ................................ [0000000000080000]
+    ................................ [00000000000a0000]
+    ................................ [00000000000c0000]
+ 
+If any of the implementations do not agree with the ref10 implementation, the program will dump
+the random data that was used, the data generated by the ref10 implementation, and diffs of the 
+ed25519-donna data against the ref10 data.
+
+## Example errors
+
+These are example error dumps (with intentionally introduced errors).
+
+### Ed25519
+
+Random data:
+
+* sk, or Secret Key
+* m, or Message
+
+Generated data:
+
+* pk, or Public Key
+* sig, or Signature
+* valid, or if the signature of the message is valid with the public key
+
+Dump:
+
+    sk:
+    0x3b,0xb7,0x17,0x7a,0x66,0xdc,0xb7,0x9a,0x90,0x25,0x07,0x99,0x96,0xf3,0x92,0xef,
+    0x78,0xf8,0xad,0x6c,0x35,0x87,0x81,0x67,0x03,0xe6,0x95,0xba,0x06,0x18,0x7c,0x9c,
+    
+    m:
+    0x7c,0x8d,0x3d,0xe1,0x92,0xee,0x7a,0xb8,0x4d,0xc9,0xfb,0x02,0x34,0x1e,0x5a,0x91,
+    0xee,0x01,0xa6,0xb8,0xab,0x37,0x3f,0x3d,0x6d,0xa2,0x47,0xe3,0x27,0x93,0x7c,0xb7,
+    0x77,0x07,0xb6,0x88,0x41,0x22,0xf3,0x3f,0xce,0xcb,0x6b,0x3e,0x2b,0x23,0x68,0x7f,
+    0x5b,0xb9,0xda,0x04,0xbb,0xae,0x42,0x50,0xf5,0xe9,0xc5,0x11,0xbd,0x52,0x76,0x98,
+    0xf1,0x87,0x09,0xb9,0x89,0x0a,0x52,0x69,0x01,0xce,0xe0,0x4a,0xa6,0x46,0x5a,0xe1,
+    0x63,0x14,0xe0,0x81,0x52,0xec,0xcd,0xcf,0x70,0x54,0x7d,0xa3,0x49,0x8b,0xf0,0x89,
+    0x70,0x07,0x12,0x2a,0xd9,0xaa,0x16,0x01,0xb2,0x16,0x3a,0xbb,0xfc,0xfa,0x13,0x5b,
+    0x69,0x83,0x92,0x70,0x95,0x76,0xa0,0x8e,0x16,0x79,0xcc,0xaa,0xb5,0x7c,0xf8,0x7a,
+    
+    ref10:
+    pk:
+    0x71,0xb0,0x5e,0x62,0x1b,0xe3,0xe7,0x36,0x91,0x8b,0xc0,0x13,0x36,0x0c,0xc9,0x04,
+    0x16,0xf5,0xff,0x48,0x0c,0x83,0x6b,0x88,0x53,0xa2,0xc6,0x0f,0xf7,0xac,0x42,0x04,
+    
+    sig:
+    0x3e,0x05,0xc5,0x37,0x16,0x0b,0x29,0x30,0x89,0xa3,0xe7,0x83,0x08,0x16,0xdd,0x96,
+    0x02,0xfa,0x0d,0x44,0x2c,0x43,0xaa,0x80,0x93,0x04,0x58,0x22,0x09,0xbf,0x11,0xa5,
+    0xcc,0xa5,0x3c,0x9f,0xa0,0xa4,0x64,0x5a,0x4a,0xdb,0x20,0xfb,0xc7,0x9b,0xfd,0x3f,
+    0x08,0xae,0xc4,0x3c,0x1e,0xd8,0xb6,0xb4,0xd2,0x6d,0x80,0x92,0xcb,0x71,0xf3,0x02,
+    
+    valid: yes
+    
+    ed25519-donna:
+    pk diff:
+    ____,____,____,____,____,____,____,____,____,____,____,____,____,____,____,____,
+    ____,____,____,____,____,____,____,____,____,____,____,____,____,____,____,____,
+    
+    sig diff:
+    0x2c,0xb9,0x25,0x14,0xd0,0x94,0xeb,0xfe,0x46,0x02,0xc2,0xe8,0xa3,0xeb,0xbf,0xb5,
+    0x72,0x84,0xbf,0xc1,0x8a,0x32,0x30,0x99,0xf7,0x58,0xfe,0x06,0xa8,0xdc,0xdc,0xab,
+    0xb5,0x57,0x03,0x33,0x87,0xce,0x54,0x55,0x6a,0x69,0x8a,0xc4,0xb7,0x2a,0xed,0x97,
+    0xb4,0x68,0xe7,0x52,0x7a,0x07,0x55,0x3b,0xa2,0x94,0xd6,0x5e,0xa1,0x61,0x80,0x08,
+    
+    valid: no
+
+In this case, the generated public key matches, but the generated signature is completely 
+different and does not validate.
+
+### Curve25519
+
+Random data:
+
+* sk, or Secret Key
+
+Generated data:
+
+* pk, or Public Key
+
+Dump:
+
+    sk:
+    0x44,0xec,0x0b,0x0e,0xa2,0x0e,0x9c,0x5b,0x8c,0xce,0x7b,0x1d,0x68,0xae,0x0f,0x9e,
+    0x81,0xe2,0x04,0x76,0xda,0x87,0xa4,0x9e,0xc9,0x4f,0x3b,0xf9,0xc3,0x89,0x63,0x70,
+    
+    
+    ref10:
+    0x24,0x55,0x55,0xc0,0xf9,0x80,0xaf,0x02,0x43,0xee,0x8c,0x7f,0xc1,0xad,0x90,0x95,
+    0x57,0x91,0x14,0x2e,0xf2,0x14,0x22,0x80,0xdd,0x4e,0x3c,0x85,0x71,0x84,0x8c,0x62,
+    
+    
+    curved25519 diff:
+    0x12,0xd1,0x61,0x2b,0x16,0xb3,0xd8,0x29,0xf8,0xa3,0xba,0x70,0x4e,0x49,0x4f,0x43,
+    0xa1,0x3c,0x6b,0x42,0x11,0x61,0xcc,0x30,0x87,0x73,0x46,0xfb,0x85,0xc7,0x9a,0x35,
+    
+    
+    curved25519-sse2 diff:
+    ____,____,____,____,____,____,____,____,____,____,____,____,____,____,____,____,
+    ____,____,____,____,____,____,____,____,____,____,____,____,____,____,____,____,
+
+
+In this case, curved25519 is totally wrong, while curved25519-sse2 matches the reference 
+implementation.
\ No newline at end of file

diff --git a/crypto/ed25519-donna/src/fuzz/build-nix.php b/crypto/ed25519-donna/src/fuzz/build-nix.php
new file mode 100644 (file)
index 0000000..c69144e
--- /dev/null
+++ b/crypto/ed25519-donna/src/fuzz/build-nix.php
@@ -0,0 +1,134 @@
+<?php
+       function echoln($str) {
+               echo $str;
+               echo "\n";
+       }
+
+       function usage($reason) {
+               echoln("Usage: php build-nix.php [flags]");
+               echoln("Flags in parantheses are optional");
+               echoln("");
+               echoln("  --bits=[32,64]");
+               echoln("  --function=[curve25519,ed25519]");
+               echoln(" (--compiler=[*gcc,clang,icc])        which compiler to use, gcc is default");
+               echoln(" (--with-openssl)                     use openssl for SHA512");
+               echoln(" (--with-sse2)                        additionally fuzz against SSE2");
+               echoln(" (--no-asm)                           don't use platform specific asm");
+               echoln("");
+               if ($reason)
+                       echoln($reason);
+       }
+
+       function cleanup() {
+               system("rm -f *.o");
+       }
+
+       function runcmd($desc, $cmd) {
+               echoln($desc);
+
+               $ret = 0;
+               system($cmd, $ret);
+               if ($ret) {
+                       cleanup();
+                       exit;
+               }
+       }
+
+       class argument {
+               var $set, $value;
+       }
+
+       class multiargument extends argument {
+               function multiargument($flag, $legal_values) {
+                       global $argc, $argv;
+
+                       $this->set = false;
+
+                       $map = array();
+                       foreach($legal_values as $value)
+                               $map[$value] = true;
+
+                       for ($i = 1; $i < $argc; $i++) {
+                               if (!preg_match("!--".$flag."=(.*)!", $argv[$i], $m))
+                                       continue;
+                               if (isset($map[$m[1]])) {
+                                       $this->value = $m[1];
+                                       $this->set = true;
+                                       return;
+                               } else {
+                                       usage("{$m[1]} is not a valid parameter to --{$flag}!");
+                                       exit(1);
+                               }
+                       }
+               }
+       }
+
+       class flag extends argument {
+               function flag($flag) {
+                       global $argc, $argv;
+
+                       $this->set = false;
+
+                       $flag = "--{$flag}";
+                       for ($i = 1; $i < $argc; $i++) {
+                               if ($argv[$i] !== $flag)
+                                       continue;
+                               $this->value = true;
+                               $this->set = true;
+                               return;
+                       }
+               }
+       }
+
+       $bits = new multiargument("bits", array("32", "64"));
+       $function = new multiargument("function", array("curve25519", "ed25519"));
+       $compiler = new multiargument("compiler", array("gcc", "clang", "icc"));
+       $with_sse2 = new flag("with-sse2");
+       $with_openssl = new flag("with-openssl");
+       $no_asm = new flag("no-asm");
+
+       $err = "";
+       if (!$bits->set)
+               $err .= "--bits not set\n";
+       if (!$function->set)
+               $err .= "--function not set\n";
+
+       if ($err !== "") {
+               usage($err);
+               exit;
+       }
+
+       $compile = ($compiler->set) ? $compiler->value : "gcc";
+       $link = "";
+       $flags = "-O3 -m{$bits->value}";
+       $ret = 0;
+
+       if ($with_openssl->set) $link .= " -lssl -lcrypto";
+       if (!$with_openssl->set) $flags .= " -DED25519_REFHASH -DED25519_TEST";
+       if ($no_asm->set) $flags .= " -DED25519_NO_INLINE_ASM";
+
+       if ($function->value === "curve25519") {
+               runcmd("building ref10..", "{$compile} {$flags} curve25519-ref10.c -c -o curve25519-ref10.o");
+               runcmd("building ed25519..", "{$compile} {$flags} ed25519-donna.c -c -o ed25519.o");
+               if ($with_sse2->set) {
+                       runcmd("building ed25519-sse2..", "{$compile} {$flags} ed25519-donna-sse2.c -c -o ed25519-sse2.o -msse2");
+                       $flags .= " -DED25519_SSE2";
+                       $link .= " ed25519-sse2.o";
+               }
+               runcmd("linking..", "{$compile} {$flags} {$link} fuzz-curve25519.c ed25519.o curve25519-ref10.o -o fuzz-curve25519");
+               echoln("fuzz-curve25519 built.");
+       } else  if ($function->value === "ed25519") {
+               runcmd("building ref10..", "{$compile} {$flags} ed25519-ref10.c -c -o ed25519-ref10.o");
+               runcmd("building ed25519..", "{$compile} {$flags} ed25519-donna.c -c -o ed25519.o");
+               if ($with_sse2->set) {
+                       runcmd("building ed25519-sse2..", "{$compile} {$flags} ed25519-donna-sse2.c -c -o ed25519-sse2.o -msse2");
+                       $flags .= " -DED25519_SSE2";
+                       $link .= " ed25519-sse2.o";
+               }
+               runcmd("linking..", "{$compile} {$flags} {$link} fuzz-ed25519.c ed25519.o ed25519-ref10.o -o fuzz-ed25519");
+               echoln("fuzz-ed25519 built.");
+       }
+
+
+       cleanup();
+?>

diff --git a/crypto/ed25519-donna/src/fuzz/curve25519-ref10.c b/crypto/ed25519-donna/src/fuzz/curve25519-ref10.c
new file mode 100644 (file)
index 0000000..efefce6
--- /dev/null
+++ b/crypto/ed25519-donna/src/fuzz/curve25519-ref10.c
@@ -0,0 +1,1272 @@
+#include <stdint.h>
+
+typedef int32_t crypto_int32;
+typedef int64_t crypto_int64;
+typedef uint64_t crypto_uint64;
+
+typedef crypto_int32 fe[10];
+
+/*
+h = 0
+*/
+
+void fe_0(fe h)
+{
+  h[0] = 0;
+  h[1] = 0;
+  h[2] = 0;
+  h[3] = 0;
+  h[4] = 0;
+  h[5] = 0;
+  h[6] = 0;
+  h[7] = 0;
+  h[8] = 0;
+  h[9] = 0;
+}
+
+/*
+h = 1
+*/
+
+void fe_1(fe h)
+{
+  h[0] = 1;
+  h[1] = 0;
+  h[2] = 0;
+  h[3] = 0;
+  h[4] = 0;
+  h[5] = 0;
+  h[6] = 0;
+  h[7] = 0;
+  h[8] = 0;
+  h[9] = 0;
+}
+
+/*
+h = f + g
+Can overlap h with f or g.
+
+Preconditions:
+   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+   |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+void fe_add(fe h,fe f,fe g)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 g0 = g[0];
+  crypto_int32 g1 = g[1];
+  crypto_int32 g2 = g[2];
+  crypto_int32 g3 = g[3];
+  crypto_int32 g4 = g[4];
+  crypto_int32 g5 = g[5];
+  crypto_int32 g6 = g[6];
+  crypto_int32 g7 = g[7];
+  crypto_int32 g8 = g[8];
+  crypto_int32 g9 = g[9];
+  crypto_int32 h0 = f0 + g0;
+  crypto_int32 h1 = f1 + g1;
+  crypto_int32 h2 = f2 + g2;
+  crypto_int32 h3 = f3 + g3;
+  crypto_int32 h4 = f4 + g4;
+  crypto_int32 h5 = f5 + g5;
+  crypto_int32 h6 = f6 + g6;
+  crypto_int32 h7 = f7 + g7;
+  crypto_int32 h8 = f8 + g8;
+  crypto_int32 h9 = f9 + g9;
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+/*
+h = f
+*/
+
+void fe_copy(fe h,fe f)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  h[0] = f0;
+  h[1] = f1;
+  h[2] = f2;
+  h[3] = f3;
+  h[4] = f4;
+  h[5] = f5;
+  h[6] = f6;
+  h[7] = f7;
+  h[8] = f8;
+  h[9] = f9;
+}
+
+
+/*
+Replace (f,g) with (g,f) if b == 1;
+replace (f,g) with (f,g) if b == 0.
+
+Preconditions: b in {0,1}.
+*/
+
+void fe_cswap(fe f,fe g,unsigned int b)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 g0 = g[0];
+  crypto_int32 g1 = g[1];
+  crypto_int32 g2 = g[2];
+  crypto_int32 g3 = g[3];
+  crypto_int32 g4 = g[4];
+  crypto_int32 g5 = g[5];
+  crypto_int32 g6 = g[6];
+  crypto_int32 g7 = g[7];
+  crypto_int32 g8 = g[8];
+  crypto_int32 g9 = g[9];
+  crypto_int32 x0 = f0 ^ g0;
+  crypto_int32 x1 = f1 ^ g1;
+  crypto_int32 x2 = f2 ^ g2;
+  crypto_int32 x3 = f3 ^ g3;
+  crypto_int32 x4 = f4 ^ g4;
+  crypto_int32 x5 = f5 ^ g5;
+  crypto_int32 x6 = f6 ^ g6;
+  crypto_int32 x7 = f7 ^ g7;
+  crypto_int32 x8 = f8 ^ g8;
+  crypto_int32 x9 = f9 ^ g9;
+  b = -b;
+  x0 &= b;
+  x1 &= b;
+  x2 &= b;
+  x3 &= b;
+  x4 &= b;
+  x5 &= b;
+  x6 &= b;
+  x7 &= b;
+  x8 &= b;
+  x9 &= b;
+  f[0] = f0 ^ x0;
+  f[1] = f1 ^ x1;
+  f[2] = f2 ^ x2;
+  f[3] = f3 ^ x3;
+  f[4] = f4 ^ x4;
+  f[5] = f5 ^ x5;
+  f[6] = f6 ^ x6;
+  f[7] = f7 ^ x7;
+  f[8] = f8 ^ x8;
+  f[9] = f9 ^ x9;
+  g[0] = g0 ^ x0;
+  g[1] = g1 ^ x1;
+  g[2] = g2 ^ x2;
+  g[3] = g3 ^ x3;
+  g[4] = g4 ^ x4;
+  g[5] = g5 ^ x5;
+  g[6] = g6 ^ x6;
+  g[7] = g7 ^ x7;
+  g[8] = g8 ^ x8;
+  g[9] = g9 ^ x9;
+}
+
+static crypto_uint64 load_3(const unsigned char *in)
+{
+  crypto_uint64 result;
+  result = (crypto_uint64) in[0];
+  result |= ((crypto_uint64) in[1]) << 8;
+  result |= ((crypto_uint64) in[2]) << 16;
+  return result;
+}
+
+static crypto_uint64 load_4(const unsigned char *in)
+{
+  crypto_uint64 result;
+  result = (crypto_uint64) in[0];
+  result |= ((crypto_uint64) in[1]) << 8;
+  result |= ((crypto_uint64) in[2]) << 16;
+  result |= ((crypto_uint64) in[3]) << 24;
+  return result;
+}
+
+void fe_frombytes(fe h,const unsigned char *s)
+{
+  crypto_int64 h0 = load_4(s);
+  crypto_int64 h1 = load_3(s + 4) << 6;
+  crypto_int64 h2 = load_3(s + 7) << 5;
+  crypto_int64 h3 = load_3(s + 10) << 3;
+  crypto_int64 h4 = load_3(s + 13) << 2;
+  crypto_int64 h5 = load_4(s + 16);
+  crypto_int64 h6 = load_3(s + 20) << 7;
+  crypto_int64 h7 = load_3(s + 23) << 5;
+  crypto_int64 h8 = load_3(s + 26) << 4;
+  crypto_int64 h9 = load_3(s + 29) << 2;
+  crypto_int64 carry0;
+  crypto_int64 carry1;
+  crypto_int64 carry2;
+  crypto_int64 carry3;
+  crypto_int64 carry4;
+  crypto_int64 carry5;
+  crypto_int64 carry6;
+  crypto_int64 carry7;
+  crypto_int64 carry8;
+  crypto_int64 carry9;
+
+  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+
+/*
+h = f * g
+Can overlap h with f or g.
+
+Preconditions:
+   |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+   |g| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+*/
+
+/*
+Notes on implementation strategy:
+
+Using schoolbook multiplication.
+Karatsuba would save a little in some cost models.
+
+Most multiplications by 2 and 19 are 32-bit precomputations;
+cheaper than 64-bit postcomputations.
+
+There is one remaining multiplication by 19 in the carry chain;
+one *19 precomputation can be merged into this,
+but the resulting data flow is considerably less clean.
+
+There are 12 carries below.
+10 of them are 2-way parallelizable and vectorizable.
+Can get away with 11 carries, but then data flow is much deeper.
+
+With tighter constraints on inputs can squeeze carries into int32.
+*/
+
+void fe_mul(fe h,fe f,fe g)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 g0 = g[0];
+  crypto_int32 g1 = g[1];
+  crypto_int32 g2 = g[2];
+  crypto_int32 g3 = g[3];
+  crypto_int32 g4 = g[4];
+  crypto_int32 g5 = g[5];
+  crypto_int32 g6 = g[6];
+  crypto_int32 g7 = g[7];
+  crypto_int32 g8 = g[8];
+  crypto_int32 g9 = g[9];
+  crypto_int32 g1_19 = 19 * g1; /* 1.4*2^29 */
+  crypto_int32 g2_19 = 19 * g2; /* 1.4*2^30; still ok */
+  crypto_int32 g3_19 = 19 * g3;
+  crypto_int32 g4_19 = 19 * g4;
+  crypto_int32 g5_19 = 19 * g5;
+  crypto_int32 g6_19 = 19 * g6;
+  crypto_int32 g7_19 = 19 * g7;
+  crypto_int32 g8_19 = 19 * g8;
+  crypto_int32 g9_19 = 19 * g9;
+  crypto_int32 f1_2 = 2 * f1;
+  crypto_int32 f3_2 = 2 * f3;
+  crypto_int32 f5_2 = 2 * f5;
+  crypto_int32 f7_2 = 2 * f7;
+  crypto_int32 f9_2 = 2 * f9;
+  crypto_int64 f0g0    = f0   * (crypto_int64) g0;
+  crypto_int64 f0g1    = f0   * (crypto_int64) g1;
+  crypto_int64 f0g2    = f0   * (crypto_int64) g2;
+  crypto_int64 f0g3    = f0   * (crypto_int64) g3;
+  crypto_int64 f0g4    = f0   * (crypto_int64) g4;
+  crypto_int64 f0g5    = f0   * (crypto_int64) g5;
+  crypto_int64 f0g6    = f0   * (crypto_int64) g6;
+  crypto_int64 f0g7    = f0   * (crypto_int64) g7;
+  crypto_int64 f0g8    = f0   * (crypto_int64) g8;
+  crypto_int64 f0g9    = f0   * (crypto_int64) g9;
+  crypto_int64 f1g0    = f1   * (crypto_int64) g0;
+  crypto_int64 f1g1_2  = f1_2 * (crypto_int64) g1;
+  crypto_int64 f1g2    = f1   * (crypto_int64) g2;
+  crypto_int64 f1g3_2  = f1_2 * (crypto_int64) g3;
+  crypto_int64 f1g4    = f1   * (crypto_int64) g4;
+  crypto_int64 f1g5_2  = f1_2 * (crypto_int64) g5;
+  crypto_int64 f1g6    = f1   * (crypto_int64) g6;
+  crypto_int64 f1g7_2  = f1_2 * (crypto_int64) g7;
+  crypto_int64 f1g8    = f1   * (crypto_int64) g8;
+  crypto_int64 f1g9_38 = f1_2 * (crypto_int64) g9_19;
+  crypto_int64 f2g0    = f2   * (crypto_int64) g0;
+  crypto_int64 f2g1    = f2   * (crypto_int64) g1;
+  crypto_int64 f2g2    = f2   * (crypto_int64) g2;
+  crypto_int64 f2g3    = f2   * (crypto_int64) g3;
+  crypto_int64 f2g4    = f2   * (crypto_int64) g4;
+  crypto_int64 f2g5    = f2   * (crypto_int64) g5;
+  crypto_int64 f2g6    = f2   * (crypto_int64) g6;
+  crypto_int64 f2g7    = f2   * (crypto_int64) g7;
+  crypto_int64 f2g8_19 = f2   * (crypto_int64) g8_19;
+  crypto_int64 f2g9_19 = f2   * (crypto_int64) g9_19;
+  crypto_int64 f3g0    = f3   * (crypto_int64) g0;
+  crypto_int64 f3g1_2  = f3_2 * (crypto_int64) g1;
+  crypto_int64 f3g2    = f3   * (crypto_int64) g2;
+  crypto_int64 f3g3_2  = f3_2 * (crypto_int64) g3;
+  crypto_int64 f3g4    = f3   * (crypto_int64) g4;
+  crypto_int64 f3g5_2  = f3_2 * (crypto_int64) g5;
+  crypto_int64 f3g6    = f3   * (crypto_int64) g6;
+  crypto_int64 f3g7_38 = f3_2 * (crypto_int64) g7_19;
+  crypto_int64 f3g8_19 = f3   * (crypto_int64) g8_19;
+  crypto_int64 f3g9_38 = f3_2 * (crypto_int64) g9_19;
+  crypto_int64 f4g0    = f4   * (crypto_int64) g0;
+  crypto_int64 f4g1    = f4   * (crypto_int64) g1;
+  crypto_int64 f4g2    = f4   * (crypto_int64) g2;
+  crypto_int64 f4g3    = f4   * (crypto_int64) g3;
+  crypto_int64 f4g4    = f4   * (crypto_int64) g4;
+  crypto_int64 f4g5    = f4   * (crypto_int64) g5;
+  crypto_int64 f4g6_19 = f4   * (crypto_int64) g6_19;
+  crypto_int64 f4g7_19 = f4   * (crypto_int64) g7_19;
+  crypto_int64 f4g8_19 = f4   * (crypto_int64) g8_19;
+  crypto_int64 f4g9_19 = f4   * (crypto_int64) g9_19;
+  crypto_int64 f5g0    = f5   * (crypto_int64) g0;
+  crypto_int64 f5g1_2  = f5_2 * (crypto_int64) g1;
+  crypto_int64 f5g2    = f5   * (crypto_int64) g2;
+  crypto_int64 f5g3_2  = f5_2 * (crypto_int64) g3;
+  crypto_int64 f5g4    = f5   * (crypto_int64) g4;
+  crypto_int64 f5g5_38 = f5_2 * (crypto_int64) g5_19;
+  crypto_int64 f5g6_19 = f5   * (crypto_int64) g6_19;
+  crypto_int64 f5g7_38 = f5_2 * (crypto_int64) g7_19;
+  crypto_int64 f5g8_19 = f5   * (crypto_int64) g8_19;
+  crypto_int64 f5g9_38 = f5_2 * (crypto_int64) g9_19;
+  crypto_int64 f6g0    = f6   * (crypto_int64) g0;
+  crypto_int64 f6g1    = f6   * (crypto_int64) g1;
+  crypto_int64 f6g2    = f6   * (crypto_int64) g2;
+  crypto_int64 f6g3    = f6   * (crypto_int64) g3;
+  crypto_int64 f6g4_19 = f6   * (crypto_int64) g4_19;
+  crypto_int64 f6g5_19 = f6   * (crypto_int64) g5_19;
+  crypto_int64 f6g6_19 = f6   * (crypto_int64) g6_19;
+  crypto_int64 f6g7_19 = f6   * (crypto_int64) g7_19;
+  crypto_int64 f6g8_19 = f6   * (crypto_int64) g8_19;
+  crypto_int64 f6g9_19 = f6   * (crypto_int64) g9_19;
+  crypto_int64 f7g0    = f7   * (crypto_int64) g0;
+  crypto_int64 f7g1_2  = f7_2 * (crypto_int64) g1;
+  crypto_int64 f7g2    = f7   * (crypto_int64) g2;
+  crypto_int64 f7g3_38 = f7_2 * (crypto_int64) g3_19;
+  crypto_int64 f7g4_19 = f7   * (crypto_int64) g4_19;
+  crypto_int64 f7g5_38 = f7_2 * (crypto_int64) g5_19;
+  crypto_int64 f7g6_19 = f7   * (crypto_int64) g6_19;
+  crypto_int64 f7g7_38 = f7_2 * (crypto_int64) g7_19;
+  crypto_int64 f7g8_19 = f7   * (crypto_int64) g8_19;
+  crypto_int64 f7g9_38 = f7_2 * (crypto_int64) g9_19;
+  crypto_int64 f8g0    = f8   * (crypto_int64) g0;
+  crypto_int64 f8g1    = f8   * (crypto_int64) g1;
+  crypto_int64 f8g2_19 = f8   * (crypto_int64) g2_19;
+  crypto_int64 f8g3_19 = f8   * (crypto_int64) g3_19;
+  crypto_int64 f8g4_19 = f8   * (crypto_int64) g4_19;
+  crypto_int64 f8g5_19 = f8   * (crypto_int64) g5_19;
+  crypto_int64 f8g6_19 = f8   * (crypto_int64) g6_19;
+  crypto_int64 f8g7_19 = f8   * (crypto_int64) g7_19;
+  crypto_int64 f8g8_19 = f8   * (crypto_int64) g8_19;
+  crypto_int64 f8g9_19 = f8   * (crypto_int64) g9_19;
+  crypto_int64 f9g0    = f9   * (crypto_int64) g0;
+  crypto_int64 f9g1_38 = f9_2 * (crypto_int64) g1_19;
+  crypto_int64 f9g2_19 = f9   * (crypto_int64) g2_19;
+  crypto_int64 f9g3_38 = f9_2 * (crypto_int64) g3_19;
+  crypto_int64 f9g4_19 = f9   * (crypto_int64) g4_19;
+  crypto_int64 f9g5_38 = f9_2 * (crypto_int64) g5_19;
+  crypto_int64 f9g6_19 = f9   * (crypto_int64) g6_19;
+  crypto_int64 f9g7_38 = f9_2 * (crypto_int64) g7_19;
+  crypto_int64 f9g8_19 = f9   * (crypto_int64) g8_19;
+  crypto_int64 f9g9_38 = f9_2 * (crypto_int64) g9_19;
+  crypto_int64 h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
+  crypto_int64 h1 = f0g1+f1g0   +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
+  crypto_int64 h2 = f0g2+f1g1_2 +f2g0   +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
+  crypto_int64 h3 = f0g3+f1g2   +f2g1   +f3g0   +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
+  crypto_int64 h4 = f0g4+f1g3_2 +f2g2   +f3g1_2 +f4g0   +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
+  crypto_int64 h5 = f0g5+f1g4   +f2g3   +f3g2   +f4g1   +f5g0   +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
+  crypto_int64 h6 = f0g6+f1g5_2 +f2g4   +f3g3_2 +f4g2   +f5g1_2 +f6g0   +f7g9_38+f8g8_19+f9g7_38;
+  crypto_int64 h7 = f0g7+f1g6   +f2g5   +f3g4   +f4g3   +f5g2   +f6g1   +f7g0   +f8g9_19+f9g8_19;
+  crypto_int64 h8 = f0g8+f1g7_2 +f2g6   +f3g5_2 +f4g4   +f5g3_2 +f6g2   +f7g1_2 +f8g0   +f9g9_38;
+  crypto_int64 h9 = f0g9+f1g8   +f2g7   +f3g6   +f4g5   +f5g4   +f6g3   +f7g2   +f8g1   +f9g0   ;
+  crypto_int64 carry0;
+  crypto_int64 carry1;
+  crypto_int64 carry2;
+  crypto_int64 carry3;
+  crypto_int64 carry4;
+  crypto_int64 carry5;
+  crypto_int64 carry6;
+  crypto_int64 carry7;
+  crypto_int64 carry8;
+  crypto_int64 carry9;
+
+  /*
+  |h0| <= (1.1*1.1*2^52*(1+19+19+19+19)+1.1*1.1*2^50*(38+38+38+38+38))
+    i.e. |h0| <= 1.2*2^59; narrower ranges for h2, h4, h6, h8
+  |h1| <= (1.1*1.1*2^51*(1+1+19+19+19+19+19+19+19+19))
+    i.e. |h1| <= 1.5*2^58; narrower ranges for h3, h5, h7, h9
+  */
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  /* |h0| <= 2^25 */
+  /* |h4| <= 2^25 */
+  /* |h1| <= 1.51*2^58 */
+  /* |h5| <= 1.51*2^58 */
+
+  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+  /* |h1| <= 2^24; from now on fits into int32 */
+  /* |h5| <= 2^24; from now on fits into int32 */
+  /* |h2| <= 1.21*2^59 */
+  /* |h6| <= 1.21*2^59 */
+
+  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+  /* |h2| <= 2^25; from now on fits into int32 unchanged */
+  /* |h6| <= 2^25; from now on fits into int32 unchanged */
+  /* |h3| <= 1.51*2^58 */
+  /* |h7| <= 1.51*2^58 */
+
+  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+  /* |h3| <= 2^24; from now on fits into int32 unchanged */
+  /* |h7| <= 2^24; from now on fits into int32 unchanged */
+  /* |h4| <= 1.52*2^33 */
+  /* |h8| <= 1.52*2^33 */
+
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+  /* |h4| <= 2^25; from now on fits into int32 unchanged */
+  /* |h8| <= 2^25; from now on fits into int32 unchanged */
+  /* |h5| <= 1.01*2^24 */
+  /* |h9| <= 1.51*2^58 */
+
+  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+  /* |h9| <= 2^24; from now on fits into int32 unchanged */
+  /* |h0| <= 1.8*2^37 */
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  /* |h0| <= 2^25; from now on fits into int32 unchanged */
+  /* |h1| <= 1.01*2^24 */
+
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+/*
+h = f * 121666
+Can overlap h with f.
+
+Preconditions:
+   |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+*/
+
+void fe_mul121666(fe h,fe f)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int64 h0 = f0 * (crypto_int64) 121666;
+  crypto_int64 h1 = f1 * (crypto_int64) 121666;
+  crypto_int64 h2 = f2 * (crypto_int64) 121666;
+  crypto_int64 h3 = f3 * (crypto_int64) 121666;
+  crypto_int64 h4 = f4 * (crypto_int64) 121666;
+  crypto_int64 h5 = f5 * (crypto_int64) 121666;
+  crypto_int64 h6 = f6 * (crypto_int64) 121666;
+  crypto_int64 h7 = f7 * (crypto_int64) 121666;
+  crypto_int64 h8 = f8 * (crypto_int64) 121666;
+  crypto_int64 h9 = f9 * (crypto_int64) 121666;
+  crypto_int64 carry0;
+  crypto_int64 carry1;
+  crypto_int64 carry2;
+  crypto_int64 carry3;
+  crypto_int64 carry4;
+  crypto_int64 carry5;
+  crypto_int64 carry6;
+  crypto_int64 carry7;
+  crypto_int64 carry8;
+  crypto_int64 carry9;
+
+  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+/*
+h = f * f
+Can overlap h with f.
+
+Preconditions:
+   |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+*/
+
+/*
+See fe_mul.c for discussion of implementation strategy.
+*/
+
+void fe_sq(fe h,fe f)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 f0_2 = 2 * f0;
+  crypto_int32 f1_2 = 2 * f1;
+  crypto_int32 f2_2 = 2 * f2;
+  crypto_int32 f3_2 = 2 * f3;
+  crypto_int32 f4_2 = 2 * f4;
+  crypto_int32 f5_2 = 2 * f5;
+  crypto_int32 f6_2 = 2 * f6;
+  crypto_int32 f7_2 = 2 * f7;
+  crypto_int32 f5_38 = 38 * f5; /* 1.31*2^30 */
+  crypto_int32 f6_19 = 19 * f6; /* 1.31*2^30 */
+  crypto_int32 f7_38 = 38 * f7; /* 1.31*2^30 */
+  crypto_int32 f8_19 = 19 * f8; /* 1.31*2^30 */
+  crypto_int32 f9_38 = 38 * f9; /* 1.31*2^30 */
+  crypto_int64 f0f0    = f0   * (crypto_int64) f0;
+  crypto_int64 f0f1_2  = f0_2 * (crypto_int64) f1;
+  crypto_int64 f0f2_2  = f0_2 * (crypto_int64) f2;
+  crypto_int64 f0f3_2  = f0_2 * (crypto_int64) f3;
+  crypto_int64 f0f4_2  = f0_2 * (crypto_int64) f4;
+  crypto_int64 f0f5_2  = f0_2 * (crypto_int64) f5;
+  crypto_int64 f0f6_2  = f0_2 * (crypto_int64) f6;
+  crypto_int64 f0f7_2  = f0_2 * (crypto_int64) f7;
+  crypto_int64 f0f8_2  = f0_2 * (crypto_int64) f8;
+  crypto_int64 f0f9_2  = f0_2 * (crypto_int64) f9;
+  crypto_int64 f1f1_2  = f1_2 * (crypto_int64) f1;
+  crypto_int64 f1f2_2  = f1_2 * (crypto_int64) f2;
+  crypto_int64 f1f3_4  = f1_2 * (crypto_int64) f3_2;
+  crypto_int64 f1f4_2  = f1_2 * (crypto_int64) f4;
+  crypto_int64 f1f5_4  = f1_2 * (crypto_int64) f5_2;
+  crypto_int64 f1f6_2  = f1_2 * (crypto_int64) f6;
+  crypto_int64 f1f7_4  = f1_2 * (crypto_int64) f7_2;
+  crypto_int64 f1f8_2  = f1_2 * (crypto_int64) f8;
+  crypto_int64 f1f9_76 = f1_2 * (crypto_int64) f9_38;
+  crypto_int64 f2f2    = f2   * (crypto_int64) f2;
+  crypto_int64 f2f3_2  = f2_2 * (crypto_int64) f3;
+  crypto_int64 f2f4_2  = f2_2 * (crypto_int64) f4;
+  crypto_int64 f2f5_2  = f2_2 * (crypto_int64) f5;
+  crypto_int64 f2f6_2  = f2_2 * (crypto_int64) f6;
+  crypto_int64 f2f7_2  = f2_2 * (crypto_int64) f7;
+  crypto_int64 f2f8_38 = f2_2 * (crypto_int64) f8_19;
+  crypto_int64 f2f9_38 = f2   * (crypto_int64) f9_38;
+  crypto_int64 f3f3_2  = f3_2 * (crypto_int64) f3;
+  crypto_int64 f3f4_2  = f3_2 * (crypto_int64) f4;
+  crypto_int64 f3f5_4  = f3_2 * (crypto_int64) f5_2;
+  crypto_int64 f3f6_2  = f3_2 * (crypto_int64) f6;
+  crypto_int64 f3f7_76 = f3_2 * (crypto_int64) f7_38;
+  crypto_int64 f3f8_38 = f3_2 * (crypto_int64) f8_19;
+  crypto_int64 f3f9_76 = f3_2 * (crypto_int64) f9_38;
+  crypto_int64 f4f4    = f4   * (crypto_int64) f4;
+  crypto_int64 f4f5_2  = f4_2 * (crypto_int64) f5;
+  crypto_int64 f4f6_38 = f4_2 * (crypto_int64) f6_19;
+  crypto_int64 f4f7_38 = f4   * (crypto_int64) f7_38;
+  crypto_int64 f4f8_38 = f4_2 * (crypto_int64) f8_19;
+  crypto_int64 f4f9_38 = f4   * (crypto_int64) f9_38;
+  crypto_int64 f5f5_38 = f5   * (crypto_int64) f5_38;
+  crypto_int64 f5f6_38 = f5_2 * (crypto_int64) f6_19;
+  crypto_int64 f5f7_76 = f5_2 * (crypto_int64) f7_38;
+  crypto_int64 f5f8_38 = f5_2 * (crypto_int64) f8_19;
+  crypto_int64 f5f9_76 = f5_2 * (crypto_int64) f9_38;
+  crypto_int64 f6f6_19 = f6   * (crypto_int64) f6_19;
+  crypto_int64 f6f7_38 = f6   * (crypto_int64) f7_38;
+  crypto_int64 f6f8_38 = f6_2 * (crypto_int64) f8_19;
+  crypto_int64 f6f9_38 = f6   * (crypto_int64) f9_38;
+  crypto_int64 f7f7_38 = f7   * (crypto_int64) f7_38;
+  crypto_int64 f7f8_38 = f7_2 * (crypto_int64) f8_19;
+  crypto_int64 f7f9_76 = f7_2 * (crypto_int64) f9_38;
+  crypto_int64 f8f8_19 = f8   * (crypto_int64) f8_19;
+  crypto_int64 f8f9_38 = f8   * (crypto_int64) f9_38;
+  crypto_int64 f9f9_38 = f9   * (crypto_int64) f9_38;
+  crypto_int64 h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
+  crypto_int64 h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
+  crypto_int64 h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
+  crypto_int64 h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
+  crypto_int64 h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
+  crypto_int64 h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
+  crypto_int64 h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
+  crypto_int64 h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
+  crypto_int64 h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
+  crypto_int64 h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
+  crypto_int64 carry0;
+  crypto_int64 carry1;
+  crypto_int64 carry2;
+  crypto_int64 carry3;
+  crypto_int64 carry4;
+  crypto_int64 carry5;
+  crypto_int64 carry6;
+  crypto_int64 carry7;
+  crypto_int64 carry8;
+  crypto_int64 carry9;
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+
+  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+
+  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+
+  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+/*
+h = f - g
+Can overlap h with f or g.
+
+Preconditions:
+   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+   |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+void fe_sub(fe h,fe f,fe g)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 g0 = g[0];
+  crypto_int32 g1 = g[1];
+  crypto_int32 g2 = g[2];
+  crypto_int32 g3 = g[3];
+  crypto_int32 g4 = g[4];
+  crypto_int32 g5 = g[5];
+  crypto_int32 g6 = g[6];
+  crypto_int32 g7 = g[7];
+  crypto_int32 g8 = g[8];
+  crypto_int32 g9 = g[9];
+  crypto_int32 h0 = f0 - g0;
+  crypto_int32 h1 = f1 - g1;
+  crypto_int32 h2 = f2 - g2;
+  crypto_int32 h3 = f3 - g3;
+  crypto_int32 h4 = f4 - g4;
+  crypto_int32 h5 = f5 - g5;
+  crypto_int32 h6 = f6 - g6;
+  crypto_int32 h7 = f7 - g7;
+  crypto_int32 h8 = f8 - g8;
+  crypto_int32 h9 = f9 - g9;
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+/*
+Preconditions:
+  |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+Write p=2^255-19; q=floor(h/p).
+Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
+
+Proof:
+  Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
+  Also have |h-2^230 h9|<2^230 so |19 2^(-255)(h-2^230 h9)|<1/4.
+
+  Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
+  Then 0<y<1.
+
+  Write r=h-pq.
+  Have 0<=r<=p-1=2^255-20.
+  Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
+
+  Write x=r+19(2^-255)r+y.
+  Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
+
+  Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
+  so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
+*/
+
+void fe_tobytes(unsigned char *s,fe h)
+{
+  crypto_int32 h0 = h[0];
+  crypto_int32 h1 = h[1];
+  crypto_int32 h2 = h[2];
+  crypto_int32 h3 = h[3];
+  crypto_int32 h4 = h[4];
+  crypto_int32 h5 = h[5];
+  crypto_int32 h6 = h[6];
+  crypto_int32 h7 = h[7];
+  crypto_int32 h8 = h[8];
+  crypto_int32 h9 = h[9];
+  crypto_int32 q;
+  crypto_int32 carry0;
+  crypto_int32 carry1;
+  crypto_int32 carry2;
+  crypto_int32 carry3;
+  crypto_int32 carry4;
+  crypto_int32 carry5;
+  crypto_int32 carry6;
+  crypto_int32 carry7;
+  crypto_int32 carry8;
+  crypto_int32 carry9;
+
+  q = (19 * h9 + (((crypto_int32) 1) << 24)) >> 25;
+  q = (h0 + q) >> 26;
+  q = (h1 + q) >> 25;
+  q = (h2 + q) >> 26;
+  q = (h3 + q) >> 25;
+  q = (h4 + q) >> 26;
+  q = (h5 + q) >> 25;
+  q = (h6 + q) >> 26;
+  q = (h7 + q) >> 25;
+  q = (h8 + q) >> 26;
+  q = (h9 + q) >> 25;
+
+  /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
+  h0 += 19 * q;
+  /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
+
+  carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25;
+  carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26;
+  carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25;
+  carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26;
+  carry9 = h9 >> 25;               h9 -= carry9 << 25;
+                  /* h10 = carry9 */
+
+  /*
+  Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
+  Have h0+...+2^230 h9 between 0 and 2^255-1;
+  evidently 2^255 h10-2^255 q = 0.
+  Goal: Output h0+...+2^230 h9.
+  */
+
+  s[0] = h0 >> 0;
+  s[1] = h0 >> 8;
+  s[2] = h0 >> 16;
+  s[3] = (h0 >> 24) | (h1 << 2);
+  s[4] = h1 >> 6;
+  s[5] = h1 >> 14;
+  s[6] = (h1 >> 22) | (h2 << 3);
+  s[7] = h2 >> 5;
+  s[8] = h2 >> 13;
+  s[9] = (h2 >> 21) | (h3 << 5);
+  s[10] = h3 >> 3;
+  s[11] = h3 >> 11;
+  s[12] = (h3 >> 19) | (h4 << 6);
+  s[13] = h4 >> 2;
+  s[14] = h4 >> 10;
+  s[15] = h4 >> 18;
+  s[16] = h5 >> 0;
+  s[17] = h5 >> 8;
+  s[18] = h5 >> 16;
+  s[19] = (h5 >> 24) | (h6 << 1);
+  s[20] = h6 >> 7;
+  s[21] = h6 >> 15;
+  s[22] = (h6 >> 23) | (h7 << 3);
+  s[23] = h7 >> 5;
+  s[24] = h7 >> 13;
+  s[25] = (h7 >> 21) | (h8 << 4);
+  s[26] = h8 >> 4;
+  s[27] = h8 >> 12;
+  s[28] = (h8 >> 20) | (h9 << 6);
+  s[29] = h9 >> 2;
+  s[30] = h9 >> 10;
+  s[31] = h9 >> 18;
+}
+
+void fe_invert(fe out,fe z)
+{
+  fe t0;
+  fe t1;
+  fe t2;
+  fe t3;
+  int i;
+
+
+/* qhasm: fe z1 */
+
+/* qhasm: fe z2 */
+
+/* qhasm: fe z8 */
+
+/* qhasm: fe z9 */
+
+/* qhasm: fe z11 */
+
+/* qhasm: fe z22 */
+
+/* qhasm: fe z_5_0 */
+
+/* qhasm: fe z_10_5 */
+
+/* qhasm: fe z_10_0 */
+
+/* qhasm: fe z_20_10 */
+
+/* qhasm: fe z_20_0 */
+
+/* qhasm: fe z_40_20 */
+
+/* qhasm: fe z_40_0 */
+
+/* qhasm: fe z_50_10 */
+
+/* qhasm: fe z_50_0 */
+
+/* qhasm: fe z_100_50 */
+
+/* qhasm: fe z_100_0 */
+
+/* qhasm: fe z_200_100 */
+
+/* qhasm: fe z_200_0 */
+
+/* qhasm: fe z_250_50 */
+
+/* qhasm: fe z_250_0 */
+
+/* qhasm: fe z_255_5 */
+
+/* qhasm: fe z_255_21 */
+
+/* qhasm: enter pow225521 */
+
+/* qhasm: z2 = z1^2^1 */
+/* asm 1: fe_sq(>z2=fe#1,<z1=fe#11); for (i = 1;i < 1;++i) fe_sq(>z2=fe#1,>z2=fe#1); */
+/* asm 2: fe_sq(>z2=t0,<z1=z); for (i = 1;i < 1;++i) fe_sq(>z2=t0,>z2=t0); */
+fe_sq(t0,z); for (i = 1;i < 1;++i) fe_sq(t0,t0);
+
+/* qhasm: z8 = z2^2^2 */
+/* asm 1: fe_sq(>z8=fe#2,<z2=fe#1); for (i = 1;i < 2;++i) fe_sq(>z8=fe#2,>z8=fe#2); */
+/* asm 2: fe_sq(>z8=t1,<z2=t0); for (i = 1;i < 2;++i) fe_sq(>z8=t1,>z8=t1); */
+fe_sq(t1,t0); for (i = 1;i < 2;++i) fe_sq(t1,t1);
+
+/* qhasm: z9 = z1*z8 */
+/* asm 1: fe_mul(>z9=fe#2,<z1=fe#11,<z8=fe#2); */
+/* asm 2: fe_mul(>z9=t1,<z1=z,<z8=t1); */
+fe_mul(t1,z,t1);
+
+/* qhasm: z11 = z2*z9 */
+/* asm 1: fe_mul(>z11=fe#1,<z2=fe#1,<z9=fe#2); */
+/* asm 2: fe_mul(>z11=t0,<z2=t0,<z9=t1); */
+fe_mul(t0,t0,t1);
+
+/* qhasm: z22 = z11^2^1 */
+/* asm 1: fe_sq(>z22=fe#3,<z11=fe#1); for (i = 1;i < 1;++i) fe_sq(>z22=fe#3,>z22=fe#3); */
+/* asm 2: fe_sq(>z22=t2,<z11=t0); for (i = 1;i < 1;++i) fe_sq(>z22=t2,>z22=t2); */
+fe_sq(t2,t0); for (i = 1;i < 1;++i) fe_sq(t2,t2);
+
+/* qhasm: z_5_0 = z9*z22 */
+/* asm 1: fe_mul(>z_5_0=fe#2,<z9=fe#2,<z22=fe#3); */
+/* asm 2: fe_mul(>z_5_0=t1,<z9=t1,<z22=t2); */
+fe_mul(t1,t1,t2);
+
+/* qhasm: z_10_5 = z_5_0^2^5 */
+/* asm 1: fe_sq(>z_10_5=fe#3,<z_5_0=fe#2); for (i = 1;i < 5;++i) fe_sq(>z_10_5=fe#3,>z_10_5=fe#3); */
+/* asm 2: fe_sq(>z_10_5=t2,<z_5_0=t1); for (i = 1;i < 5;++i) fe_sq(>z_10_5=t2,>z_10_5=t2); */
+fe_sq(t2,t1); for (i = 1;i < 5;++i) fe_sq(t2,t2);
+
+/* qhasm: z_10_0 = z_10_5*z_5_0 */
+/* asm 1: fe_mul(>z_10_0=fe#2,<z_10_5=fe#3,<z_5_0=fe#2); */
+/* asm 2: fe_mul(>z_10_0=t1,<z_10_5=t2,<z_5_0=t1); */
+fe_mul(t1,t2,t1);
+
+/* qhasm: z_20_10 = z_10_0^2^10 */
+/* asm 1: fe_sq(>z_20_10=fe#3,<z_10_0=fe#2); for (i = 1;i < 10;++i) fe_sq(>z_20_10=fe#3,>z_20_10=fe#3); */
+/* asm 2: fe_sq(>z_20_10=t2,<z_10_0=t1); for (i = 1;i < 10;++i) fe_sq(>z_20_10=t2,>z_20_10=t2); */
+fe_sq(t2,t1); for (i = 1;i < 10;++i) fe_sq(t2,t2);
+
+/* qhasm: z_20_0 = z_20_10*z_10_0 */
+/* asm 1: fe_mul(>z_20_0=fe#3,<z_20_10=fe#3,<z_10_0=fe#2); */
+/* asm 2: fe_mul(>z_20_0=t2,<z_20_10=t2,<z_10_0=t1); */
+fe_mul(t2,t2,t1);
+
+/* qhasm: z_40_20 = z_20_0^2^20 */
+/* asm 1: fe_sq(>z_40_20=fe#4,<z_20_0=fe#3); for (i = 1;i < 20;++i) fe_sq(>z_40_20=fe#4,>z_40_20=fe#4); */
+/* asm 2: fe_sq(>z_40_20=t3,<z_20_0=t2); for (i = 1;i < 20;++i) fe_sq(>z_40_20=t3,>z_40_20=t3); */
+fe_sq(t3,t2); for (i = 1;i < 20;++i) fe_sq(t3,t3);
+
+/* qhasm: z_40_0 = z_40_20*z_20_0 */
+/* asm 1: fe_mul(>z_40_0=fe#3,<z_40_20=fe#4,<z_20_0=fe#3); */
+/* asm 2: fe_mul(>z_40_0=t2,<z_40_20=t3,<z_20_0=t2); */
+fe_mul(t2,t3,t2);
+
+/* qhasm: z_50_10 = z_40_0^2^10 */
+/* asm 1: fe_sq(>z_50_10=fe#3,<z_40_0=fe#3); for (i = 1;i < 10;++i) fe_sq(>z_50_10=fe#3,>z_50_10=fe#3); */
+/* asm 2: fe_sq(>z_50_10=t2,<z_40_0=t2); for (i = 1;i < 10;++i) fe_sq(>z_50_10=t2,>z_50_10=t2); */
+fe_sq(t2,t2); for (i = 1;i < 10;++i) fe_sq(t2,t2);
+
+/* qhasm: z_50_0 = z_50_10*z_10_0 */
+/* asm 1: fe_mul(>z_50_0=fe#2,<z_50_10=fe#3,<z_10_0=fe#2); */
+/* asm 2: fe_mul(>z_50_0=t1,<z_50_10=t2,<z_10_0=t1); */
+fe_mul(t1,t2,t1);
+
+/* qhasm: z_100_50 = z_50_0^2^50 */
+/* asm 1: fe_sq(>z_100_50=fe#3,<z_50_0=fe#2); for (i = 1;i < 50;++i) fe_sq(>z_100_50=fe#3,>z_100_50=fe#3); */
+/* asm 2: fe_sq(>z_100_50=t2,<z_50_0=t1); for (i = 1;i < 50;++i) fe_sq(>z_100_50=t2,>z_100_50=t2); */
+fe_sq(t2,t1); for (i = 1;i < 50;++i) fe_sq(t2,t2);
+
+/* qhasm: z_100_0 = z_100_50*z_50_0 */
+/* asm 1: fe_mul(>z_100_0=fe#3,<z_100_50=fe#3,<z_50_0=fe#2); */
+/* asm 2: fe_mul(>z_100_0=t2,<z_100_50=t2,<z_50_0=t1); */
+fe_mul(t2,t2,t1);
+
+/* qhasm: z_200_100 = z_100_0^2^100 */
+/* asm 1: fe_sq(>z_200_100=fe#4,<z_100_0=fe#3); for (i = 1;i < 100;++i) fe_sq(>z_200_100=fe#4,>z_200_100=fe#4); */
+/* asm 2: fe_sq(>z_200_100=t3,<z_100_0=t2); for (i = 1;i < 100;++i) fe_sq(>z_200_100=t3,>z_200_100=t3); */
+fe_sq(t3,t2); for (i = 1;i < 100;++i) fe_sq(t3,t3);
+
+/* qhasm: z_200_0 = z_200_100*z_100_0 */
+/* asm 1: fe_mul(>z_200_0=fe#3,<z_200_100=fe#4,<z_100_0=fe#3); */
+/* asm 2: fe_mul(>z_200_0=t2,<z_200_100=t3,<z_100_0=t2); */
+fe_mul(t2,t3,t2);
+
+/* qhasm: z_250_50 = z_200_0^2^50 */
+/* asm 1: fe_sq(>z_250_50=fe#3,<z_200_0=fe#3); for (i = 1;i < 50;++i) fe_sq(>z_250_50=fe#3,>z_250_50=fe#3); */
+/* asm 2: fe_sq(>z_250_50=t2,<z_200_0=t2); for (i = 1;i < 50;++i) fe_sq(>z_250_50=t2,>z_250_50=t2); */
+fe_sq(t2,t2); for (i = 1;i < 50;++i) fe_sq(t2,t2);
+
+/* qhasm: z_250_0 = z_250_50*z_50_0 */
+/* asm 1: fe_mul(>z_250_0=fe#2,<z_250_50=fe#3,<z_50_0=fe#2); */
+/* asm 2: fe_mul(>z_250_0=t1,<z_250_50=t2,<z_50_0=t1); */
+fe_mul(t1,t2,t1);
+
+/* qhasm: z_255_5 = z_250_0^2^5 */
+/* asm 1: fe_sq(>z_255_5=fe#2,<z_250_0=fe#2); for (i = 1;i < 5;++i) fe_sq(>z_255_5=fe#2,>z_255_5=fe#2); */
+/* asm 2: fe_sq(>z_255_5=t1,<z_250_0=t1); for (i = 1;i < 5;++i) fe_sq(>z_255_5=t1,>z_255_5=t1); */
+fe_sq(t1,t1); for (i = 1;i < 5;++i) fe_sq(t1,t1);
+
+/* qhasm: z_255_21 = z_255_5*z11 */
+/* asm 1: fe_mul(>z_255_21=fe#12,<z_255_5=fe#2,<z11=fe#1); */
+/* asm 2: fe_mul(>z_255_21=out,<z_255_5=t1,<z11=t0); */
+fe_mul(out,t1,t0);
+
+/* qhasm: return */
+
+  return;
+}
+
+
+int crypto_scalarmult_ref10(unsigned char *q,
+  const unsigned char *n,
+  const unsigned char *p)
+{
+  unsigned char e[32];
+  unsigned int i;
+  fe x1;
+  fe x2;
+  fe z2;
+  fe x3;
+  fe z3;
+  fe tmp0;
+  fe tmp1;
+  int pos;
+  unsigned int swap;
+  unsigned int b;
+
+  for (i = 0;i < 32;++i) e[i] = n[i];
+  e[0] &= 248;
+  e[31] &= 127;
+  e[31] |= 64;
+  fe_frombytes(x1,p);
+  fe_1(x2);
+  fe_0(z2);
+  fe_copy(x3,x1);
+  fe_1(z3);
+
+  swap = 0;
+  for (pos = 254;pos >= 0;--pos) {
+    b = e[pos / 8] >> (pos & 7);
+    b &= 1;
+    swap ^= b;
+    fe_cswap(x2,x3,swap);
+    fe_cswap(z2,z3,swap);
+    swap = b;
+/* qhasm: fe X2 */
+
+/* qhasm: fe Z2 */
+
+/* qhasm: fe X3 */
+
+/* qhasm: fe Z3 */
+
+/* qhasm: fe X4 */
+
+/* qhasm: fe Z4 */
+
+/* qhasm: fe X5 */
+
+/* qhasm: fe Z5 */
+
+/* qhasm: fe A */
+
+/* qhasm: fe B */
+
+/* qhasm: fe C */
+
+/* qhasm: fe D */
+
+/* qhasm: fe E */
+
+/* qhasm: fe AA */
+
+/* qhasm: fe BB */
+
+/* qhasm: fe DA */
+
+/* qhasm: fe CB */
+
+/* qhasm: fe t0 */
+
+/* qhasm: fe t1 */
+
+/* qhasm: fe t2 */
+
+/* qhasm: fe t3 */
+
+/* qhasm: fe t4 */
+
+/* qhasm: enter ladder */
+
+/* qhasm: D = X3-Z3 */
+/* asm 1: fe_sub(>D=fe#5,<X3=fe#3,<Z3=fe#4); */
+/* asm 2: fe_sub(>D=tmp0,<X3=x3,<Z3=z3); */
+fe_sub(tmp0,x3,z3);
+
+/* qhasm: B = X2-Z2 */
+/* asm 1: fe_sub(>B=fe#6,<X2=fe#1,<Z2=fe#2); */
+/* asm 2: fe_sub(>B=tmp1,<X2=x2,<Z2=z2); */
+fe_sub(tmp1,x2,z2);
+
+/* qhasm: A = X2+Z2 */
+/* asm 1: fe_add(>A=fe#1,<X2=fe#1,<Z2=fe#2); */
+/* asm 2: fe_add(>A=x2,<X2=x2,<Z2=z2); */
+fe_add(x2,x2,z2);
+
+/* qhasm: C = X3+Z3 */
+/* asm 1: fe_add(>C=fe#2,<X3=fe#3,<Z3=fe#4); */
+/* asm 2: fe_add(>C=z2,<X3=x3,<Z3=z3); */
+fe_add(z2,x3,z3);
+
+/* qhasm: DA = D*A */
+/* asm 1: fe_mul(>DA=fe#4,<D=fe#5,<A=fe#1); */
+/* asm 2: fe_mul(>DA=z3,<D=tmp0,<A=x2); */
+fe_mul(z3,tmp0,x2);
+
+/* qhasm: CB = C*B */
+/* asm 1: fe_mul(>CB=fe#2,<C=fe#2,<B=fe#6); */
+/* asm 2: fe_mul(>CB=z2,<C=z2,<B=tmp1); */
+fe_mul(z2,z2,tmp1);
+
+/* qhasm: BB = B^2 */
+/* asm 1: fe_sq(>BB=fe#5,<B=fe#6); */
+/* asm 2: fe_sq(>BB=tmp0,<B=tmp1); */
+fe_sq(tmp0,tmp1);
+
+/* qhasm: AA = A^2 */
+/* asm 1: fe_sq(>AA=fe#6,<A=fe#1); */
+/* asm 2: fe_sq(>AA=tmp1,<A=x2); */
+fe_sq(tmp1,x2);
+
+/* qhasm: t0 = DA+CB */
+/* asm 1: fe_add(>t0=fe#3,<DA=fe#4,<CB=fe#2); */
+/* asm 2: fe_add(>t0=x3,<DA=z3,<CB=z2); */
+fe_add(x3,z3,z2);
+
+/* qhasm: assign x3 to t0 */
+
+/* qhasm: t1 = DA-CB */
+/* asm 1: fe_sub(>t1=fe#2,<DA=fe#4,<CB=fe#2); */
+/* asm 2: fe_sub(>t1=z2,<DA=z3,<CB=z2); */
+fe_sub(z2,z3,z2);
+
+/* qhasm: X4 = AA*BB */
+/* asm 1: fe_mul(>X4=fe#1,<AA=fe#6,<BB=fe#5); */
+/* asm 2: fe_mul(>X4=x2,<AA=tmp1,<BB=tmp0); */
+fe_mul(x2,tmp1,tmp0);
+
+/* qhasm: E = AA-BB */
+/* asm 1: fe_sub(>E=fe#6,<AA=fe#6,<BB=fe#5); */
+/* asm 2: fe_sub(>E=tmp1,<AA=tmp1,<BB=tmp0); */
+fe_sub(tmp1,tmp1,tmp0);
+
+/* qhasm: t2 = t1^2 */
+/* asm 1: fe_sq(>t2=fe#2,<t1=fe#2); */
+/* asm 2: fe_sq(>t2=z2,<t1=z2); */
+fe_sq(z2,z2);
+
+/* qhasm: t3 = a24*E */
+/* asm 1: fe_mul121666(>t3=fe#4,<E=fe#6); */
+/* asm 2: fe_mul121666(>t3=z3,<E=tmp1); */
+fe_mul121666(z3,tmp1);
+
+/* qhasm: X5 = t0^2 */
+/* asm 1: fe_sq(>X5=fe#3,<t0=fe#3); */
+/* asm 2: fe_sq(>X5=x3,<t0=x3); */
+fe_sq(x3,x3);
+
+/* qhasm: t4 = BB+t3 */
+/* asm 1: fe_add(>t4=fe#5,<BB=fe#5,<t3=fe#4); */
+/* asm 2: fe_add(>t4=tmp0,<BB=tmp0,<t3=z3); */
+fe_add(tmp0,tmp0,z3);
+
+/* qhasm: Z5 = X1*t2 */
+/* asm 1: fe_mul(>Z5=fe#4,x1,<t2=fe#2); */
+/* asm 2: fe_mul(>Z5=z3,x1,<t2=z2); */
+fe_mul(z3,x1,z2);
+
+/* qhasm: Z4 = E*t4 */
+/* asm 1: fe_mul(>Z4=fe#2,<E=fe#6,<t4=fe#5); */
+/* asm 2: fe_mul(>Z4=z2,<E=tmp1,<t4=tmp0); */
+fe_mul(z2,tmp1,tmp0);
+
+/* qhasm: return */
+  }
+  fe_cswap(x2,x3,swap);
+  fe_cswap(z2,z3,swap);
+
+  fe_invert(z2,z2);
+  fe_mul(x2,x2,z2);
+  fe_tobytes(q,x2);
+  return 0;
+}
+
+static const unsigned char basepoint[32] = {9};
+
+int crypto_scalarmult_base_ref10(unsigned char *q,const unsigned char *n)
+{
+  return crypto_scalarmult_ref10(q,n,basepoint);
+}
+

diff --git a/crypto/ed25519-donna/src/fuzz/curve25519-ref10.h b/crypto/ed25519-donna/src/fuzz/curve25519-ref10.h
new file mode 100644 (file)
index 0000000..fc005b5
--- /dev/null
+++ b/crypto/ed25519-donna/src/fuzz/curve25519-ref10.h
@@ -0,0 +1,8 @@
+#ifndef CURVE25519_REF10_H
+#define CURVE25519_REF10_H
+
+int crypto_scalarmult_base_ref10(unsigned char *q,const unsigned char *n);
+int crypto_scalarmult_ref10(unsigned char *q, const unsigned char *n, const unsigned char *p);
+
+#endif /* CURVE25519_REF10_H */
+

diff --git a/crypto/ed25519-donna/src/fuzz/ed25519-donna-sse2.c b/crypto/ed25519-donna/src/fuzz/ed25519-donna-sse2.c
new file mode 100644 (file)
index 0000000..ba47b1e
--- /dev/null
+++ b/crypto/ed25519-donna/src/fuzz/ed25519-donna-sse2.c
@@ -0,0 +1,3 @@
+#define ED25519_SUFFIX _sse2
+#define ED25519_SSE2
+#include "../ed25519.c"

diff --git a/crypto/ed25519-donna/src/fuzz/ed25519-donna.c b/crypto/ed25519-donna/src/fuzz/ed25519-donna.c
new file mode 100644 (file)
index 0000000..45d03b6
--- /dev/null
+++ b/crypto/ed25519-donna/src/fuzz/ed25519-donna.c
@@ -0,0 +1 @@
+#include "../ed25519.c"

diff --git a/crypto/ed25519-donna/src/fuzz/ed25519-donna.h b/crypto/ed25519-donna/src/fuzz/ed25519-donna.h
new file mode 100644 (file)
index 0000000..7cd72e3
--- /dev/null
+++ b/crypto/ed25519-donna/src/fuzz/ed25519-donna.h
@@ -0,0 +1,34 @@
+#ifndef ED25519_H
+#define ED25519_H
+
+#include <stdlib.h>
+
+typedef unsigned char ed25519_signature[64];
+typedef unsigned char ed25519_public_key[32];
+typedef unsigned char ed25519_secret_key[32];
+
+typedef unsigned char curved25519_key[32];
+
+void ed25519_publickey(const ed25519_secret_key sk, ed25519_public_key pk);
+int ed25519_sign_open(const unsigned char *m, size_t mlen, const ed25519_public_key pk, const ed25519_signature RS);
+void ed25519_sign(const unsigned char *m, size_t mlen, const ed25519_secret_key sk, const ed25519_public_key pk, ed25519_signature RS);
+
+int ed25519_sign_open_batch(const unsigned char **m, size_t *mlen, const unsigned char **pk, const unsigned char **RS, size_t num, int *valid);
+
+void ed25519_randombytes_unsafe(void *out, size_t count);
+
+void curved25519_scalarmult_basepoint(curved25519_key pk, const curved25519_key e);
+
+#if defined(ED25519_SSE2)
+void ed25519_publickey_sse2(const ed25519_secret_key sk, ed25519_public_key pk);
+int ed25519_sign_open_sse2(const unsigned char *m, size_t mlen, const ed25519_public_key pk, const ed25519_signature RS);
+void ed25519_sign_sse2(const unsigned char *m, size_t mlen, const ed25519_secret_key sk, const ed25519_public_key pk, ed25519_signature RS);
+
+int ed25519_sign_open_batch_sse2(const unsigned char **m, size_t *mlen, const unsigned char **pk, const unsigned char **RS, size_t num, int *valid);
+
+void ed25519_randombytes_unsafe_sse2(void *out, size_t count);
+
+void curved25519_scalarmult_basepoint_sse2(curved25519_key pk, const curved25519_key e);
+#endif
+
+#endif // ED25519_H

diff --git a/crypto/ed25519-donna/src/fuzz/ed25519-ref10.c b/crypto/ed25519-donna/src/fuzz/ed25519-ref10.c
new file mode 100644 (file)
index 0000000..a8e802d
--- /dev/null
+++ b/crypto/ed25519-donna/src/fuzz/ed25519-ref10.c
@@ -0,0 +1,4647 @@
+#include <stdint.h>
+#include <stddef.h>
+#include <string.h>
+
+static int crypto_verify_32(const unsigned char *x,const unsigned char *y)
+{
+  unsigned int differentbits = 0;
+#define F(i) differentbits |= x[i] ^ y[i];
+  F(0)
+  F(1)
+  F(2)
+  F(3)
+  F(4)
+  F(5)
+  F(6)
+  F(7)
+  F(8)
+  F(9)
+  F(10)
+  F(11)
+  F(12)
+  F(13)
+  F(14)
+  F(15)
+  F(16)
+  F(17)
+  F(18)
+  F(19)
+  F(20)
+  F(21)
+  F(22)
+  F(23)
+  F(24)
+  F(25)
+  F(26)
+  F(27)
+  F(28)
+  F(29)
+  F(30)
+  F(31)
+  return (1 & ((differentbits - 1) >> 8)) - 1;
+}
+
+#if defined(ED25519_REFHASH)
+
+/* reference/slow SHA-512. really, do not use this */
+
+#define HASH_BLOCK_SIZE 128
+#define HASH_DIGEST_SIZE 64
+
+typedef struct sha512_state_t {
+       uint64_t H[8];
+       uint64_t T[2];
+       uint32_t leftover;
+       uint8_t buffer[HASH_BLOCK_SIZE];
+} sha512_state;
+
+typedef sha512_state ed25519_hash_context;
+
+static const uint64_t sha512_constants[80] = {
+       0x428a2f98d728ae22ull, 0x7137449123ef65cdull, 0xb5c0fbcfec4d3b2full, 0xe9b5dba58189dbbcull,
+       0x3956c25bf348b538ull, 0x59f111f1b605d019ull, 0x923f82a4af194f9bull, 0xab1c5ed5da6d8118ull,
+       0xd807aa98a3030242ull, 0x12835b0145706fbeull, 0x243185be4ee4b28cull, 0x550c7dc3d5ffb4e2ull,
+       0x72be5d74f27b896full, 0x80deb1fe3b1696b1ull, 0x9bdc06a725c71235ull, 0xc19bf174cf692694ull,
+       0xe49b69c19ef14ad2ull, 0xefbe4786384f25e3ull, 0x0fc19dc68b8cd5b5ull, 0x240ca1cc77ac9c65ull,
+       0x2de92c6f592b0275ull, 0x4a7484aa6ea6e483ull, 0x5cb0a9dcbd41fbd4ull, 0x76f988da831153b5ull,
+       0x983e5152ee66dfabull, 0xa831c66d2db43210ull, 0xb00327c898fb213full, 0xbf597fc7beef0ee4ull,
+       0xc6e00bf33da88fc2ull, 0xd5a79147930aa725ull, 0x06ca6351e003826full, 0x142929670a0e6e70ull,
+       0x27b70a8546d22ffcull, 0x2e1b21385c26c926ull, 0x4d2c6dfc5ac42aedull, 0x53380d139d95b3dfull,
+       0x650a73548baf63deull, 0x766a0abb3c77b2a8ull, 0x81c2c92e47edaee6ull, 0x92722c851482353bull,
+       0xa2bfe8a14cf10364ull, 0xa81a664bbc423001ull, 0xc24b8b70d0f89791ull, 0xc76c51a30654be30ull,
+       0xd192e819d6ef5218ull, 0xd69906245565a910ull, 0xf40e35855771202aull, 0x106aa07032bbd1b8ull,
+       0x19a4c116b8d2d0c8ull, 0x1e376c085141ab53ull, 0x2748774cdf8eeb99ull, 0x34b0bcb5e19b48a8ull,
+       0x391c0cb3c5c95a63ull, 0x4ed8aa4ae3418acbull, 0x5b9cca4f7763e373ull, 0x682e6ff3d6b2b8a3ull,
+       0x748f82ee5defb2fcull, 0x78a5636f43172f60ull, 0x84c87814a1f0ab72ull, 0x8cc702081a6439ecull,
+       0x90befffa23631e28ull, 0xa4506cebde82bde9ull, 0xbef9a3f7b2c67915ull, 0xc67178f2e372532bull,
+       0xca273eceea26619cull, 0xd186b8c721c0c207ull, 0xeada7dd6cde0eb1eull, 0xf57d4f7fee6ed178ull,
+       0x06f067aa72176fbaull, 0x0a637dc5a2c898a6ull, 0x113f9804bef90daeull, 0x1b710b35131c471bull,
+       0x28db77f523047d84ull, 0x32caab7b40c72493ull, 0x3c9ebe0a15c9bebcull, 0x431d67c49c100d4cull,
+       0x4cc5d4becb3e42b6ull, 0x597f299cfc657e2aull, 0x5fcb6fab3ad6faecull, 0x6c44198c4a475817ull
+};
+
+static uint64_t
+sha512_ROTR64(uint64_t x, int k) {
+       return (x >> k) | (x << (64 - k));
+}
+
+static uint64_t
+sha512_LOAD64_BE(const uint8_t *p) {
+       return 
+               ((uint64_t)p[0] << 56) |
+               ((uint64_t)p[1] << 48) |
+               ((uint64_t)p[2] << 40) |
+               ((uint64_t)p[3] << 32) |
+               ((uint64_t)p[4] << 24) |
+               ((uint64_t)p[5] << 16) |
+               ((uint64_t)p[6] <<  8) |
+               ((uint64_t)p[7]      );
+}
+
+static void
+sha512_STORE64_BE(uint8_t *p, uint64_t v) {
+       p[0] = (uint8_t)(v >> 56);
+       p[1] = (uint8_t)(v >> 48);
+       p[2] = (uint8_t)(v >> 40);
+       p[3] = (uint8_t)(v >> 32);
+       p[4] = (uint8_t)(v >> 24);
+       p[5] = (uint8_t)(v >> 16);
+       p[6] = (uint8_t)(v >>  8);
+       p[7] = (uint8_t)(v      );
+}
+
+#define Ch(x,y,z)  (z ^ (x & (y ^ z)))
+#define Maj(x,y,z) (((x | y) & z) | (x & y))
+#define S0(x)      (sha512_ROTR64(x, 28) ^ sha512_ROTR64(x, 34) ^ sha512_ROTR64(x, 39))
+#define S1(x)      (sha512_ROTR64(x, 14) ^ sha512_ROTR64(x, 18) ^ sha512_ROTR64(x, 41))
+#define G0(x)      (sha512_ROTR64(x,  1) ^ sha512_ROTR64(x,  8) ^ (x >>  7))
+#define G1(x)      (sha512_ROTR64(x, 19) ^ sha512_ROTR64(x, 61) ^ (x >>  6))
+#define W0(in,i)   (sha512_LOAD64_BE(&in[i * 8]))
+#define W1(i)      (G1(w[i - 2]) + w[i - 7] + G0(w[i - 15]) + w[i - 16])
+#define STEP(i) \
+       t1 = S0(r[0]) + Maj(r[0], r[1], r[2]); \
+       t0 = r[7] + S1(r[4]) + Ch(r[4], r[5], r[6]) + sha512_constants[i] + w[i]; \
+       r[7] = r[6]; \
+       r[6] = r[5]; \
+       r[5] = r[4]; \
+       r[4] = r[3] + t0; \
+       r[3] = r[2]; \
+       r[2] = r[1]; \
+       r[1] = r[0]; \
+       r[0] = t0 + t1;
+
+static void
+sha512_blocks(sha512_state *S, const uint8_t *in, size_t blocks) {
+       uint64_t r[8], w[80], t0, t1;
+       size_t i;
+
+       for (i = 0; i < 8; i++) r[i] = S->H[i];
+
+       while (blocks--) {
+               for (i =  0; i < 16; i++) { w[i] = W0(in, i); }
+               for (i = 16; i < 80; i++) { w[i] = W1(i); }
+               for (i =  0; i < 80; i++) { STEP(i); }
+               for (i =  0; i <  8; i++) { r[i] += S->H[i]; S->H[i] = r[i]; }
+               S->T[0] += HASH_BLOCK_SIZE * 8;
+               S->T[1] += (!S->T[0]) ? 1 : 0;
+               in += HASH_BLOCK_SIZE;
+       }
+}
+
+static void
+ed25519_hash_init(sha512_state *S) {
+       S->H[0] = 0x6a09e667f3bcc908ull;
+       S->H[1] = 0xbb67ae8584caa73bull;
+       S->H[2] = 0x3c6ef372fe94f82bull;
+       S->H[3] = 0xa54ff53a5f1d36f1ull;
+       S->H[4] = 0x510e527fade682d1ull;
+       S->H[5] = 0x9b05688c2b3e6c1full;
+       S->H[6] = 0x1f83d9abfb41bd6bull;
+       S->H[7] = 0x5be0cd19137e2179ull;
+       S->T[0] = 0;
+       S->T[1] = 0;
+       S->leftover = 0;
+}
+
+static void
+ed25519_hash_update(sha512_state *S, const uint8_t *in, size_t inlen) {
+       size_t blocks, want;
+
+       /* handle the previous data */
+       if (S->leftover) {
+               want = (HASH_BLOCK_SIZE - S->leftover);
+               want = (want < inlen) ? want : inlen;
+               memcpy(S->buffer + S->leftover, in, want);
+               S->leftover += (uint32_t)want;
+               if (S->leftover < HASH_BLOCK_SIZE)
+                       return;
+               in += want;
+               inlen -= want;
+               sha512_blocks(S, S->buffer, 1);
+       }
+
+       /* handle the current data */
+       blocks = (inlen & ~(HASH_BLOCK_SIZE - 1));
+       S->leftover = (uint32_t)(inlen - blocks);
+       if (blocks) {
+               sha512_blocks(S, in, blocks / HASH_BLOCK_SIZE);
+               in += blocks;
+       }
+
+       /* handle leftover data */
+       if (S->leftover)
+               memcpy(S->buffer, in, S->leftover);
+}
+
+static void
+ed25519_hash_final(sha512_state *S, uint8_t *hash) {
+       uint64_t t0 = S->T[0] + (S->leftover * 8), t1 = S->T[1];
+
+       S->buffer[S->leftover] = 0x80;
+       if (S->leftover <= 111) {
+               memset(S->buffer + S->leftover + 1, 0, 111 - S->leftover);
+       } else {
+               memset(S->buffer + S->leftover + 1, 0, 127 - S->leftover);
+               sha512_blocks(S, S->buffer, 1);
+               memset(S->buffer, 0, 112);
+       }
+
+       sha512_STORE64_BE(S->buffer + 112, t1);
+       sha512_STORE64_BE(S->buffer + 120, t0);
+       sha512_blocks(S, S->buffer, 1);
+
+       sha512_STORE64_BE(&hash[ 0], S->H[0]);
+       sha512_STORE64_BE(&hash[ 8], S->H[1]);
+       sha512_STORE64_BE(&hash[16], S->H[2]);
+       sha512_STORE64_BE(&hash[24], S->H[3]);
+       sha512_STORE64_BE(&hash[32], S->H[4]);
+       sha512_STORE64_BE(&hash[40], S->H[5]);
+       sha512_STORE64_BE(&hash[48], S->H[6]);
+       sha512_STORE64_BE(&hash[56], S->H[7]);
+}
+
+static void
+crypto_hash_sha512(unsigned char *hash, const unsigned char *in, size_t inlen) {
+       ed25519_hash_context ctx;
+       ed25519_hash_init(&ctx);
+       ed25519_hash_update(&ctx, in, inlen);
+       ed25519_hash_final(&ctx, hash);
+}
+
+#else
+
+#include <openssl/sha.h>
+
+static void
+crypto_hash_sha512(unsigned char *hash, const unsigned char *in, size_t inlen) {
+       SHA512(in, inlen, hash);
+}
+
+#endif
+
+
+
+
+typedef int32_t crypto_int32;
+typedef uint32_t crypto_uint32;
+typedef int64_t crypto_int64;
+typedef uint64_t crypto_uint64;
+
+typedef crypto_int32 fe[10];
+
+/*
+h = 0
+*/
+
+static void fe_0(fe h)
+{
+  h[0] = 0;
+  h[1] = 0;
+  h[2] = 0;
+  h[3] = 0;
+  h[4] = 0;
+  h[5] = 0;
+  h[6] = 0;
+  h[7] = 0;
+  h[8] = 0;
+  h[9] = 0;
+}
+
+/*
+h = 1
+*/
+
+static void fe_1(fe h)
+{
+  h[0] = 1;
+  h[1] = 0;
+  h[2] = 0;
+  h[3] = 0;
+  h[4] = 0;
+  h[5] = 0;
+  h[6] = 0;
+  h[7] = 0;
+  h[8] = 0;
+  h[9] = 0;
+}
+
+/*
+h = f + g
+Can overlap h with f or g.
+
+Preconditions:
+   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+   |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+static void fe_add(fe h,const fe f,const fe g)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 g0 = g[0];
+  crypto_int32 g1 = g[1];
+  crypto_int32 g2 = g[2];
+  crypto_int32 g3 = g[3];
+  crypto_int32 g4 = g[4];
+  crypto_int32 g5 = g[5];
+  crypto_int32 g6 = g[6];
+  crypto_int32 g7 = g[7];
+  crypto_int32 g8 = g[8];
+  crypto_int32 g9 = g[9];
+  crypto_int32 h0 = f0 + g0;
+  crypto_int32 h1 = f1 + g1;
+  crypto_int32 h2 = f2 + g2;
+  crypto_int32 h3 = f3 + g3;
+  crypto_int32 h4 = f4 + g4;
+  crypto_int32 h5 = f5 + g5;
+  crypto_int32 h6 = f6 + g6;
+  crypto_int32 h7 = f7 + g7;
+  crypto_int32 h8 = f8 + g8;
+  crypto_int32 h9 = f9 + g9;
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+
+/*
+Replace (f,g) with (g,g) if b == 1;
+replace (f,g) with (f,g) if b == 0.
+
+Preconditions: b in {0,1}.
+*/
+
+static void fe_cmov(fe f,const fe g,unsigned int b)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 g0 = g[0];
+  crypto_int32 g1 = g[1];
+  crypto_int32 g2 = g[2];
+  crypto_int32 g3 = g[3];
+  crypto_int32 g4 = g[4];
+  crypto_int32 g5 = g[5];
+  crypto_int32 g6 = g[6];
+  crypto_int32 g7 = g[7];
+  crypto_int32 g8 = g[8];
+  crypto_int32 g9 = g[9];
+  crypto_int32 x0 = f0 ^ g0;
+  crypto_int32 x1 = f1 ^ g1;
+  crypto_int32 x2 = f2 ^ g2;
+  crypto_int32 x3 = f3 ^ g3;
+  crypto_int32 x4 = f4 ^ g4;
+  crypto_int32 x5 = f5 ^ g5;
+  crypto_int32 x6 = f6 ^ g6;
+  crypto_int32 x7 = f7 ^ g7;
+  crypto_int32 x8 = f8 ^ g8;
+  crypto_int32 x9 = f9 ^ g9;
+  b = -b;
+  x0 &= b;
+  x1 &= b;
+  x2 &= b;
+  x3 &= b;
+  x4 &= b;
+  x5 &= b;
+  x6 &= b;
+  x7 &= b;
+  x8 &= b;
+  x9 &= b;
+  f[0] = f0 ^ x0;
+  f[1] = f1 ^ x1;
+  f[2] = f2 ^ x2;
+  f[3] = f3 ^ x3;
+  f[4] = f4 ^ x4;
+  f[5] = f5 ^ x5;
+  f[6] = f6 ^ x6;
+  f[7] = f7 ^ x7;
+  f[8] = f8 ^ x8;
+  f[9] = f9 ^ x9;
+}
+
+
+/*
+h = f
+*/
+
+static void fe_copy(fe h,const fe f)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  h[0] = f0;
+  h[1] = f1;
+  h[2] = f2;
+  h[3] = f3;
+  h[4] = f4;
+  h[5] = f5;
+  h[6] = f6;
+  h[7] = f7;
+  h[8] = f8;
+  h[9] = f9;
+}
+
+
+static crypto_uint64 load_3(const unsigned char *in)
+{
+  crypto_uint64 result;
+  result = (crypto_uint64) in[0];
+  result |= ((crypto_uint64) in[1]) << 8;
+  result |= ((crypto_uint64) in[2]) << 16;
+  return result;
+}
+
+static crypto_uint64 load_4(const unsigned char *in)
+{
+  crypto_uint64 result;
+  result = (crypto_uint64) in[0];
+  result |= ((crypto_uint64) in[1]) << 8;
+  result |= ((crypto_uint64) in[2]) << 16;
+  result |= ((crypto_uint64) in[3]) << 24;
+  return result;
+}
+
+/*
+Ignores top bit of h.
+*/
+
+static void fe_frombytes(fe h,const unsigned char *s)
+{
+  crypto_int64 h0 = load_4(s);
+  crypto_int64 h1 = load_3(s + 4) << 6;
+  crypto_int64 h2 = load_3(s + 7) << 5;
+  crypto_int64 h3 = load_3(s + 10) << 3;
+  crypto_int64 h4 = load_3(s + 13) << 2;
+  crypto_int64 h5 = load_4(s + 16);
+  crypto_int64 h6 = load_3(s + 20) << 7;
+  crypto_int64 h7 = load_3(s + 23) << 5;
+  crypto_int64 h8 = load_3(s + 26) << 4;
+  crypto_int64 h9 = (load_3(s + 29) & 8388607) << 2;
+  crypto_int64 carry0;
+  crypto_int64 carry1;
+  crypto_int64 carry2;
+  crypto_int64 carry3;
+  crypto_int64 carry4;
+  crypto_int64 carry5;
+  crypto_int64 carry6;
+  crypto_int64 carry7;
+  crypto_int64 carry8;
+  crypto_int64 carry9;
+
+  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+/*
+Preconditions:
+  |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+
+Write p=2^255-19; q=floor(h/p).
+Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
+
+Proof:
+  Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
+  Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
+
+  Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
+  Then 0<y<1.
+
+  Write r=h-pq.
+  Have 0<=r<=p-1=2^255-20.
+  Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.
+
+  Write x=r+19(2^-255)r+y.
+  Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.
+
+  Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
+  so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
+*/
+
+static void fe_tobytes(unsigned char *s,const fe h)
+{
+  crypto_int32 h0 = h[0];
+  crypto_int32 h1 = h[1];
+  crypto_int32 h2 = h[2];
+  crypto_int32 h3 = h[3];
+  crypto_int32 h4 = h[4];
+  crypto_int32 h5 = h[5];
+  crypto_int32 h6 = h[6];
+  crypto_int32 h7 = h[7];
+  crypto_int32 h8 = h[8];
+  crypto_int32 h9 = h[9];
+  crypto_int32 q;
+  crypto_int32 carry0;
+  crypto_int32 carry1;
+  crypto_int32 carry2;
+  crypto_int32 carry3;
+  crypto_int32 carry4;
+  crypto_int32 carry5;
+  crypto_int32 carry6;
+  crypto_int32 carry7;
+  crypto_int32 carry8;
+  crypto_int32 carry9;
+
+  q = (19 * h9 + (((crypto_int32) 1) << 24)) >> 25;
+  q = (h0 + q) >> 26;
+  q = (h1 + q) >> 25;
+  q = (h2 + q) >> 26;
+  q = (h3 + q) >> 25;
+  q = (h4 + q) >> 26;
+  q = (h5 + q) >> 25;
+  q = (h6 + q) >> 26;
+  q = (h7 + q) >> 25;
+  q = (h8 + q) >> 26;
+  q = (h9 + q) >> 25;
+
+  /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
+  h0 += 19 * q;
+  /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
+
+  carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25;
+  carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26;
+  carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25;
+  carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26;
+  carry9 = h9 >> 25;               h9 -= carry9 << 25;
+                  /* h10 = carry9 */
+
+  /*
+  Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
+  Have h0+...+2^230 h9 between 0 and 2^255-1;
+  evidently 2^255 h10-2^255 q = 0.
+  Goal: Output h0+...+2^230 h9.
+  */
+
+  s[0] = h0 >> 0;
+  s[1] = h0 >> 8;
+  s[2] = h0 >> 16;
+  s[3] = (h0 >> 24) | (h1 << 2);
+  s[4] = h1 >> 6;
+  s[5] = h1 >> 14;
+  s[6] = (h1 >> 22) | (h2 << 3);
+  s[7] = h2 >> 5;
+  s[8] = h2 >> 13;
+  s[9] = (h2 >> 21) | (h3 << 5);
+  s[10] = h3 >> 3;
+  s[11] = h3 >> 11;
+  s[12] = (h3 >> 19) | (h4 << 6);
+  s[13] = h4 >> 2;
+  s[14] = h4 >> 10;
+  s[15] = h4 >> 18;
+  s[16] = h5 >> 0;
+  s[17] = h5 >> 8;
+  s[18] = h5 >> 16;
+  s[19] = (h5 >> 24) | (h6 << 1);
+  s[20] = h6 >> 7;
+  s[21] = h6 >> 15;
+  s[22] = (h6 >> 23) | (h7 << 3);
+  s[23] = h7 >> 5;
+  s[24] = h7 >> 13;
+  s[25] = (h7 >> 21) | (h8 << 4);
+  s[26] = h8 >> 4;
+  s[27] = h8 >> 12;
+  s[28] = (h8 >> 20) | (h9 << 6);
+  s[29] = h9 >> 2;
+  s[30] = h9 >> 10;
+  s[31] = h9 >> 18;
+}
+
+
+/*
+h = f - g
+Can overlap h with f or g.
+
+Preconditions:
+   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+   |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+static void fe_sub(fe h,const fe f,const fe g)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 g0 = g[0];
+  crypto_int32 g1 = g[1];
+  crypto_int32 g2 = g[2];
+  crypto_int32 g3 = g[3];
+  crypto_int32 g4 = g[4];
+  crypto_int32 g5 = g[5];
+  crypto_int32 g6 = g[6];
+  crypto_int32 g7 = g[7];
+  crypto_int32 g8 = g[8];
+  crypto_int32 g9 = g[9];
+  crypto_int32 h0 = f0 - g0;
+  crypto_int32 h1 = f1 - g1;
+  crypto_int32 h2 = f2 - g2;
+  crypto_int32 h3 = f3 - g3;
+  crypto_int32 h4 = f4 - g4;
+  crypto_int32 h5 = f5 - g5;
+  crypto_int32 h6 = f6 - g6;
+  crypto_int32 h7 = f7 - g7;
+  crypto_int32 h8 = f8 - g8;
+  crypto_int32 h9 = f9 - g9;
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+
+/*
+h = f * f
+Can overlap h with f.
+
+Preconditions:
+   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+*/
+
+/*
+See fe_mul.c for discussion of implementation strategy.
+*/
+
+static void fe_sq(fe h,const fe f)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 f0_2 = 2 * f0;
+  crypto_int32 f1_2 = 2 * f1;
+  crypto_int32 f2_2 = 2 * f2;
+  crypto_int32 f3_2 = 2 * f3;
+  crypto_int32 f4_2 = 2 * f4;
+  crypto_int32 f5_2 = 2 * f5;
+  crypto_int32 f6_2 = 2 * f6;
+  crypto_int32 f7_2 = 2 * f7;
+  crypto_int32 f5_38 = 38 * f5; /* 1.959375*2^30 */
+  crypto_int32 f6_19 = 19 * f6; /* 1.959375*2^30 */
+  crypto_int32 f7_38 = 38 * f7; /* 1.959375*2^30 */
+  crypto_int32 f8_19 = 19 * f8; /* 1.959375*2^30 */
+  crypto_int32 f9_38 = 38 * f9; /* 1.959375*2^30 */
+  crypto_int64 f0f0    = f0   * (crypto_int64) f0;
+  crypto_int64 f0f1_2  = f0_2 * (crypto_int64) f1;
+  crypto_int64 f0f2_2  = f0_2 * (crypto_int64) f2;
+  crypto_int64 f0f3_2  = f0_2 * (crypto_int64) f3;
+  crypto_int64 f0f4_2  = f0_2 * (crypto_int64) f4;
+  crypto_int64 f0f5_2  = f0_2 * (crypto_int64) f5;
+  crypto_int64 f0f6_2  = f0_2 * (crypto_int64) f6;
+  crypto_int64 f0f7_2  = f0_2 * (crypto_int64) f7;
+  crypto_int64 f0f8_2  = f0_2 * (crypto_int64) f8;
+  crypto_int64 f0f9_2  = f0_2 * (crypto_int64) f9;
+  crypto_int64 f1f1_2  = f1_2 * (crypto_int64) f1;
+  crypto_int64 f1f2_2  = f1_2 * (crypto_int64) f2;
+  crypto_int64 f1f3_4  = f1_2 * (crypto_int64) f3_2;
+  crypto_int64 f1f4_2  = f1_2 * (crypto_int64) f4;
+  crypto_int64 f1f5_4  = f1_2 * (crypto_int64) f5_2;
+  crypto_int64 f1f6_2  = f1_2 * (crypto_int64) f6;
+  crypto_int64 f1f7_4  = f1_2 * (crypto_int64) f7_2;
+  crypto_int64 f1f8_2  = f1_2 * (crypto_int64) f8;
+  crypto_int64 f1f9_76 = f1_2 * (crypto_int64) f9_38;
+  crypto_int64 f2f2    = f2   * (crypto_int64) f2;
+  crypto_int64 f2f3_2  = f2_2 * (crypto_int64) f3;
+  crypto_int64 f2f4_2  = f2_2 * (crypto_int64) f4;
+  crypto_int64 f2f5_2  = f2_2 * (crypto_int64) f5;
+  crypto_int64 f2f6_2  = f2_2 * (crypto_int64) f6;
+  crypto_int64 f2f7_2  = f2_2 * (crypto_int64) f7;
+  crypto_int64 f2f8_38 = f2_2 * (crypto_int64) f8_19;
+  crypto_int64 f2f9_38 = f2   * (crypto_int64) f9_38;
+  crypto_int64 f3f3_2  = f3_2 * (crypto_int64) f3;
+  crypto_int64 f3f4_2  = f3_2 * (crypto_int64) f4;
+  crypto_int64 f3f5_4  = f3_2 * (crypto_int64) f5_2;
+  crypto_int64 f3f6_2  = f3_2 * (crypto_int64) f6;
+  crypto_int64 f3f7_76 = f3_2 * (crypto_int64) f7_38;
+  crypto_int64 f3f8_38 = f3_2 * (crypto_int64) f8_19;
+  crypto_int64 f3f9_76 = f3_2 * (crypto_int64) f9_38;
+  crypto_int64 f4f4    = f4   * (crypto_int64) f4;
+  crypto_int64 f4f5_2  = f4_2 * (crypto_int64) f5;
+  crypto_int64 f4f6_38 = f4_2 * (crypto_int64) f6_19;
+  crypto_int64 f4f7_38 = f4   * (crypto_int64) f7_38;
+  crypto_int64 f4f8_38 = f4_2 * (crypto_int64) f8_19;
+  crypto_int64 f4f9_38 = f4   * (crypto_int64) f9_38;
+  crypto_int64 f5f5_38 = f5   * (crypto_int64) f5_38;
+  crypto_int64 f5f6_38 = f5_2 * (crypto_int64) f6_19;
+  crypto_int64 f5f7_76 = f5_2 * (crypto_int64) f7_38;
+  crypto_int64 f5f8_38 = f5_2 * (crypto_int64) f8_19;
+  crypto_int64 f5f9_76 = f5_2 * (crypto_int64) f9_38;
+  crypto_int64 f6f6_19 = f6   * (crypto_int64) f6_19;
+  crypto_int64 f6f7_38 = f6   * (crypto_int64) f7_38;
+  crypto_int64 f6f8_38 = f6_2 * (crypto_int64) f8_19;
+  crypto_int64 f6f9_38 = f6   * (crypto_int64) f9_38;
+  crypto_int64 f7f7_38 = f7   * (crypto_int64) f7_38;
+  crypto_int64 f7f8_38 = f7_2 * (crypto_int64) f8_19;
+  crypto_int64 f7f9_76 = f7_2 * (crypto_int64) f9_38;
+  crypto_int64 f8f8_19 = f8   * (crypto_int64) f8_19;
+  crypto_int64 f8f9_38 = f8   * (crypto_int64) f9_38;
+  crypto_int64 f9f9_38 = f9   * (crypto_int64) f9_38;
+  crypto_int64 h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
+  crypto_int64 h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
+  crypto_int64 h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
+  crypto_int64 h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
+  crypto_int64 h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
+  crypto_int64 h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
+  crypto_int64 h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
+  crypto_int64 h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
+  crypto_int64 h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
+  crypto_int64 h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
+  crypto_int64 carry0;
+  crypto_int64 carry1;
+  crypto_int64 carry2;
+  crypto_int64 carry3;
+  crypto_int64 carry4;
+  crypto_int64 carry5;
+  crypto_int64 carry6;
+  crypto_int64 carry7;
+  crypto_int64 carry8;
+  crypto_int64 carry9;
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+
+  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+
+  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+
+  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+/*
+h = 2 * f * f
+Can overlap h with f.
+
+Preconditions:
+   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+*/
+
+/*
+See fe_mul.c for discussion of implementation strategy.
+*/
+
+static void fe_sq2(fe h,const fe f)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 f0_2 = 2 * f0;
+  crypto_int32 f1_2 = 2 * f1;
+  crypto_int32 f2_2 = 2 * f2;
+  crypto_int32 f3_2 = 2 * f3;
+  crypto_int32 f4_2 = 2 * f4;
+  crypto_int32 f5_2 = 2 * f5;
+  crypto_int32 f6_2 = 2 * f6;
+  crypto_int32 f7_2 = 2 * f7;
+  crypto_int32 f5_38 = 38 * f5; /* 1.959375*2^30 */
+  crypto_int32 f6_19 = 19 * f6; /* 1.959375*2^30 */
+  crypto_int32 f7_38 = 38 * f7; /* 1.959375*2^30 */
+  crypto_int32 f8_19 = 19 * f8; /* 1.959375*2^30 */
+  crypto_int32 f9_38 = 38 * f9; /* 1.959375*2^30 */
+  crypto_int64 f0f0    = f0   * (crypto_int64) f0;
+  crypto_int64 f0f1_2  = f0_2 * (crypto_int64) f1;
+  crypto_int64 f0f2_2  = f0_2 * (crypto_int64) f2;
+  crypto_int64 f0f3_2  = f0_2 * (crypto_int64) f3;
+  crypto_int64 f0f4_2  = f0_2 * (crypto_int64) f4;
+  crypto_int64 f0f5_2  = f0_2 * (crypto_int64) f5;
+  crypto_int64 f0f6_2  = f0_2 * (crypto_int64) f6;
+  crypto_int64 f0f7_2  = f0_2 * (crypto_int64) f7;
+  crypto_int64 f0f8_2  = f0_2 * (crypto_int64) f8;
+  crypto_int64 f0f9_2  = f0_2 * (crypto_int64) f9;
+  crypto_int64 f1f1_2  = f1_2 * (crypto_int64) f1;
+  crypto_int64 f1f2_2  = f1_2 * (crypto_int64) f2;
+  crypto_int64 f1f3_4  = f1_2 * (crypto_int64) f3_2;
+  crypto_int64 f1f4_2  = f1_2 * (crypto_int64) f4;
+  crypto_int64 f1f5_4  = f1_2 * (crypto_int64) f5_2;
+  crypto_int64 f1f6_2  = f1_2 * (crypto_int64) f6;
+  crypto_int64 f1f7_4  = f1_2 * (crypto_int64) f7_2;
+  crypto_int64 f1f8_2  = f1_2 * (crypto_int64) f8;
+  crypto_int64 f1f9_76 = f1_2 * (crypto_int64) f9_38;
+  crypto_int64 f2f2    = f2   * (crypto_int64) f2;
+  crypto_int64 f2f3_2  = f2_2 * (crypto_int64) f3;
+  crypto_int64 f2f4_2  = f2_2 * (crypto_int64) f4;
+  crypto_int64 f2f5_2  = f2_2 * (crypto_int64) f5;
+  crypto_int64 f2f6_2  = f2_2 * (crypto_int64) f6;
+  crypto_int64 f2f7_2  = f2_2 * (crypto_int64) f7;
+  crypto_int64 f2f8_38 = f2_2 * (crypto_int64) f8_19;
+  crypto_int64 f2f9_38 = f2   * (crypto_int64) f9_38;
+  crypto_int64 f3f3_2  = f3_2 * (crypto_int64) f3;
+  crypto_int64 f3f4_2  = f3_2 * (crypto_int64) f4;
+  crypto_int64 f3f5_4  = f3_2 * (crypto_int64) f5_2;
+  crypto_int64 f3f6_2  = f3_2 * (crypto_int64) f6;
+  crypto_int64 f3f7_76 = f3_2 * (crypto_int64) f7_38;
+  crypto_int64 f3f8_38 = f3_2 * (crypto_int64) f8_19;
+  crypto_int64 f3f9_76 = f3_2 * (crypto_int64) f9_38;
+  crypto_int64 f4f4    = f4   * (crypto_int64) f4;
+  crypto_int64 f4f5_2  = f4_2 * (crypto_int64) f5;
+  crypto_int64 f4f6_38 = f4_2 * (crypto_int64) f6_19;
+  crypto_int64 f4f7_38 = f4   * (crypto_int64) f7_38;
+  crypto_int64 f4f8_38 = f4_2 * (crypto_int64) f8_19;
+  crypto_int64 f4f9_38 = f4   * (crypto_int64) f9_38;
+  crypto_int64 f5f5_38 = f5   * (crypto_int64) f5_38;
+  crypto_int64 f5f6_38 = f5_2 * (crypto_int64) f6_19;
+  crypto_int64 f5f7_76 = f5_2 * (crypto_int64) f7_38;
+  crypto_int64 f5f8_38 = f5_2 * (crypto_int64) f8_19;
+  crypto_int64 f5f9_76 = f5_2 * (crypto_int64) f9_38;
+  crypto_int64 f6f6_19 = f6   * (crypto_int64) f6_19;
+  crypto_int64 f6f7_38 = f6   * (crypto_int64) f7_38;
+  crypto_int64 f6f8_38 = f6_2 * (crypto_int64) f8_19;
+  crypto_int64 f6f9_38 = f6   * (crypto_int64) f9_38;
+  crypto_int64 f7f7_38 = f7   * (crypto_int64) f7_38;
+  crypto_int64 f7f8_38 = f7_2 * (crypto_int64) f8_19;
+  crypto_int64 f7f9_76 = f7_2 * (crypto_int64) f9_38;
+  crypto_int64 f8f8_19 = f8   * (crypto_int64) f8_19;
+  crypto_int64 f8f9_38 = f8   * (crypto_int64) f9_38;
+  crypto_int64 f9f9_38 = f9   * (crypto_int64) f9_38;
+  crypto_int64 h0 = f0f0  +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
+  crypto_int64 h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
+  crypto_int64 h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
+  crypto_int64 h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
+  crypto_int64 h4 = f0f4_2+f1f3_4 +f2f2   +f5f9_76+f6f8_38+f7f7_38;
+  crypto_int64 h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
+  crypto_int64 h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
+  crypto_int64 h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
+  crypto_int64 h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4   +f9f9_38;
+  crypto_int64 h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
+  crypto_int64 carry0;
+  crypto_int64 carry1;
+  crypto_int64 carry2;
+  crypto_int64 carry3;
+  crypto_int64 carry4;
+  crypto_int64 carry5;
+  crypto_int64 carry6;
+  crypto_int64 carry7;
+  crypto_int64 carry8;
+  crypto_int64 carry9;
+
+  h0 += h0;
+  h1 += h1;
+  h2 += h2;
+  h3 += h3;
+  h4 += h4;
+  h5 += h5;
+  h6 += h6;
+  h7 += h7;
+  h8 += h8;
+  h9 += h9;
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+
+  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+
+  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+
+  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+
+  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+/*
+h = f * g
+Can overlap h with f or g.
+
+Preconditions:
+   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+   |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
+
+Postconditions:
+   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
+*/
+
+/*
+Notes on implementation strategy:
+
+Using schoolbook multiplication.
+Karatsuba would save a little in some cost models.
+
+Most multiplications by 2 and 19 are 32-bit precomputations;
+cheaper than 64-bit postcomputations.
+
+There is one remaining multiplication by 19 in the carry chain;
+one *19 precomputation can be merged into this,
+but the resulting data flow is considerably less clean.
+
+There are 12 carries below.
+10 of them are 2-way parallelizable and vectorizable.
+Can get away with 11 carries, but then data flow is much deeper.
+
+With tighter constraints on inputs can squeeze carries into int32.
+*/
+
+static void fe_mul(fe h,const fe f,const fe g)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 g0 = g[0];
+  crypto_int32 g1 = g[1];
+  crypto_int32 g2 = g[2];
+  crypto_int32 g3 = g[3];
+  crypto_int32 g4 = g[4];
+  crypto_int32 g5 = g[5];
+  crypto_int32 g6 = g[6];
+  crypto_int32 g7 = g[7];
+  crypto_int32 g8 = g[8];
+  crypto_int32 g9 = g[9];
+  crypto_int32 g1_19 = 19 * g1; /* 1.959375*2^29 */
+  crypto_int32 g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
+  crypto_int32 g3_19 = 19 * g3;
+  crypto_int32 g4_19 = 19 * g4;
+  crypto_int32 g5_19 = 19 * g5;
+  crypto_int32 g6_19 = 19 * g6;
+  crypto_int32 g7_19 = 19 * g7;
+  crypto_int32 g8_19 = 19 * g8;
+  crypto_int32 g9_19 = 19 * g9;
+  crypto_int32 f1_2 = 2 * f1;
+  crypto_int32 f3_2 = 2 * f3;
+  crypto_int32 f5_2 = 2 * f5;
+  crypto_int32 f7_2 = 2 * f7;
+  crypto_int32 f9_2 = 2 * f9;
+  crypto_int64 f0g0    = f0   * (crypto_int64) g0;
+  crypto_int64 f0g1    = f0   * (crypto_int64) g1;
+  crypto_int64 f0g2    = f0   * (crypto_int64) g2;
+  crypto_int64 f0g3    = f0   * (crypto_int64) g3;
+  crypto_int64 f0g4    = f0   * (crypto_int64) g4;
+  crypto_int64 f0g5    = f0   * (crypto_int64) g5;
+  crypto_int64 f0g6    = f0   * (crypto_int64) g6;
+  crypto_int64 f0g7    = f0   * (crypto_int64) g7;
+  crypto_int64 f0g8    = f0   * (crypto_int64) g8;
+  crypto_int64 f0g9    = f0   * (crypto_int64) g9;
+  crypto_int64 f1g0    = f1   * (crypto_int64) g0;
+  crypto_int64 f1g1_2  = f1_2 * (crypto_int64) g1;
+  crypto_int64 f1g2    = f1   * (crypto_int64) g2;
+  crypto_int64 f1g3_2  = f1_2 * (crypto_int64) g3;
+  crypto_int64 f1g4    = f1   * (crypto_int64) g4;
+  crypto_int64 f1g5_2  = f1_2 * (crypto_int64) g5;
+  crypto_int64 f1g6    = f1   * (crypto_int64) g6;
+  crypto_int64 f1g7_2  = f1_2 * (crypto_int64) g7;
+  crypto_int64 f1g8    = f1   * (crypto_int64) g8;
+  crypto_int64 f1g9_38 = f1_2 * (crypto_int64) g9_19;
+  crypto_int64 f2g0    = f2   * (crypto_int64) g0;
+  crypto_int64 f2g1    = f2   * (crypto_int64) g1;
+  crypto_int64 f2g2    = f2   * (crypto_int64) g2;
+  crypto_int64 f2g3    = f2   * (crypto_int64) g3;
+  crypto_int64 f2g4    = f2   * (crypto_int64) g4;
+  crypto_int64 f2g5    = f2   * (crypto_int64) g5;
+  crypto_int64 f2g6    = f2   * (crypto_int64) g6;
+  crypto_int64 f2g7    = f2   * (crypto_int64) g7;
+  crypto_int64 f2g8_19 = f2   * (crypto_int64) g8_19;
+  crypto_int64 f2g9_19 = f2   * (crypto_int64) g9_19;
+  crypto_int64 f3g0    = f3   * (crypto_int64) g0;
+  crypto_int64 f3g1_2  = f3_2 * (crypto_int64) g1;
+  crypto_int64 f3g2    = f3   * (crypto_int64) g2;
+  crypto_int64 f3g3_2  = f3_2 * (crypto_int64) g3;
+  crypto_int64 f3g4    = f3   * (crypto_int64) g4;
+  crypto_int64 f3g5_2  = f3_2 * (crypto_int64) g5;
+  crypto_int64 f3g6    = f3   * (crypto_int64) g6;
+  crypto_int64 f3g7_38 = f3_2 * (crypto_int64) g7_19;
+  crypto_int64 f3g8_19 = f3   * (crypto_int64) g8_19;
+  crypto_int64 f3g9_38 = f3_2 * (crypto_int64) g9_19;
+  crypto_int64 f4g0    = f4   * (crypto_int64) g0;
+  crypto_int64 f4g1    = f4   * (crypto_int64) g1;
+  crypto_int64 f4g2    = f4   * (crypto_int64) g2;
+  crypto_int64 f4g3    = f4   * (crypto_int64) g3;
+  crypto_int64 f4g4    = f4   * (crypto_int64) g4;
+  crypto_int64 f4g5    = f4   * (crypto_int64) g5;
+  crypto_int64 f4g6_19 = f4   * (crypto_int64) g6_19;
+  crypto_int64 f4g7_19 = f4   * (crypto_int64) g7_19;
+  crypto_int64 f4g8_19 = f4   * (crypto_int64) g8_19;
+  crypto_int64 f4g9_19 = f4   * (crypto_int64) g9_19;
+  crypto_int64 f5g0    = f5   * (crypto_int64) g0;
+  crypto_int64 f5g1_2  = f5_2 * (crypto_int64) g1;
+  crypto_int64 f5g2    = f5   * (crypto_int64) g2;
+  crypto_int64 f5g3_2  = f5_2 * (crypto_int64) g3;
+  crypto_int64 f5g4    = f5   * (crypto_int64) g4;
+  crypto_int64 f5g5_38 = f5_2 * (crypto_int64) g5_19;
+  crypto_int64 f5g6_19 = f5   * (crypto_int64) g6_19;
+  crypto_int64 f5g7_38 = f5_2 * (crypto_int64) g7_19;
+  crypto_int64 f5g8_19 = f5   * (crypto_int64) g8_19;
+  crypto_int64 f5g9_38 = f5_2 * (crypto_int64) g9_19;
+  crypto_int64 f6g0    = f6   * (crypto_int64) g0;
+  crypto_int64 f6g1    = f6   * (crypto_int64) g1;
+  crypto_int64 f6g2    = f6   * (crypto_int64) g2;
+  crypto_int64 f6g3    = f6   * (crypto_int64) g3;
+  crypto_int64 f6g4_19 = f6   * (crypto_int64) g4_19;
+  crypto_int64 f6g5_19 = f6   * (crypto_int64) g5_19;
+  crypto_int64 f6g6_19 = f6   * (crypto_int64) g6_19;
+  crypto_int64 f6g7_19 = f6   * (crypto_int64) g7_19;
+  crypto_int64 f6g8_19 = f6   * (crypto_int64) g8_19;
+  crypto_int64 f6g9_19 = f6   * (crypto_int64) g9_19;
+  crypto_int64 f7g0    = f7   * (crypto_int64) g0;
+  crypto_int64 f7g1_2  = f7_2 * (crypto_int64) g1;
+  crypto_int64 f7g2    = f7   * (crypto_int64) g2;
+  crypto_int64 f7g3_38 = f7_2 * (crypto_int64) g3_19;
+  crypto_int64 f7g4_19 = f7   * (crypto_int64) g4_19;
+  crypto_int64 f7g5_38 = f7_2 * (crypto_int64) g5_19;
+  crypto_int64 f7g6_19 = f7   * (crypto_int64) g6_19;
+  crypto_int64 f7g7_38 = f7_2 * (crypto_int64) g7_19;
+  crypto_int64 f7g8_19 = f7   * (crypto_int64) g8_19;
+  crypto_int64 f7g9_38 = f7_2 * (crypto_int64) g9_19;
+  crypto_int64 f8g0    = f8   * (crypto_int64) g0;
+  crypto_int64 f8g1    = f8   * (crypto_int64) g1;
+  crypto_int64 f8g2_19 = f8   * (crypto_int64) g2_19;
+  crypto_int64 f8g3_19 = f8   * (crypto_int64) g3_19;
+  crypto_int64 f8g4_19 = f8   * (crypto_int64) g4_19;
+  crypto_int64 f8g5_19 = f8   * (crypto_int64) g5_19;
+  crypto_int64 f8g6_19 = f8   * (crypto_int64) g6_19;
+  crypto_int64 f8g7_19 = f8   * (crypto_int64) g7_19;
+  crypto_int64 f8g8_19 = f8   * (crypto_int64) g8_19;
+  crypto_int64 f8g9_19 = f8   * (crypto_int64) g9_19;
+  crypto_int64 f9g0    = f9   * (crypto_int64) g0;
+  crypto_int64 f9g1_38 = f9_2 * (crypto_int64) g1_19;
+  crypto_int64 f9g2_19 = f9   * (crypto_int64) g2_19;
+  crypto_int64 f9g3_38 = f9_2 * (crypto_int64) g3_19;
+  crypto_int64 f9g4_19 = f9   * (crypto_int64) g4_19;
+  crypto_int64 f9g5_38 = f9_2 * (crypto_int64) g5_19;
+  crypto_int64 f9g6_19 = f9   * (crypto_int64) g6_19;
+  crypto_int64 f9g7_38 = f9_2 * (crypto_int64) g7_19;
+  crypto_int64 f9g8_19 = f9   * (crypto_int64) g8_19;
+  crypto_int64 f9g9_38 = f9_2 * (crypto_int64) g9_19;
+  crypto_int64 h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
+  crypto_int64 h1 = f0g1+f1g0   +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
+  crypto_int64 h2 = f0g2+f1g1_2 +f2g0   +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
+  crypto_int64 h3 = f0g3+f1g2   +f2g1   +f3g0   +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
+  crypto_int64 h4 = f0g4+f1g3_2 +f2g2   +f3g1_2 +f4g0   +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
+  crypto_int64 h5 = f0g5+f1g4   +f2g3   +f3g2   +f4g1   +f5g0   +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
+  crypto_int64 h6 = f0g6+f1g5_2 +f2g4   +f3g3_2 +f4g2   +f5g1_2 +f6g0   +f7g9_38+f8g8_19+f9g7_38;
+  crypto_int64 h7 = f0g7+f1g6   +f2g5   +f3g4   +f4g3   +f5g2   +f6g1   +f7g0   +f8g9_19+f9g8_19;
+  crypto_int64 h8 = f0g8+f1g7_2 +f2g6   +f3g5_2 +f4g4   +f5g3_2 +f6g2   +f7g1_2 +f8g0   +f9g9_38;
+  crypto_int64 h9 = f0g9+f1g8   +f2g7   +f3g6   +f4g5   +f5g4   +f6g3   +f7g2   +f8g1   +f9g0   ;
+  crypto_int64 carry0;
+  crypto_int64 carry1;
+  crypto_int64 carry2;
+  crypto_int64 carry3;
+  crypto_int64 carry4;
+  crypto_int64 carry5;
+  crypto_int64 carry6;
+  crypto_int64 carry7;
+  crypto_int64 carry8;
+  crypto_int64 carry9;
+
+  /*
+  |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
+    i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
+  |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
+    i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9
+  */
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  /* |h0| <= 2^25 */
+  /* |h4| <= 2^25 */
+  /* |h1| <= 1.71*2^59 */
+  /* |h5| <= 1.71*2^59 */
+
+  carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
+  carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
+  /* |h1| <= 2^24; from now on fits into int32 */
+  /* |h5| <= 2^24; from now on fits into int32 */
+  /* |h2| <= 1.41*2^60 */
+  /* |h6| <= 1.41*2^60 */
+
+  carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
+  carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
+  /* |h2| <= 2^25; from now on fits into int32 unchanged */
+  /* |h6| <= 2^25; from now on fits into int32 unchanged */
+  /* |h3| <= 1.71*2^59 */
+  /* |h7| <= 1.71*2^59 */
+
+  carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
+  carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
+  /* |h3| <= 2^24; from now on fits into int32 unchanged */
+  /* |h7| <= 2^24; from now on fits into int32 unchanged */
+  /* |h4| <= 1.72*2^34 */
+  /* |h8| <= 1.41*2^60 */
+
+  carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
+  carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
+  /* |h4| <= 2^25; from now on fits into int32 unchanged */
+  /* |h8| <= 2^25; from now on fits into int32 unchanged */
+  /* |h5| <= 1.01*2^24 */
+  /* |h9| <= 1.71*2^59 */
+
+  carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
+  /* |h9| <= 2^24; from now on fits into int32 unchanged */
+  /* |h0| <= 1.1*2^39 */
+
+  carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
+  /* |h0| <= 2^25; from now on fits into int32 unchanged */
+  /* |h1| <= 1.01*2^24 */
+
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+
+/*
+return 1 if f is in {1,3,5,...,q-2}
+return 0 if f is in {0,2,4,...,q-1}
+
+Preconditions:
+   |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+static int fe_isnegative(const fe f)
+{
+  unsigned char s[32];
+  fe_tobytes(s,f);
+  return s[0] & 1;
+}
+
+
+/*
+return 1 if f == 0
+return 0 if f != 0
+
+Preconditions:
+   |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
+*/
+
+static const unsigned char zero[32] = {0};
+
+static int fe_isnonzero(const fe f)
+{
+  unsigned char s[32];
+  fe_tobytes(s,f);
+  return crypto_verify_32(s,zero);
+}
+
+/*
+h = -f
+
+Preconditions:
+   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+
+Postconditions:
+   |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
+*/
+
+static void fe_neg(fe h,const fe f)
+{
+  crypto_int32 f0 = f[0];
+  crypto_int32 f1 = f[1];
+  crypto_int32 f2 = f[2];
+  crypto_int32 f3 = f[3];
+  crypto_int32 f4 = f[4];
+  crypto_int32 f5 = f[5];
+  crypto_int32 f6 = f[6];
+  crypto_int32 f7 = f[7];
+  crypto_int32 f8 = f[8];
+  crypto_int32 f9 = f[9];
+  crypto_int32 h0 = -f0;
+  crypto_int32 h1 = -f1;
+  crypto_int32 h2 = -f2;
+  crypto_int32 h3 = -f3;
+  crypto_int32 h4 = -f4;
+  crypto_int32 h5 = -f5;
+  crypto_int32 h6 = -f6;
+  crypto_int32 h7 = -f7;
+  crypto_int32 h8 = -f8;
+  crypto_int32 h9 = -f9;
+  h[0] = h0;
+  h[1] = h1;
+  h[2] = h2;
+  h[3] = h3;
+  h[4] = h4;
+  h[5] = h5;
+  h[6] = h6;
+  h[7] = h7;
+  h[8] = h8;
+  h[9] = h9;
+}
+
+static void fe_invert(fe out,const fe z)
+{
+  fe t0;
+  fe t1;
+  fe t2;
+  fe t3;
+  int i;
+
+
+/* qhasm: fe z1 */
+
+/* qhasm: fe z2 */
+
+/* qhasm: fe z8 */
+
+/* qhasm: fe z9 */
+
+/* qhasm: fe z11 */
+
+/* qhasm: fe z22 */
+
+/* qhasm: fe z_5_0 */
+
+/* qhasm: fe z_10_5 */
+
+/* qhasm: fe z_10_0 */
+
+/* qhasm: fe z_20_10 */
+
+/* qhasm: fe z_20_0 */
+
+/* qhasm: fe z_40_20 */
+
+/* qhasm: fe z_40_0 */
+
+/* qhasm: fe z_50_10 */
+
+/* qhasm: fe z_50_0 */
+
+/* qhasm: fe z_100_50 */
+
+/* qhasm: fe z_100_0 */
+
+/* qhasm: fe z_200_100 */
+
+/* qhasm: fe z_200_0 */
+
+/* qhasm: fe z_250_50 */
+
+/* qhasm: fe z_250_0 */
+
+/* qhasm: fe z_255_5 */
+
+/* qhasm: fe z_255_21 */
+
+/* qhasm: enter pow225521 */
+
+/* qhasm: z2 = z1^2^1 */
+/* asm 1: fe_sq(>z2=fe#1,<z1=fe#11); for (i = 1;i < 1;++i) fe_sq(>z2=fe#1,>z2=fe#1); */
+/* asm 2: fe_sq(>z2=t0,<z1=z); for (i = 1;i < 1;++i) fe_sq(>z2=t0,>z2=t0); */
+fe_sq(t0,z); for (i = 1;i < 1;++i) fe_sq(t0,t0);
+
+/* qhasm: z8 = z2^2^2 */
+/* asm 1: fe_sq(>z8=fe#2,<z2=fe#1); for (i = 1;i < 2;++i) fe_sq(>z8=fe#2,>z8=fe#2); */
+/* asm 2: fe_sq(>z8=t1,<z2=t0); for (i = 1;i < 2;++i) fe_sq(>z8=t1,>z8=t1); */
+fe_sq(t1,t0); for (i = 1;i < 2;++i) fe_sq(t1,t1);
+
+/* qhasm: z9 = z1*z8 */
+/* asm 1: fe_mul(>z9=fe#2,<z1=fe#11,<z8=fe#2); */
+/* asm 2: fe_mul(>z9=t1,<z1=z,<z8=t1); */
+fe_mul(t1,z,t1);
+
+/* qhasm: z11 = z2*z9 */
+/* asm 1: fe_mul(>z11=fe#1,<z2=fe#1,<z9=fe#2); */
+/* asm 2: fe_mul(>z11=t0,<z2=t0,<z9=t1); */
+fe_mul(t0,t0,t1);
+
+/* qhasm: z22 = z11^2^1 */
+/* asm 1: fe_sq(>z22=fe#3,<z11=fe#1); for (i = 1;i < 1;++i) fe_sq(>z22=fe#3,>z22=fe#3); */
+/* asm 2: fe_sq(>z22=t2,<z11=t0); for (i = 1;i < 1;++i) fe_sq(>z22=t2,>z22=t2); */
+fe_sq(t2,t0); for (i = 1;i < 1;++i) fe_sq(t2,t2);
+
+/* qhasm: z_5_0 = z9*z22 */
+/* asm 1: fe_mul(>z_5_0=fe#2,<z9=fe#2,<z22=fe#3); */
+/* asm 2: fe_mul(>z_5_0=t1,<z9=t1,<z22=t2); */
+fe_mul(t1,t1,t2);
+
+/* qhasm: z_10_5 = z_5_0^2^5 */
+/* asm 1: fe_sq(>z_10_5=fe#3,<z_5_0=fe#2); for (i = 1;i < 5;++i) fe_sq(>z_10_5=fe#3,>z_10_5=fe#3); */
+/* asm 2: fe_sq(>z_10_5=t2,<z_5_0=t1); for (i = 1;i < 5;++i) fe_sq(>z_10_5=t2,>z_10_5=t2); */
+fe_sq(t2,t1); for (i = 1;i < 5;++i) fe_sq(t2,t2);
+
+/* qhasm: z_10_0 = z_10_5*z_5_0 */
+/* asm 1: fe_mul(>z_10_0=fe#2,<z_10_5=fe#3,<z_5_0=fe#2); */
+/* asm 2: fe_mul(>z_10_0=t1,<z_10_5=t2,<z_5_0=t1); */
+fe_mul(t1,t2,t1);
+
+/* qhasm: z_20_10 = z_10_0^2^10 */
+/* asm 1: fe_sq(>z_20_10=fe#3,<z_10_0=fe#2); for (i = 1;i < 10;++i) fe_sq(>z_20_10=fe#3,>z_20_10=fe#3); */
+/* asm 2: fe_sq(>z_20_10=t2,<z_10_0=t1); for (i = 1;i < 10;++i) fe_sq(>z_20_10=t2,>z_20_10=t2); */
+fe_sq(t2,t1); for (i = 1;i < 10;++i) fe_sq(t2,t2);
+
+/* qhasm: z_20_0 = z_20_10*z_10_0 */
+/* asm 1: fe_mul(>z_20_0=fe#3,<z_20_10=fe#3,<z_10_0=fe#2); */
+/* asm 2: fe_mul(>z_20_0=t2,<z_20_10=t2,<z_10_0=t1); */
+fe_mul(t2,t2,t1);
+
+/* qhasm: z_40_20 = z_20_0^2^20 */
+/* asm 1: fe_sq(>z_40_20=fe#4,<z_20_0=fe#3); for (i = 1;i < 20;++i) fe_sq(>z_40_20=fe#4,>z_40_20=fe#4); */
+/* asm 2: fe_sq(>z_40_20=t3,<z_20_0=t2); for (i = 1;i < 20;++i) fe_sq(>z_40_20=t3,>z_40_20=t3); */
+fe_sq(t3,t2); for (i = 1;i < 20;++i) fe_sq(t3,t3);
+
+/* qhasm: z_40_0 = z_40_20*z_20_0 */
+/* asm 1: fe_mul(>z_40_0=fe#3,<z_40_20=fe#4,<z_20_0=fe#3); */
+/* asm 2: fe_mul(>z_40_0=t2,<z_40_20=t3,<z_20_0=t2); */
+fe_mul(t2,t3,t2);
+
+/* qhasm: z_50_10 = z_40_0^2^10 */
+/* asm 1: fe_sq(>z_50_10=fe#3,<z_40_0=fe#3); for (i = 1;i < 10;++i) fe_sq(>z_50_10=fe#3,>z_50_10=fe#3); */
+/* asm 2: fe_sq(>z_50_10=t2,<z_40_0=t2); for (i = 1;i < 10;++i) fe_sq(>z_50_10=t2,>z_50_10=t2); */
+fe_sq(t2,t2); for (i = 1;i < 10;++i) fe_sq(t2,t2);
+
+/* qhasm: z_50_0 = z_50_10*z_10_0 */
+/* asm 1: fe_mul(>z_50_0=fe#2,<z_50_10=fe#3,<z_10_0=fe#2); */
+/* asm 2: fe_mul(>z_50_0=t1,<z_50_10=t2,<z_10_0=t1); */
+fe_mul(t1,t2,t1);
+
+/* qhasm: z_100_50 = z_50_0^2^50 */
+/* asm 1: fe_sq(>z_100_50=fe#3,<z_50_0=fe#2); for (i = 1;i < 50;++i) fe_sq(>z_100_50=fe#3,>z_100_50=fe#3); */
+/* asm 2: fe_sq(>z_100_50=t2,<z_50_0=t1); for (i = 1;i < 50;++i) fe_sq(>z_100_50=t2,>z_100_50=t2); */
+fe_sq(t2,t1); for (i = 1;i < 50;++i) fe_sq(t2,t2);
+
+/* qhasm: z_100_0 = z_100_50*z_50_0 */
+/* asm 1: fe_mul(>z_100_0=fe#3,<z_100_50=fe#3,<z_50_0=fe#2); */
+/* asm 2: fe_mul(>z_100_0=t2,<z_100_50=t2,<z_50_0=t1); */
+fe_mul(t2,t2,t1);
+
+/* qhasm: z_200_100 = z_100_0^2^100 */
+/* asm 1: fe_sq(>z_200_100=fe#4,<z_100_0=fe#3); for (i = 1;i < 100;++i) fe_sq(>z_200_100=fe#4,>z_200_100=fe#4); */
+/* asm 2: fe_sq(>z_200_100=t3,<z_100_0=t2); for (i = 1;i < 100;++i) fe_sq(>z_200_100=t3,>z_200_100=t3); */
+fe_sq(t3,t2); for (i = 1;i < 100;++i) fe_sq(t3,t3);
+
+/* qhasm: z_200_0 = z_200_100*z_100_0 */
+/* asm 1: fe_mul(>z_200_0=fe#3,<z_200_100=fe#4,<z_100_0=fe#3); */
+/* asm 2: fe_mul(>z_200_0=t2,<z_200_100=t3,<z_100_0=t2); */
+fe_mul(t2,t3,t2);
+
+/* qhasm: z_250_50 = z_200_0^2^50 */
+/* asm 1: fe_sq(>z_250_50=fe#3,<z_200_0=fe#3); for (i = 1;i < 50;++i) fe_sq(>z_250_50=fe#3,>z_250_50=fe#3); */
+/* asm 2: fe_sq(>z_250_50=t2,<z_200_0=t2); for (i = 1;i < 50;++i) fe_sq(>z_250_50=t2,>z_250_50=t2); */
+fe_sq(t2,t2); for (i = 1;i < 50;++i) fe_sq(t2,t2);
+
+/* qhasm: z_250_0 = z_250_50*z_50_0 */
+/* asm 1: fe_mul(>z_250_0=fe#2,<z_250_50=fe#3,<z_50_0=fe#2); */
+/* asm 2: fe_mul(>z_250_0=t1,<z_250_50=t2,<z_50_0=t1); */
+fe_mul(t1,t2,t1);
+
+/* qhasm: z_255_5 = z_250_0^2^5 */
+/* asm 1: fe_sq(>z_255_5=fe#2,<z_250_0=fe#2); for (i = 1;i < 5;++i) fe_sq(>z_255_5=fe#2,>z_255_5=fe#2); */
+/* asm 2: fe_sq(>z_255_5=t1,<z_250_0=t1); for (i = 1;i < 5;++i) fe_sq(>z_255_5=t1,>z_255_5=t1); */
+fe_sq(t1,t1); for (i = 1;i < 5;++i) fe_sq(t1,t1);
+
+/* qhasm: z_255_21 = z_255_5*z11 */
+/* asm 1: fe_mul(>z_255_21=fe#12,<z_255_5=fe#2,<z11=fe#1); */
+/* asm 2: fe_mul(>z_255_21=out,<z_255_5=t1,<z11=t0); */
+fe_mul(out,t1,t0);
+
+/* qhasm: return */
+
+  return;
+}
+
+
+static void fe_pow22523(fe out,const fe z)
+{
+  fe t0;
+  fe t1;
+  fe t2;
+  int i;
+
+
+/* qhasm: fe z1 */
+
+/* qhasm: fe z2 */
+
+/* qhasm: fe z8 */
+
+/* qhasm: fe z9 */
+
+/* qhasm: fe z11 */
+
+/* qhasm: fe z22 */
+
+/* qhasm: fe z_5_0 */
+
+/* qhasm: fe z_10_5 */
+
+/* qhasm: fe z_10_0 */
+
+/* qhasm: fe z_20_10 */
+
+/* qhasm: fe z_20_0 */
+
+/* qhasm: fe z_40_20 */
+
+/* qhasm: fe z_40_0 */
+
+/* qhasm: fe z_50_10 */
+
+/* qhasm: fe z_50_0 */
+
+/* qhasm: fe z_100_50 */
+
+/* qhasm: fe z_100_0 */
+
+/* qhasm: fe z_200_100 */
+
+/* qhasm: fe z_200_0 */
+
+/* qhasm: fe z_250_50 */
+
+/* qhasm: fe z_250_0 */
+
+/* qhasm: fe z_252_2 */
+
+/* qhasm: fe z_252_3 */
+
+/* qhasm: enter pow22523 */
+
+/* qhasm: z2 = z1^2^1 */
+/* asm 1: fe_sq(>z2=fe#1,<z1=fe#11); for (i = 1;i < 1;++i) fe_sq(>z2=fe#1,>z2=fe#1); */
+/* asm 2: fe_sq(>z2=t0,<z1=z); for (i = 1;i < 1;++i) fe_sq(>z2=t0,>z2=t0); */
+fe_sq(t0,z); for (i = 1;i < 1;++i) fe_sq(t0,t0);
+
+/* qhasm: z8 = z2^2^2 */
+/* asm 1: fe_sq(>z8=fe#2,<z2=fe#1); for (i = 1;i < 2;++i) fe_sq(>z8=fe#2,>z8=fe#2); */
+/* asm 2: fe_sq(>z8=t1,<z2=t0); for (i = 1;i < 2;++i) fe_sq(>z8=t1,>z8=t1); */
+fe_sq(t1,t0); for (i = 1;i < 2;++i) fe_sq(t1,t1);
+
+/* qhasm: z9 = z1*z8 */
+/* asm 1: fe_mul(>z9=fe#2,<z1=fe#11,<z8=fe#2); */
+/* asm 2: fe_mul(>z9=t1,<z1=z,<z8=t1); */
+fe_mul(t1,z,t1);
+
+/* qhasm: z11 = z2*z9 */
+/* asm 1: fe_mul(>z11=fe#1,<z2=fe#1,<z9=fe#2); */
+/* asm 2: fe_mul(>z11=t0,<z2=t0,<z9=t1); */
+fe_mul(t0,t0,t1);
+
+/* qhasm: z22 = z11^2^1 */
+/* asm 1: fe_sq(>z22=fe#1,<z11=fe#1); for (i = 1;i < 1;++i) fe_sq(>z22=fe#1,>z22=fe#1); */
+/* asm 2: fe_sq(>z22=t0,<z11=t0); for (i = 1;i < 1;++i) fe_sq(>z22=t0,>z22=t0); */
+fe_sq(t0,t0); for (i = 1;i < 1;++i) fe_sq(t0,t0);
+
+/* qhasm: z_5_0 = z9*z22 */
+/* asm 1: fe_mul(>z_5_0=fe#1,<z9=fe#2,<z22=fe#1); */
+/* asm 2: fe_mul(>z_5_0=t0,<z9=t1,<z22=t0); */
+fe_mul(t0,t1,t0);
+
+/* qhasm: z_10_5 = z_5_0^2^5 */
+/* asm 1: fe_sq(>z_10_5=fe#2,<z_5_0=fe#1); for (i = 1;i < 5;++i) fe_sq(>z_10_5=fe#2,>z_10_5=fe#2); */
+/* asm 2: fe_sq(>z_10_5=t1,<z_5_0=t0); for (i = 1;i < 5;++i) fe_sq(>z_10_5=t1,>z_10_5=t1); */
+fe_sq(t1,t0); for (i = 1;i < 5;++i) fe_sq(t1,t1);
+
+/* qhasm: z_10_0 = z_10_5*z_5_0 */
+/* asm 1: fe_mul(>z_10_0=fe#1,<z_10_5=fe#2,<z_5_0=fe#1); */
+/* asm 2: fe_mul(>z_10_0=t0,<z_10_5=t1,<z_5_0=t0); */
+fe_mul(t0,t1,t0);
+
+/* qhasm: z_20_10 = z_10_0^2^10 */
+/* asm 1: fe_sq(>z_20_10=fe#2,<z_10_0=fe#1); for (i = 1;i < 10;++i) fe_sq(>z_20_10=fe#2,>z_20_10=fe#2); */
+/* asm 2: fe_sq(>z_20_10=t1,<z_10_0=t0); for (i = 1;i < 10;++i) fe_sq(>z_20_10=t1,>z_20_10=t1); */
+fe_sq(t1,t0); for (i = 1;i < 10;++i) fe_sq(t1,t1);
+
+/* qhasm: z_20_0 = z_20_10*z_10_0 */
+/* asm 1: fe_mul(>z_20_0=fe#2,<z_20_10=fe#2,<z_10_0=fe#1); */
+/* asm 2: fe_mul(>z_20_0=t1,<z_20_10=t1,<z_10_0=t0); */
+fe_mul(t1,t1,t0);
+
+/* qhasm: z_40_20 = z_20_0^2^20 */
+/* asm 1: fe_sq(>z_40_20=fe#3,<z_20_0=fe#2); for (i = 1;i < 20;++i) fe_sq(>z_40_20=fe#3,>z_40_20=fe#3); */
+/* asm 2: fe_sq(>z_40_20=t2,<z_20_0=t1); for (i = 1;i < 20;++i) fe_sq(>z_40_20=t2,>z_40_20=t2); */
+fe_sq(t2,t1); for (i = 1;i < 20;++i) fe_sq(t2,t2);
+
+/* qhasm: z_40_0 = z_40_20*z_20_0 */
+/* asm 1: fe_mul(>z_40_0=fe#2,<z_40_20=fe#3,<z_20_0=fe#2); */
+/* asm 2: fe_mul(>z_40_0=t1,<z_40_20=t2,<z_20_0=t1); */
+fe_mul(t1,t2,t1);
+
+/* qhasm: z_50_10 = z_40_0^2^10 */
+/* asm 1: fe_sq(>z_50_10=fe#2,<z_40_0=fe#2); for (i = 1;i < 10;++i) fe_sq(>z_50_10=fe#2,>z_50_10=fe#2); */
+/* asm 2: fe_sq(>z_50_10=t1,<z_40_0=t1); for (i = 1;i < 10;++i) fe_sq(>z_50_10=t1,>z_50_10=t1); */
+fe_sq(t1,t1); for (i = 1;i < 10;++i) fe_sq(t1,t1);
+
+/* qhasm: z_50_0 = z_50_10*z_10_0 */
+/* asm 1: fe_mul(>z_50_0=fe#1,<z_50_10=fe#2,<z_10_0=fe#1); */
+/* asm 2: fe_mul(>z_50_0=t0,<z_50_10=t1,<z_10_0=t0); */
+fe_mul(t0,t1,t0);
+
+/* qhasm: z_100_50 = z_50_0^2^50 */
+/* asm 1: fe_sq(>z_100_50=fe#2,<z_50_0=fe#1); for (i = 1;i < 50;++i) fe_sq(>z_100_50=fe#2,>z_100_50=fe#2); */
+/* asm 2: fe_sq(>z_100_50=t1,<z_50_0=t0); for (i = 1;i < 50;++i) fe_sq(>z_100_50=t1,>z_100_50=t1); */
+fe_sq(t1,t0); for (i = 1;i < 50;++i) fe_sq(t1,t1);
+
+/* qhasm: z_100_0 = z_100_50*z_50_0 */
+/* asm 1: fe_mul(>z_100_0=fe#2,<z_100_50=fe#2,<z_50_0=fe#1); */
+/* asm 2: fe_mul(>z_100_0=t1,<z_100_50=t1,<z_50_0=t0); */
+fe_mul(t1,t1,t0);
+
+/* qhasm: z_200_100 = z_100_0^2^100 */
+/* asm 1: fe_sq(>z_200_100=fe#3,<z_100_0=fe#2); for (i = 1;i < 100;++i) fe_sq(>z_200_100=fe#3,>z_200_100=fe#3); */
+/* asm 2: fe_sq(>z_200_100=t2,<z_100_0=t1); for (i = 1;i < 100;++i) fe_sq(>z_200_100=t2,>z_200_100=t2); */
+fe_sq(t2,t1); for (i = 1;i < 100;++i) fe_sq(t2,t2);
+
+/* qhasm: z_200_0 = z_200_100*z_100_0 */
+/* asm 1: fe_mul(>z_200_0=fe#2,<z_200_100=fe#3,<z_100_0=fe#2); */
+/* asm 2: fe_mul(>z_200_0=t1,<z_200_100=t2,<z_100_0=t1); */
+fe_mul(t1,t2,t1);
+
+/* qhasm: z_250_50 = z_200_0^2^50 */
+/* asm 1: fe_sq(>z_250_50=fe#2,<z_200_0=fe#2); for (i = 1;i < 50;++i) fe_sq(>z_250_50=fe#2,>z_250_50=fe#2); */
+/* asm 2: fe_sq(>z_250_50=t1,<z_200_0=t1); for (i = 1;i < 50;++i) fe_sq(>z_250_50=t1,>z_250_50=t1); */
+fe_sq(t1,t1); for (i = 1;i < 50;++i) fe_sq(t1,t1);
+
+/* qhasm: z_250_0 = z_250_50*z_50_0 */
+/* asm 1: fe_mul(>z_250_0=fe#1,<z_250_50=fe#2,<z_50_0=fe#1); */
+/* asm 2: fe_mul(>z_250_0=t0,<z_250_50=t1,<z_50_0=t0); */
+fe_mul(t0,t1,t0);
+
+/* qhasm: z_252_2 = z_250_0^2^2 */
+/* asm 1: fe_sq(>z_252_2=fe#1,<z_250_0=fe#1); for (i = 1;i < 2;++i) fe_sq(>z_252_2=fe#1,>z_252_2=fe#1); */
+/* asm 2: fe_sq(>z_252_2=t0,<z_250_0=t0); for (i = 1;i < 2;++i) fe_sq(>z_252_2=t0,>z_252_2=t0); */
+fe_sq(t0,t0); for (i = 1;i < 2;++i) fe_sq(t0,t0);
+
+/* qhasm: z_252_3 = z_252_2*z1 */
+/* asm 1: fe_mul(>z_252_3=fe#12,<z_252_2=fe#1,<z1=fe#11); */
+/* asm 2: fe_mul(>z_252_3=out,<z_252_2=t0,<z1=z); */
+fe_mul(out,t0,z);
+
+/* qhasm: return */
+
+
+  return;
+}
+
+
+/*
+ge means group element.
+
+Here the group is the set of pairs (x,y) of field elements (see fe.h)
+satisfying -x^2 + y^2 = 1 + d x^2y^2
+where d = -121665/121666.
+
+Representations:
+  ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
+  ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
+  ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
+  ge_precomp (Duif): (y+x,y-x,2dxy)
+*/
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+} ge_p2;
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+  fe T;
+} ge_p3;
+
+typedef struct {
+  fe X;
+  fe Y;
+  fe Z;
+  fe T;
+} ge_p1p1;
+
+typedef struct {
+  fe yplusx;
+  fe yminusx;
+  fe xy2d;
+} ge_precomp;
+
+typedef struct {
+  fe YplusX;
+  fe YminusX;
+  fe Z;
+  fe T2d;
+} ge_cached;
+
+static const fe d = {
+-10913610,13857413,-15372611,6949391,114729,-8787816,-6275908,-3247719,-18696448,-12055116
+} ;
+
+static const fe sqrtm1 = {
+-32595792,-7943725,9377950,3500415,12389472,-272473,-25146209,-2005654,326686,11406482
+} ;
+
+static const fe d2 = {
+-21827239,-5839606,-30745221,13898782,229458,15978800,-12551817,-6495438,29715968,9444199
+} ;
+
+static ge_precomp Bi[8] = {
+ {
+  { 25967493,-14356035,29566456,3660896,-12694345,4014787,27544626,-11754271,-6079156,2047605 },
+  { -12545711,934262,-2722910,3049990,-727428,9406986,12720692,5043384,19500929,-15469378 },
+  { -8738181,4489570,9688441,-14785194,10184609,-12363380,29287919,11864899,-24514362,-4438546 },
+ },
+ {
+  { 15636291,-9688557,24204773,-7912398,616977,-16685262,27787600,-14772189,28944400,-1550024 },
+  { 16568933,4717097,-11556148,-1102322,15682896,-11807043,16354577,-11775962,7689662,11199574 },
+  { 30464156,-5976125,-11779434,-15670865,23220365,15915852,7512774,10017326,-17749093,-9920357 },
+ },
+ {
+  { 10861363,11473154,27284546,1981175,-30064349,12577861,32867885,14515107,-15438304,10819380 },
+  { 4708026,6336745,20377586,9066809,-11272109,6594696,-25653668,12483688,-12668491,5581306 },
+  { 19563160,16186464,-29386857,4097519,10237984,-4348115,28542350,13850243,-23678021,-15815942 },
+ },
+ {
+  { 5153746,9909285,1723747,-2777874,30523605,5516873,19480852,5230134,-23952439,-15175766 },
+  { -30269007,-3463509,7665486,10083793,28475525,1649722,20654025,16520125,30598449,7715701 },
+  { 28881845,14381568,9657904,3680757,-20181635,7843316,-31400660,1370708,29794553,-1409300 },
+ },
+ {
+  { -22518993,-6692182,14201702,-8745502,-23510406,8844726,18474211,-1361450,-13062696,13821877 },
+  { -6455177,-7839871,3374702,-4740862,-27098617,-10571707,31655028,-7212327,18853322,-14220951 },
+  { 4566830,-12963868,-28974889,-12240689,-7602672,-2830569,-8514358,-10431137,2207753,-3209784 },
+ },
+ {
+  { -25154831,-4185821,29681144,7868801,-6854661,-9423865,-12437364,-663000,-31111463,-16132436 },
+  { 25576264,-2703214,7349804,-11814844,16472782,9300885,3844789,15725684,171356,6466918 },
+  { 23103977,13316479,9739013,-16149481,817875,-15038942,8965339,-14088058,-30714912,16193877 },
+ },
+ {
+  { -33521811,3180713,-2394130,14003687,-16903474,-16270840,17238398,4729455,-18074513,9256800 },
+  { -25182317,-4174131,32336398,5036987,-21236817,11360617,22616405,9761698,-19827198,630305 },
+  { -13720693,2639453,-24237460,-7406481,9494427,-5774029,-6554551,-15960994,-2449256,-14291300 },
+ },
+ {
+  { -3151181,-5046075,9282714,6866145,-31907062,-863023,-18940575,15033784,25105118,-7894876 },
+  { -24326370,15950226,-31801215,-14592823,-11662737,-5090925,1573892,-2625887,2198790,-15804619 },
+  { -3099351,10324967,-2241613,7453183,-5446979,-2735503,-13812022,-16236442,-32461234,-12290683 },
+ },
+} ;
+
+
+/* base[i][j] = (j+1)*256^i*B */
+static ge_precomp base[32][8] = {
+{
+ {
+  { 25967493,-14356035,29566456,3660896,-12694345,4014787,27544626,-11754271,-6079156,2047605 },
+  { -12545711,934262,-2722910,3049990,-727428,9406986,12720692,5043384,19500929,-15469378 },
+  { -8738181,4489570,9688441,-14785194,10184609,-12363380,29287919,11864899,-24514362,-4438546 },
+ },
+ {
+  { -12815894,-12976347,-21581243,11784320,-25355658,-2750717,-11717903,-3814571,-358445,-10211303 },
+  { -21703237,6903825,27185491,6451973,-29577724,-9554005,-15616551,11189268,-26829678,-5319081 },
+  { 26966642,11152617,32442495,15396054,14353839,-12752335,-3128826,-9541118,-15472047,-4166697 },
+ },
+ {
+  { 15636291,-9688557,24204773,-7912398,616977,-16685262,27787600,-14772189,28944400,-1550024 },
+  { 16568933,4717097,-11556148,-1102322,15682896,-11807043,16354577,-11775962,7689662,11199574 },
+  { 30464156,-5976125,-11779434,-15670865,23220365,15915852,7512774,10017326,-17749093,-9920357 },
+ },
+ {
+  { -17036878,13921892,10945806,-6033431,27105052,-16084379,-28926210,15006023,3284568,-6276540 },
+  { 23599295,-8306047,-11193664,-7687416,13236774,10506355,7464579,9656445,13059162,10374397 },
+  { 7798556,16710257,3033922,2874086,28997861,2835604,32406664,-3839045,-641708,-101325 },
+ },
+ {
+  { 10861363,11473154,27284546,1981175,-30064349,12577861,32867885,14515107,-15438304,10819380 },
+  { 4708026,6336745,20377586,9066809,-11272109,6594696,-25653668,12483688,-12668491,5581306 },
+  { 19563160,16186464,-29386857,4097519,10237984,-4348115,28542350,13850243,-23678021,-15815942 },
+ },
+ {
+  { -15371964,-12862754,32573250,4720197,-26436522,5875511,-19188627,-15224819,-9818940,-12085777 },
+  { -8549212,109983,15149363,2178705,22900618,4543417,3044240,-15689887,1762328,14866737 },
+  { -18199695,-15951423,-10473290,1707278,-17185920,3916101,-28236412,3959421,27914454,4383652 },
+ },
+ {
+  { 5153746,9909285,1723747,-2777874,30523605,5516873,19480852,5230134,-23952439,-15175766 },
+  { -30269007,-3463509,7665486,10083793,28475525,1649722,20654025,16520125,30598449,7715701 },
+  { 28881845,14381568,9657904,3680757,-20181635,7843316,-31400660,1370708,29794553,-1409300 },
+ },
+ {
+  { 14499471,-2729599,-33191113,-4254652,28494862,14271267,30290735,10876454,-33154098,2381726 },
+  { -7195431,-2655363,-14730155,462251,-27724326,3941372,-6236617,3696005,-32300832,15351955 },
+  { 27431194,8222322,16448760,-3907995,-18707002,11938355,-32961401,-2970515,29551813,10109425 },
+ },
+},
+{
+ {
+  { -13657040,-13155431,-31283750,11777098,21447386,6519384,-2378284,-1627556,10092783,-4764171 },
+  { 27939166,14210322,4677035,16277044,-22964462,-12398139,-32508754,12005538,-17810127,12803510 },
+  { 17228999,-15661624,-1233527,300140,-1224870,-11714777,30364213,-9038194,18016357,4397660 },
+ },
+ {
+  { -10958843,-7690207,4776341,-14954238,27850028,-15602212,-26619106,14544525,-17477504,982639 },
+  { 29253598,15796703,-2863982,-9908884,10057023,3163536,7332899,-4120128,-21047696,9934963 },
+  { 5793303,16271923,-24131614,-10116404,29188560,1206517,-14747930,4559895,-30123922,-10897950 },
+ },
+ {
+  { -27643952,-11493006,16282657,-11036493,28414021,-15012264,24191034,4541697,-13338309,5500568 },
+  { 12650548,-1497113,9052871,11355358,-17680037,-8400164,-17430592,12264343,10874051,13524335 },
+  { 25556948,-3045990,714651,2510400,23394682,-10415330,33119038,5080568,-22528059,5376628 },
+ },
+ {
+  { -26088264,-4011052,-17013699,-3537628,-6726793,1920897,-22321305,-9447443,4535768,1569007 },
+  { -2255422,14606630,-21692440,-8039818,28430649,8775819,-30494562,3044290,31848280,12543772 },
+  { -22028579,2943893,-31857513,6777306,13784462,-4292203,-27377195,-2062731,7718482,14474653 },
+ },
+ {
+  { 2385315,2454213,-22631320,46603,-4437935,-15680415,656965,-7236665,24316168,-5253567 },
+  { 13741529,10911568,-33233417,-8603737,-20177830,-1033297,33040651,-13424532,-20729456,8321686 },
+  { 21060490,-2212744,15712757,-4336099,1639040,10656336,23845965,-11874838,-9984458,608372 },
+ },
+ {
+  { -13672732,-15087586,-10889693,-7557059,-6036909,11305547,1123968,-6780577,27229399,23887 },
+  { -23244140,-294205,-11744728,14712571,-29465699,-2029617,12797024,-6440308,-1633405,16678954 },
+  { -29500620,4770662,-16054387,14001338,7830047,9564805,-1508144,-4795045,-17169265,4904953 },
+ },
+ {
+  { 24059557,14617003,19037157,-15039908,19766093,-14906429,5169211,16191880,2128236,-4326833 },
+  { -16981152,4124966,-8540610,-10653797,30336522,-14105247,-29806336,916033,-6882542,-2986532 },
+  { -22630907,12419372,-7134229,-7473371,-16478904,16739175,285431,2763829,15736322,4143876 },
+ },
+ {
+  { 2379352,11839345,-4110402,-5988665,11274298,794957,212801,-14594663,23527084,-16458268 },
+  { 33431127,-11130478,-17838966,-15626900,8909499,8376530,-32625340,4087881,-15188911,-14416214 },
+  { 1767683,7197987,-13205226,-2022635,-13091350,448826,5799055,4357868,-4774191,-16323038 },
+ },
+},
+{
+ {
+  { 6721966,13833823,-23523388,-1551314,26354293,-11863321,23365147,-3949732,7390890,2759800 },
+  { 4409041,2052381,23373853,10530217,7676779,-12885954,21302353,-4264057,1244380,-12919645 },
+  { -4421239,7169619,4982368,-2957590,30256825,-2777540,14086413,9208236,15886429,16489664 },
+ },
+ {
+  { 1996075,10375649,14346367,13311202,-6874135,-16438411,-13693198,398369,-30606455,-712933 },
+  { -25307465,9795880,-2777414,14878809,-33531835,14780363,13348553,12076947,-30836462,5113182 },
+  { -17770784,11797796,31950843,13929123,-25888302,12288344,-30341101,-7336386,13847711,5387222 },
+ },
+ {
+  { -18582163,-3416217,17824843,-2340966,22744343,-10442611,8763061,3617786,-19600662,10370991 },
+  { 20246567,-14369378,22358229,-543712,18507283,-10413996,14554437,-8746092,32232924,16763880 },
+  { 9648505,10094563,26416693,14745928,-30374318,-6472621,11094161,15689506,3140038,-16510092 },
+ },
+ {
+  { -16160072,5472695,31895588,4744994,8823515,10365685,-27224800,9448613,-28774454,366295 },
+  { 19153450,11523972,-11096490,-6503142,-24647631,5420647,28344573,8041113,719605,11671788 },
+  { 8678025,2694440,-6808014,2517372,4964326,11152271,-15432916,-15266516,27000813,-10195553 },
+ },
+ {
+  { -15157904,7134312,8639287,-2814877,-7235688,10421742,564065,5336097,6750977,-14521026 },
+  { 11836410,-3979488,26297894,16080799,23455045,15735944,1695823,-8819122,8169720,16220347 },
+  { -18115838,8653647,17578566,-6092619,-8025777,-16012763,-11144307,-2627664,-5990708,-14166033 },
+ },
+ {
+  { -23308498,-10968312,15213228,-10081214,-30853605,-11050004,27884329,2847284,2655861,1738395 },
+  { -27537433,-14253021,-25336301,-8002780,-9370762,8129821,21651608,-3239336,-19087449,-11005278 },
+  { 1533110,3437855,23735889,459276,29970501,11335377,26030092,5821408,10478196,8544890 },
+ },
+ {
+  { 32173121,-16129311,24896207,3921497,22579056,-3410854,19270449,12217473,17789017,-3395995 },
+  { -30552961,-2228401,-15578829,-10147201,13243889,517024,15479401,-3853233,30460520,1052596 },
+  { -11614875,13323618,32618793,8175907,-15230173,12596687,27491595,-4612359,3179268,-9478891 },
+ },
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+  { -23910559,-13515526,-26299483,-4503841,25005590,-7687270,19574902,10071562,6708380,-6222424 },
+ },
+ {
+  { 2101391,-4930054,19702731,2367575,-15427167,1047675,5301017,9328700,29955601,-11678310 },
+  { 3096359,9271816,-21620864,-15521844,-14847996,-7592937,-25892142,-12635595,-9917575,6216608 },
+  { -32615849,338663,-25195611,2510422,-29213566,-13820213,24822830,-6146567,-26767480,7525079 },
+ },
+ {
+  { -23066649,-13985623,16133487,-7896178,-3389565,778788,-910336,-2782495,-19386633,11994101 },
+  { 21691500,-13624626,-641331,-14367021,3285881,-3483596,-25064666,9718258,-7477437,13381418 },
+  { 18445390,-4202236,14979846,11622458,-1727110,-3582980,23111648,-6375247,28535282,15779576 },
+ },
+ {
+  { 30098053,3089662,-9234387,16662135,-21306940,11308411,-14068454,12021730,9955285,-16303356 },
+  { 9734894,-14576830,-7473633,-9138735,2060392,11313496,-18426029,9924399,20194861,13380996 },
+  { -26378102,-7965207,-22167821,15789297,-18055342,-6168792,-1984914,15707771,26342023,10146099 },
+ },
+},
+{
+ {
+  { -26016874,-219943,21339191,-41388,19745256,-2878700,-29637280,2227040,21612326,-545728 },
+  { -13077387,1184228,23562814,-5970442,-20351244,-6348714,25764461,12243797,-20856566,11649658 },
+  { -10031494,11262626,27384172,2271902,26947504,-15997771,39944,6114064,33514190,2333242 },
+ },
+ {
+  { -21433588,-12421821,8119782,7219913,-21830522,-9016134,-6679750,-12670638,24350578,-13450001 },
+  { -4116307,-11271533,-23886186,4843615,-30088339,690623,-31536088,-10406836,8317860,12352766 },
+  { 18200138,-14475911,-33087759,-2696619,-23702521,-9102511,-23552096,-2287550,20712163,6719373 },
+ },
+ {
+  { 26656208,6075253,-7858556,1886072,-28344043,4262326,11117530,-3763210,26224235,-3297458 },
+  { -17168938,-14854097,-3395676,-16369877,-19954045,14050420,21728352,9493610,18620611,-16428628 },
+  { -13323321,13325349,11432106,5964811,18609221,6062965,-5269471,-9725556,-30701573,-16479657 },
+ },
+ {
+  { -23860538,-11233159,26961357,1640861,-32413112,-16737940,12248509,-5240639,13735342,1934062 },
+  { 25089769,6742589,17081145,-13406266,21909293,-16067981,-15136294,-3765346,-21277997,5473616 },
+  { 31883677,-7961101,1083432,-11572403,22828471,13290673,-7125085,12469656,29111212,-5451014 },
+ },
+ {
+  { 24244947,-15050407,-26262976,2791540,-14997599,16666678,24367466,6388839,-10295587,452383 },
+  { -25640782,-3417841,5217916,16224624,19987036,-4082269,-24236251,-5915248,15766062,8407814 },
+  { -20406999,13990231,15495425,16395525,5377168,15166495,-8917023,-4388953,-8067909,2276718 },
+ },
+ {
+  { 30157918,12924066,-17712050,9245753,19895028,3368142,-23827587,5096219,22740376,-7303417 },
+  { 2041139,-14256350,7783687,13876377,-25946985,-13352459,24051124,13742383,-15637599,13295222 },
+  { 33338237,-8505733,12532113,7977527,9106186,-1715251,-17720195,-4612972,-4451357,-14669444 },
+ },
+ {
+  { -20045281,5454097,-14346548,6447146,28862071,1883651,-2469266,-4141880,7770569,9620597 },
+  { 23208068,7979712,33071466,8149229,1758231,-10834995,30945528,-1694323,-33502340,-14767970 },
+  { 1439958,-16270480,-1079989,-793782,4625402,10647766,-5043801,1220118,30494170,-11440799 },
+ },
+ {
+  { -5037580,-13028295,-2970559,-3061767,15640974,-6701666,-26739026,926050,-1684339,-13333647 },
+  { 13908495,-3549272,30919928,-6273825,-21521863,7989039,9021034,9078865,3353509,4033511 },
+  { -29663431,-15113610,32259991,-344482,24295849,-12912123,23161163,8839127,27485041,7356032 },
+ },
+},
+{
+ {
+  { 9661027,705443,11980065,-5370154,-1628543,14661173,-6346142,2625015,28431036,-16771834 },
+  { -23839233,-8311415,-25945511,7480958,-17681669,-8354183,-22545972,14150565,15970762,4099461 },
+  { 29262576,16756590,26350592,-8793563,8529671,-11208050,13617293,-9937143,11465739,8317062 },
+ },
+ {
+  { -25493081,-6962928,32500200,-9419051,-23038724,-2302222,14898637,3848455,20969334,-5157516 },
+  { -20384450,-14347713,-18336405,13884722,-33039454,2842114,-21610826,-3649888,11177095,14989547 },
+  { -24496721,-11716016,16959896,2278463,12066309,10137771,13515641,2581286,-28487508,9930240 },
+ },
+ {
+  { -17751622,-2097826,16544300,-13009300,-15914807,-14949081,18345767,-13403753,16291481,-5314038 },
+  { -33229194,2553288,32678213,9875984,8534129,6889387,-9676774,6957617,4368891,9788741 },
+  { 16660756,7281060,-10830758,12911820,20108584,-8101676,-21722536,-8613148,16250552,-11111103 },
+ },
+ {
+  { -19765507,2390526,-16551031,14161980,1905286,6414907,4689584,10604807,-30190403,4782747 },
+  { -1354539,14736941,-7367442,-13292886,7710542,-14155590,-9981571,4383045,22546403,437323 },
+  { 31665577,-12180464,-16186830,1491339,-18368625,3294682,27343084,2786261,-30633590,-14097016 },
+ },
+ {
+  { -14467279,-683715,-33374107,7448552,19294360,14334329,-19690631,2355319,-19284671,-6114373 },
+  { 15121312,-15796162,6377020,-6031361,-10798111,-12957845,18952177,15496498,-29380133,11754228 },
+  { -2637277,-13483075,8488727,-14303896,12728761,-1622493,7141596,11724556,22761615,-10134141 },
+ },
+ {
+  { 16918416,11729663,-18083579,3022987,-31015732,-13339659,-28741185,-12227393,32851222,11717399 },
+  { 11166634,7338049,-6722523,4531520,-29468672,-7302055,31474879,3483633,-1193175,-4030831 },
+  { -185635,9921305,31456609,-13536438,-12013818,13348923,33142652,6546660,-19985279,-3948376 },
+ },
+ {
+  { -32460596,11266712,-11197107,-7899103,31703694,3855903,-8537131,-12833048,-30772034,-15486313 },
+  { -18006477,12709068,3991746,-6479188,-21491523,-10550425,-31135347,-16049879,10928917,3011958 },
+  { -6957757,-15594337,31696059,334240,29576716,14796075,-30831056,-12805180,18008031,10258577 },
+ },
+ {
+  { -22448644,15655569,7018479,-4410003,-30314266,-1201591,-1853465,1367120,25127874,6671743 },
+  { 29701166,-14373934,-10878120,9279288,-17568,13127210,21382910,11042292,25838796,4642684 },
+  { -20430234,14955537,-24126347,8124619,-5369288,-5990470,30468147,-13900640,18423289,4177476 },
+ },
+},
+} ;
+
+static void ge_p2_0(ge_p2 *h)
+{
+  fe_0(h->X);
+  fe_1(h->Y);
+  fe_1(h->Z);
+}
+
+static void ge_p3_0(ge_p3 *h)
+{
+  fe_0(h->X);
+  fe_1(h->Y);
+  fe_1(h->Z);
+  fe_0(h->T);
+}
+
+static void ge_precomp_0(ge_precomp *h)
+{
+  fe_1(h->yplusx);
+  fe_1(h->yminusx);
+  fe_0(h->xy2d);
+}
+
+/*
+r = p
+*/
+
+static void ge_p1p1_to_p2(ge_p2 *r,const ge_p1p1 *p)
+{
+  fe_mul(r->X,p->X,p->T);
+  fe_mul(r->Y,p->Y,p->Z);
+  fe_mul(r->Z,p->Z,p->T);
+}
+
+/*
+r = p
+*/
+
+static void ge_p1p1_to_p3(ge_p3 *r,const ge_p1p1 *p)
+{
+  fe_mul(r->X,p->X,p->T);
+  fe_mul(r->Y,p->Y,p->Z);
+  fe_mul(r->Z,p->Z,p->T);
+  fe_mul(r->T,p->X,p->Y);
+}
+
+/*
+r = p
+*/
+
+static void ge_p3_to_p2(ge_p2 *r,const ge_p3 *p)
+{
+  fe_copy(r->X,p->X);
+  fe_copy(r->Y,p->Y);
+  fe_copy(r->Z,p->Z);
+}
+
+
+/*
+r = 2 * p
+*/
+
+static void ge_p2_dbl(ge_p1p1 *r,const ge_p2 *p)
+{
+  fe t0;
+/* qhasm: enter ge_p2_dbl */
+
+/* qhasm: fe X1 */
+
+/* qhasm: fe Y1 */
+
+/* qhasm: fe Z1 */
+
+/* qhasm: fe A */
+
+/* qhasm: fe AA */
+
+/* qhasm: fe XX */
+
+/* qhasm: fe YY */
+
+/* qhasm: fe B */
+
+/* qhasm: fe X3 */
+
+/* qhasm: fe Y3 */
+
+/* qhasm: fe Z3 */
+
+/* qhasm: fe T3 */
+
+/* qhasm: XX=X1^2 */
+/* asm 1: fe_sq(>XX=fe#1,<X1=fe#11); */
+/* asm 2: fe_sq(>XX=r->X,<X1=p->X); */
+fe_sq(r->X,p->X);
+
+/* qhasm: YY=Y1^2 */
+/* asm 1: fe_sq(>YY=fe#3,<Y1=fe#12); */
+/* asm 2: fe_sq(>YY=r->Z,<Y1=p->Y); */
+fe_sq(r->Z,p->Y);
+
+/* qhasm: B=2*Z1^2 */
+/* asm 1: fe_sq2(>B=fe#4,<Z1=fe#13); */
+/* asm 2: fe_sq2(>B=r->T,<Z1=p->Z); */
+fe_sq2(r->T,p->Z);
+
+/* qhasm: A=X1+Y1 */
+/* asm 1: fe_add(>A=fe#2,<X1=fe#11,<Y1=fe#12); */
+/* asm 2: fe_add(>A=r->Y,<X1=p->X,<Y1=p->Y); */
+fe_add(r->Y,p->X,p->Y);
+
+/* qhasm: AA=A^2 */
+/* asm 1: fe_sq(>AA=fe#5,<A=fe#2); */
+/* asm 2: fe_sq(>AA=t0,<A=r->Y); */
+fe_sq(t0,r->Y);
+
+/* qhasm: Y3=YY+XX */
+/* asm 1: fe_add(>Y3=fe#2,<YY=fe#3,<XX=fe#1); */
+/* asm 2: fe_add(>Y3=r->Y,<YY=r->Z,<XX=r->X); */
+fe_add(r->Y,r->Z,r->X);
+
+/* qhasm: Z3=YY-XX */
+/* asm 1: fe_sub(>Z3=fe#3,<YY=fe#3,<XX=fe#1); */
+/* asm 2: fe_sub(>Z3=r->Z,<YY=r->Z,<XX=r->X); */
+fe_sub(r->Z,r->Z,r->X);
+
+/* qhasm: X3=AA-Y3 */
+/* asm 1: fe_sub(>X3=fe#1,<AA=fe#5,<Y3=fe#2); */
+/* asm 2: fe_sub(>X3=r->X,<AA=t0,<Y3=r->Y); */
+fe_sub(r->X,t0,r->Y);
+
+/* qhasm: T3=B-Z3 */
+/* asm 1: fe_sub(>T3=fe#4,<B=fe#4,<Z3=fe#3); */
+/* asm 2: fe_sub(>T3=r->T,<B=r->T,<Z3=r->Z); */
+fe_sub(r->T,r->T,r->Z);
+
+/* qhasm: return */
+}
+
+
+/*
+r = 2 * p
+*/
+
+static void ge_p3_dbl(ge_p1p1 *r,const ge_p3 *p)
+{
+  ge_p2 q;
+  ge_p3_to_p2(&q,p);
+  ge_p2_dbl(r,&q);
+}
+
+
+/*
+r = p
+*/
+
+static void ge_p3_to_cached(ge_cached *r,const ge_p3 *p)
+{
+  fe_add(r->YplusX,p->Y,p->X);
+  fe_sub(r->YminusX,p->Y,p->X);
+  fe_copy(r->Z,p->Z);
+  fe_mul(r->T2d,p->T,d2);
+}
+
+/*
+r = p + q
+*/
+
+static void ge_add(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q)
+{
+  fe t0;
+/* qhasm: enter ge_add */
+
+/* qhasm: fe X1 */
+
+/* qhasm: fe Y1 */
+
+/* qhasm: fe Z1 */
+
+/* qhasm: fe Z2 */
+
+/* qhasm: fe T1 */
+
+/* qhasm: fe ZZ */
+
+/* qhasm: fe YpX2 */
+
+/* qhasm: fe YmX2 */
+
+/* qhasm: fe T2d2 */
+
+/* qhasm: fe X3 */
+
+/* qhasm: fe Y3 */
+
+/* qhasm: fe Z3 */
+
+/* qhasm: fe T3 */
+
+/* qhasm: fe YpX1 */
+
+/* qhasm: fe YmX1 */
+
+/* qhasm: fe A */
+
+/* qhasm: fe B */
+
+/* qhasm: fe C */
+
+/* qhasm: fe D */
+
+/* qhasm: YpX1 = Y1+X1 */
+/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
+/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
+fe_add(r->X,p->Y,p->X);
+
+/* qhasm: YmX1 = Y1-X1 */
+/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
+/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
+fe_sub(r->Y,p->Y,p->X);
+
+/* qhasm: A = YpX1*YpX2 */
+/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<YpX2=fe#15); */
+/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<YpX2=q->YplusX); */
+fe_mul(r->Z,r->X,q->YplusX);
+
+/* qhasm: B = YmX1*YmX2 */
+/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<YmX2=fe#16); */
+/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<YmX2=q->YminusX); */
+fe_mul(r->Y,r->Y,q->YminusX);
+
+/* qhasm: C = T2d2*T1 */
+/* asm 1: fe_mul(>C=fe#4,<T2d2=fe#18,<T1=fe#14); */
+/* asm 2: fe_mul(>C=r->T,<T2d2=q->T2d,<T1=p->T); */
+fe_mul(r->T,q->T2d,p->T);
+
+/* qhasm: ZZ = Z1*Z2 */
+/* asm 1: fe_mul(>ZZ=fe#1,<Z1=fe#13,<Z2=fe#17); */
+/* asm 2: fe_mul(>ZZ=r->X,<Z1=p->Z,<Z2=q->Z); */
+fe_mul(r->X,p->Z,q->Z);
+
+/* qhasm: D = 2*ZZ */
+/* asm 1: fe_add(>D=fe#5,<ZZ=fe#1,<ZZ=fe#1); */
+/* asm 2: fe_add(>D=t0,<ZZ=r->X,<ZZ=r->X); */
+fe_add(t0,r->X,r->X);
+
+/* qhasm: X3 = A-B */
+/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
+/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
+fe_sub(r->X,r->Z,r->Y);
+
+/* qhasm: Y3 = A+B */
+/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
+/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
+fe_add(r->Y,r->Z,r->Y);
+
+/* qhasm: Z3 = D+C */
+/* asm 1: fe_add(>Z3=fe#3,<D=fe#5,<C=fe#4); */
+/* asm 2: fe_add(>Z3=r->Z,<D=t0,<C=r->T); */
+fe_add(r->Z,t0,r->T);
+
+/* qhasm: T3 = D-C */
+/* asm 1: fe_sub(>T3=fe#4,<D=fe#5,<C=fe#4); */
+/* asm 2: fe_sub(>T3=r->T,<D=t0,<C=r->T); */
+fe_sub(r->T,t0,r->T);
+
+/* qhasm: return */
+}
+
+
+/*
+r = p - q
+*/
+
+static void ge_sub(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q)
+{
+  fe t0;
+/* qhasm: enter ge_sub */
+
+/* qhasm: fe X1 */
+
+/* qhasm: fe Y1 */
+
+/* qhasm: fe Z1 */
+
+/* qhasm: fe Z2 */
+
+/* qhasm: fe T1 */
+
+/* qhasm: fe ZZ */
+
+/* qhasm: fe YpX2 */
+
+/* qhasm: fe YmX2 */
+
+/* qhasm: fe T2d2 */
+
+/* qhasm: fe X3 */
+
+/* qhasm: fe Y3 */
+
+/* qhasm: fe Z3 */
+
+/* qhasm: fe T3 */
+
+/* qhasm: fe YpX1 */
+
+/* qhasm: fe YmX1 */
+
+/* qhasm: fe A */
+
+/* qhasm: fe B */
+
+/* qhasm: fe C */
+
+/* qhasm: fe D */
+
+/* qhasm: YpX1 = Y1+X1 */
+/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
+/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
+fe_add(r->X,p->Y,p->X);
+
+/* qhasm: YmX1 = Y1-X1 */
+/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
+/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
+fe_sub(r->Y,p->Y,p->X);
+
+/* qhasm: A = YpX1*YmX2 */
+/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<YmX2=fe#16); */
+/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<YmX2=q->YminusX); */
+fe_mul(r->Z,r->X,q->YminusX);
+
+/* qhasm: B = YmX1*YpX2 */
+/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<YpX2=fe#15); */
+/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<YpX2=q->YplusX); */
+fe_mul(r->Y,r->Y,q->YplusX);
+
+/* qhasm: C = T2d2*T1 */
+/* asm 1: fe_mul(>C=fe#4,<T2d2=fe#18,<T1=fe#14); */
+/* asm 2: fe_mul(>C=r->T,<T2d2=q->T2d,<T1=p->T); */
+fe_mul(r->T,q->T2d,p->T);
+
+/* qhasm: ZZ = Z1*Z2 */
+/* asm 1: fe_mul(>ZZ=fe#1,<Z1=fe#13,<Z2=fe#17); */
+/* asm 2: fe_mul(>ZZ=r->X,<Z1=p->Z,<Z2=q->Z); */
+fe_mul(r->X,p->Z,q->Z);
+
+/* qhasm: D = 2*ZZ */
+/* asm 1: fe_add(>D=fe#5,<ZZ=fe#1,<ZZ=fe#1); */
+/* asm 2: fe_add(>D=t0,<ZZ=r->X,<ZZ=r->X); */
+fe_add(t0,r->X,r->X);
+
+/* qhasm: X3 = A-B */
+/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
+/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
+fe_sub(r->X,r->Z,r->Y);
+
+/* qhasm: Y3 = A+B */
+/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
+/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
+fe_add(r->Y,r->Z,r->Y);
+
+/* qhasm: Z3 = D-C */
+/* asm 1: fe_sub(>Z3=fe#3,<D=fe#5,<C=fe#4); */
+/* asm 2: fe_sub(>Z3=r->Z,<D=t0,<C=r->T); */
+fe_sub(r->Z,t0,r->T);
+
+/* qhasm: T3 = D+C */
+/* asm 1: fe_add(>T3=fe#4,<D=fe#5,<C=fe#4); */
+/* asm 2: fe_add(>T3=r->T,<D=t0,<C=r->T); */
+fe_add(r->T,t0,r->T);
+
+/* qhasm: return */
+}
+
+
+/*
+r = p + q
+*/
+
+static void ge_madd(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q)
+{
+  fe t0;
+/* qhasm: enter ge_madd */
+
+/* qhasm: fe X1 */
+
+/* qhasm: fe Y1 */
+
+/* qhasm: fe Z1 */
+
+/* qhasm: fe T1 */
+
+/* qhasm: fe ypx2 */
+
+/* qhasm: fe ymx2 */
+
+/* qhasm: fe xy2d2 */
+
+/* qhasm: fe X3 */
+
+/* qhasm: fe Y3 */
+
+/* qhasm: fe Z3 */
+
+/* qhasm: fe T3 */
+
+/* qhasm: fe YpX1 */
+
+/* qhasm: fe YmX1 */
+
+/* qhasm: fe A */
+
+/* qhasm: fe B */
+
+/* qhasm: fe C */
+
+/* qhasm: fe D */
+
+/* qhasm: YpX1 = Y1+X1 */
+/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
+/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
+fe_add(r->X,p->Y,p->X);
+
+/* qhasm: YmX1 = Y1-X1 */
+/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
+/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
+fe_sub(r->Y,p->Y,p->X);
+
+/* qhasm: A = YpX1*ypx2 */
+/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<ypx2=fe#15); */
+/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<ypx2=q->yplusx); */
+fe_mul(r->Z,r->X,q->yplusx);
+
+/* qhasm: B = YmX1*ymx2 */
+/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<ymx2=fe#16); */
+/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<ymx2=q->yminusx); */
+fe_mul(r->Y,r->Y,q->yminusx);
+
+/* qhasm: C = xy2d2*T1 */
+/* asm 1: fe_mul(>C=fe#4,<xy2d2=fe#17,<T1=fe#14); */
+/* asm 2: fe_mul(>C=r->T,<xy2d2=q->xy2d,<T1=p->T); */
+fe_mul(r->T,q->xy2d,p->T);
+
+/* qhasm: D = 2*Z1 */
+/* asm 1: fe_add(>D=fe#5,<Z1=fe#13,<Z1=fe#13); */
+/* asm 2: fe_add(>D=t0,<Z1=p->Z,<Z1=p->Z); */
+fe_add(t0,p->Z,p->Z);
+
+/* qhasm: X3 = A-B */
+/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
+/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
+fe_sub(r->X,r->Z,r->Y);
+
+/* qhasm: Y3 = A+B */
+/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
+/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
+fe_add(r->Y,r->Z,r->Y);
+
+/* qhasm: Z3 = D+C */
+/* asm 1: fe_add(>Z3=fe#3,<D=fe#5,<C=fe#4); */
+/* asm 2: fe_add(>Z3=r->Z,<D=t0,<C=r->T); */
+fe_add(r->Z,t0,r->T);
+
+/* qhasm: T3 = D-C */
+/* asm 1: fe_sub(>T3=fe#4,<D=fe#5,<C=fe#4); */
+/* asm 2: fe_sub(>T3=r->T,<D=t0,<C=r->T); */
+fe_sub(r->T,t0,r->T);
+
+/* qhasm: return */
+}
+
+
+/*
+r = p - q
+*/
+
+static void ge_msub(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q)
+{
+  fe t0;
+/* qhasm: enter ge_msub */
+
+/* qhasm: fe X1 */
+
+/* qhasm: fe Y1 */
+
+/* qhasm: fe Z1 */
+
+/* qhasm: fe T1 */
+
+/* qhasm: fe ypx2 */
+
+/* qhasm: fe ymx2 */
+
+/* qhasm: fe xy2d2 */
+
+/* qhasm: fe X3 */
+
+/* qhasm: fe Y3 */
+
+/* qhasm: fe Z3 */
+
+/* qhasm: fe T3 */
+
+/* qhasm: fe YpX1 */
+
+/* qhasm: fe YmX1 */
+
+/* qhasm: fe A */
+
+/* qhasm: fe B */
+
+/* qhasm: fe C */
+
+/* qhasm: fe D */
+
+/* qhasm: YpX1 = Y1+X1 */
+/* asm 1: fe_add(>YpX1=fe#1,<Y1=fe#12,<X1=fe#11); */
+/* asm 2: fe_add(>YpX1=r->X,<Y1=p->Y,<X1=p->X); */
+fe_add(r->X,p->Y,p->X);
+
+/* qhasm: YmX1 = Y1-X1 */
+/* asm 1: fe_sub(>YmX1=fe#2,<Y1=fe#12,<X1=fe#11); */
+/* asm 2: fe_sub(>YmX1=r->Y,<Y1=p->Y,<X1=p->X); */
+fe_sub(r->Y,p->Y,p->X);
+
+/* qhasm: A = YpX1*ymx2 */
+/* asm 1: fe_mul(>A=fe#3,<YpX1=fe#1,<ymx2=fe#16); */
+/* asm 2: fe_mul(>A=r->Z,<YpX1=r->X,<ymx2=q->yminusx); */
+fe_mul(r->Z,r->X,q->yminusx);
+
+/* qhasm: B = YmX1*ypx2 */
+/* asm 1: fe_mul(>B=fe#2,<YmX1=fe#2,<ypx2=fe#15); */
+/* asm 2: fe_mul(>B=r->Y,<YmX1=r->Y,<ypx2=q->yplusx); */
+fe_mul(r->Y,r->Y,q->yplusx);
+
+/* qhasm: C = xy2d2*T1 */
+/* asm 1: fe_mul(>C=fe#4,<xy2d2=fe#17,<T1=fe#14); */
+/* asm 2: fe_mul(>C=r->T,<xy2d2=q->xy2d,<T1=p->T); */
+fe_mul(r->T,q->xy2d,p->T);
+
+/* qhasm: D = 2*Z1 */
+/* asm 1: fe_add(>D=fe#5,<Z1=fe#13,<Z1=fe#13); */
+/* asm 2: fe_add(>D=t0,<Z1=p->Z,<Z1=p->Z); */
+fe_add(t0,p->Z,p->Z);
+
+/* qhasm: X3 = A-B */
+/* asm 1: fe_sub(>X3=fe#1,<A=fe#3,<B=fe#2); */
+/* asm 2: fe_sub(>X3=r->X,<A=r->Z,<B=r->Y); */
+fe_sub(r->X,r->Z,r->Y);
+
+/* qhasm: Y3 = A+B */
+/* asm 1: fe_add(>Y3=fe#2,<A=fe#3,<B=fe#2); */
+/* asm 2: fe_add(>Y3=r->Y,<A=r->Z,<B=r->Y); */
+fe_add(r->Y,r->Z,r->Y);
+
+/* qhasm: Z3 = D-C */
+/* asm 1: fe_sub(>Z3=fe#3,<D=fe#5,<C=fe#4); */
+/* asm 2: fe_sub(>Z3=r->Z,<D=t0,<C=r->T); */
+fe_sub(r->Z,t0,r->T);
+
+/* qhasm: T3 = D+C */
+/* asm 1: fe_add(>T3=fe#4,<D=fe#5,<C=fe#4); */
+/* asm 2: fe_add(>T3=r->T,<D=t0,<C=r->T); */
+fe_add(r->T,t0,r->T);
+
+/* qhasm: return */
+}
+
+
+static void ge_p3_tobytes(unsigned char *s,const ge_p3 *h)
+{
+  fe recip;
+  fe x;
+  fe y;
+
+  fe_invert(recip,h->Z);
+  fe_mul(x,h->X,recip);
+  fe_mul(y,h->Y,recip);
+  fe_tobytes(s,y);
+  s[31] ^= fe_isnegative(x) << 7;
+}
+
+static void ge_tobytes(unsigned char *s,const ge_p2 *h)
+{
+  fe recip;
+  fe x;
+  fe y;
+
+  fe_invert(recip,h->Z);
+  fe_mul(x,h->X,recip);
+  fe_mul(y,h->Y,recip);
+  fe_tobytes(s,y);
+  s[31] ^= fe_isnegative(x) << 7;
+}
+
+static int ge_frombytes_negate_vartime(ge_p3 *h,const unsigned char *s)
+{
+  fe u;
+  fe v;
+  fe v3;
+  fe vxx;
+  fe check;
+
+  fe_frombytes(h->Y,s);
+  fe_1(h->Z);
+  fe_sq(u,h->Y);
+  fe_mul(v,u,d);
+  fe_sub(u,u,h->Z);       /* u = y^2-1 */
+  fe_add(v,v,h->Z);       /* v = dy^2+1 */
+
+  fe_sq(v3,v);
+  fe_mul(v3,v3,v);        /* v3 = v^3 */
+  fe_sq(h->X,v3);
+  fe_mul(h->X,h->X,v);
+  fe_mul(h->X,h->X,u);    /* x = uv^7 */
+
+  fe_pow22523(h->X,h->X); /* x = (uv^7)^((q-5)/8) */
+  fe_mul(h->X,h->X,v3);
+  fe_mul(h->X,h->X,u);    /* x = uv^3(uv^7)^((q-5)/8) */
+
+  fe_sq(vxx,h->X);
+  fe_mul(vxx,vxx,v);
+  fe_sub(check,vxx,u);    /* vx^2-u */
+  if (fe_isnonzero(check)) {
+    fe_add(check,vxx,u);  /* vx^2+u */
+    if (fe_isnonzero(check)) return -1;
+    fe_mul(h->X,h->X,sqrtm1);
+  }
+
+  if (fe_isnegative(h->X) == (s[31] >> 7))
+    fe_neg(h->X,h->X);
+
+  fe_mul(h->T,h->X,h->Y);
+  return 0;
+}
+
+
+static void slide(signed char *r,const unsigned char *a)
+{
+  int i;
+  int b;
+  int k;
+
+  for (i = 0;i < 256;++i)
+    r[i] = 1 & (a[i >> 3] >> (i & 7));
+
+  for (i = 0;i < 256;++i)
+    if (r[i]) {
+      for (b = 1;b <= 6 && i + b < 256;++b) {
+        if (r[i + b]) {
+          if (r[i] + (r[i + b] << b) <= 15) {
+            r[i] += r[i + b] << b; r[i + b] = 0;
+          } else if (r[i] - (r[i + b] << b) >= -15) {
+            r[i] -= r[i + b] << b;
+            for (k = i + b;k < 256;++k) {
+              if (!r[k]) {
+                r[k] = 1;
+                break;
+              }
+              r[k] = 0;
+            }
+          } else
+            break;
+        }
+      }
+    }
+
+}
+
+
+/*
+r = a * A + b * B
+where a = a[0]+256*a[1]+...+256^31 a[31].
+and b = b[0]+256*b[1]+...+256^31 b[31].
+B is the Ed25519 base point (x,4/5) with x positive.
+*/
+
+static void ge_double_scalarmult_vartime(ge_p2 *r,const unsigned char *a,const ge_p3 *A,const unsigned char *b)
+{
+  signed char aslide[256];
+  signed char bslide[256];
+  ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
+  ge_p1p1 t;
+  ge_p3 u;
+  ge_p3 A2;
+  int i;
+
+  slide(aslide,a);
+  slide(bslide,b);
+
+  ge_p3_to_cached(&Ai[0],A);
+  ge_p3_dbl(&t,A); ge_p1p1_to_p3(&A2,&t);
+  ge_add(&t,&A2,&Ai[0]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[1],&u);
+  ge_add(&t,&A2,&Ai[1]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[2],&u);
+  ge_add(&t,&A2,&Ai[2]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[3],&u);
+  ge_add(&t,&A2,&Ai[3]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[4],&u);
+  ge_add(&t,&A2,&Ai[4]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[5],&u);
+  ge_add(&t,&A2,&Ai[5]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[6],&u);
+  ge_add(&t,&A2,&Ai[6]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[7],&u);
+
+  ge_p2_0(r);
+
+  for (i = 255;i >= 0;--i) {
+    if (aslide[i] || bslide[i]) break;
+  }
+
+  for (;i >= 0;--i) {
+    ge_p2_dbl(&t,r);
+
+    if (aslide[i] > 0) {
+      ge_p1p1_to_p3(&u,&t);
+      ge_add(&t,&u,&Ai[aslide[i]/2]);
+    } else if (aslide[i] < 0) {
+      ge_p1p1_to_p3(&u,&t);
+      ge_sub(&t,&u,&Ai[(-aslide[i])/2]);
+    }
+
+    if (bslide[i] > 0) {
+      ge_p1p1_to_p3(&u,&t);
+      ge_madd(&t,&u,&Bi[bslide[i]/2]);
+    } else if (bslide[i] < 0) {
+      ge_p1p1_to_p3(&u,&t);
+      ge_msub(&t,&u,&Bi[(-bslide[i])/2]);
+    }
+
+    ge_p1p1_to_p2(r,&t);
+  }
+}
+
+static unsigned char equal(signed char b,signed char c)
+{
+  unsigned char ub = b;
+  unsigned char uc = c;
+  unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */
+  crypto_uint32 y = x; /* 0: yes; 1..255: no */
+  y -= 1; /* 4294967295: yes; 0..254: no */
+  y >>= 31; /* 1: yes; 0: no */
+  return y;
+}
+
+static unsigned char negative(signed char b)
+{
+  unsigned long long x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */
+  x >>= 63; /* 1: yes; 0: no */
+  return x;
+}
+
+static void cmov(ge_precomp *t,ge_precomp *u,unsigned char b)
+{
+  fe_cmov(t->yplusx,u->yplusx,b);
+  fe_cmov(t->yminusx,u->yminusx,b);
+  fe_cmov(t->xy2d,u->xy2d,b);
+}
+
+
+
+static void select(ge_precomp *t,int pos,signed char b)
+{
+  ge_precomp minust;
+  unsigned char bnegative = negative(b);
+  unsigned char babs = b - (((-bnegative) & b) << 1);
+
+  ge_precomp_0(t);
+  cmov(t,&base[pos][0],equal(babs,1));
+  cmov(t,&base[pos][1],equal(babs,2));
+  cmov(t,&base[pos][2],equal(babs,3));
+  cmov(t,&base[pos][3],equal(babs,4));
+  cmov(t,&base[pos][4],equal(babs,5));
+  cmov(t,&base[pos][5],equal(babs,6));
+  cmov(t,&base[pos][6],equal(babs,7));
+  cmov(t,&base[pos][7],equal(babs,8));
+  fe_copy(minust.yplusx,t->yminusx);
+  fe_copy(minust.yminusx,t->yplusx);
+  fe_neg(minust.xy2d,t->xy2d);
+  cmov(t,&minust,bnegative);
+}
+
+/*
+h = a * B
+where a = a[0]+256*a[1]+...+256^31 a[31]
+B is the Ed25519 base point (x,4/5) with x positive.
+
+Preconditions:
+  a[31] <= 127
+*/
+
+static void ge_scalarmult_base(ge_p3 *h,const unsigned char *a)
+{
+  signed char e[64];
+  signed char carry;
+  ge_p1p1 r;
+  ge_p2 s;
+  ge_precomp t;
+  int i;
+
+  for (i = 0;i < 32;++i) {
+    e[2 * i + 0] = (a[i] >> 0) & 15;
+    e[2 * i + 1] = (a[i] >> 4) & 15;
+  }
+  /* each e[i] is between 0 and 15 */
+  /* e[63] is between 0 and 7 */
+
+  carry = 0;
+  for (i = 0;i < 63;++i) {
+    e[i] += carry;
+    carry = e[i] + 8;
+    carry >>= 4;
+    e[i] -= carry << 4;
+  }
+  e[63] += carry;
+  /* each e[i] is between -8 and 8 */
+
+  ge_p3_0(h);
+  for (i = 1;i < 64;i += 2) {
+    select(&t,i / 2,e[i]);
+    ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r);
+  }
+
+  ge_p3_dbl(&r,h);  ge_p1p1_to_p2(&s,&r);
+  ge_p2_dbl(&r,&s); ge_p1p1_to_p2(&s,&r);
+  ge_p2_dbl(&r,&s); ge_p1p1_to_p2(&s,&r);
+  ge_p2_dbl(&r,&s); ge_p1p1_to_p3(h,&r);
+
+  for (i = 0;i < 64;i += 2) {
+    select(&t,i / 2,e[i]);
+    ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r);
+  }
+}
+
+/*
+Input:
+  s[0]+256*s[1]+...+256^63*s[63] = s
+
+Output:
+  s[0]+256*s[1]+...+256^31*s[31] = s mod l
+  where l = 2^252 + 27742317777372353535851937790883648493.
+  Overwrites s in place.
+*/
+
+static void sc_reduce(unsigned char *s)
+{
+  crypto_int64 s0 = 2097151 & load_3(s);
+  crypto_int64 s1 = 2097151 & (load_4(s + 2) >> 5);
+  crypto_int64 s2 = 2097151 & (load_3(s + 5) >> 2);
+  crypto_int64 s3 = 2097151 & (load_4(s + 7) >> 7);
+  crypto_int64 s4 = 2097151 & (load_4(s + 10) >> 4);
+  crypto_int64 s5 = 2097151 & (load_3(s + 13) >> 1);
+  crypto_int64 s6 = 2097151 & (load_4(s + 15) >> 6);
+  crypto_int64 s7 = 2097151 & (load_3(s + 18) >> 3);
+  crypto_int64 s8 = 2097151 & load_3(s + 21);
+  crypto_int64 s9 = 2097151 & (load_4(s + 23) >> 5);
+  crypto_int64 s10 = 2097151 & (load_3(s + 26) >> 2);
+  crypto_int64 s11 = 2097151 & (load_4(s + 28) >> 7);
+  crypto_int64 s12 = 2097151 & (load_4(s + 31) >> 4);
+  crypto_int64 s13 = 2097151 & (load_3(s + 34) >> 1);
+  crypto_int64 s14 = 2097151 & (load_4(s + 36) >> 6);
+  crypto_int64 s15 = 2097151 & (load_3(s + 39) >> 3);
+  crypto_int64 s16 = 2097151 & load_3(s + 42);
+  crypto_int64 s17 = 2097151 & (load_4(s + 44) >> 5);
+  crypto_int64 s18 = 2097151 & (load_3(s + 47) >> 2);
+  crypto_int64 s19 = 2097151 & (load_4(s + 49) >> 7);
+  crypto_int64 s20 = 2097151 & (load_4(s + 52) >> 4);
+  crypto_int64 s21 = 2097151 & (load_3(s + 55) >> 1);
+  crypto_int64 s22 = 2097151 & (load_4(s + 57) >> 6);
+  crypto_int64 s23 = (load_4(s + 60) >> 3);
+  crypto_int64 carry0;
+  crypto_int64 carry1;
+  crypto_int64 carry2;
+  crypto_int64 carry3;
+  crypto_int64 carry4;
+  crypto_int64 carry5;
+  crypto_int64 carry6;
+  crypto_int64 carry7;
+  crypto_int64 carry8;
+  crypto_int64 carry9;
+  crypto_int64 carry10;
+  crypto_int64 carry11;
+  crypto_int64 carry12;
+  crypto_int64 carry13;
+  crypto_int64 carry14;
+  crypto_int64 carry15;
+  crypto_int64 carry16;
+
+  s11 += s23 * 666643;
+  s12 += s23 * 470296;
+  s13 += s23 * 654183;
+  s14 -= s23 * 997805;
+  s15 += s23 * 136657;
+  s16 -= s23 * 683901;
+  s23 = 0;
+
+  s10 += s22 * 666643;
+  s11 += s22 * 470296;
+  s12 += s22 * 654183;
+  s13 -= s22 * 997805;
+  s14 += s22 * 136657;
+  s15 -= s22 * 683901;
+  s22 = 0;
+
+  s9 += s21 * 666643;
+  s10 += s21 * 470296;
+  s11 += s21 * 654183;
+  s12 -= s21 * 997805;
+  s13 += s21 * 136657;
+  s14 -= s21 * 683901;
+  s21 = 0;
+
+  s8 += s20 * 666643;
+  s9 += s20 * 470296;
+  s10 += s20 * 654183;
+  s11 -= s20 * 997805;
+  s12 += s20 * 136657;
+  s13 -= s20 * 683901;
+  s20 = 0;
+
+  s7 += s19 * 666643;
+  s8 += s19 * 470296;
+  s9 += s19 * 654183;
+  s10 -= s19 * 997805;
+  s11 += s19 * 136657;
+  s12 -= s19 * 683901;
+  s19 = 0;
+
+  s6 += s18 * 666643;
+  s7 += s18 * 470296;
+  s8 += s18 * 654183;
+  s9 -= s18 * 997805;
+  s10 += s18 * 136657;
+  s11 -= s18 * 683901;
+  s18 = 0;
+
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
+  carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
+  carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
+
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+  carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
+  carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
+
+  s5 += s17 * 666643;
+  s6 += s17 * 470296;
+  s7 += s17 * 654183;
+  s8 -= s17 * 997805;
+  s9 += s17 * 136657;
+  s10 -= s17 * 683901;
+  s17 = 0;
+
+  s4 += s16 * 666643;
+  s5 += s16 * 470296;
+  s6 += s16 * 654183;
+  s7 -= s16 * 997805;
+  s8 += s16 * 136657;
+  s9 -= s16 * 683901;
+  s16 = 0;
+
+  s3 += s15 * 666643;
+  s4 += s15 * 470296;
+  s5 += s15 * 654183;
+  s6 -= s15 * 997805;
+  s7 += s15 * 136657;
+  s8 -= s15 * 683901;
+  s15 = 0;
+
+  s2 += s14 * 666643;
+  s3 += s14 * 470296;
+  s4 += s14 * 654183;
+  s5 -= s14 * 997805;
+  s6 += s14 * 136657;
+  s7 -= s14 * 683901;
+  s14 = 0;
+
+  s1 += s13 * 666643;
+  s2 += s13 * 470296;
+  s3 += s13 * 654183;
+  s4 -= s13 * 997805;
+  s5 += s13 * 136657;
+  s6 -= s13 * 683901;
+  s13 = 0;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+
+  carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
+
+  s[0] = s0 >> 0;
+  s[1] = s0 >> 8;
+  s[2] = (s0 >> 16) | (s1 << 5);
+  s[3] = s1 >> 3;
+  s[4] = s1 >> 11;
+  s[5] = (s1 >> 19) | (s2 << 2);
+  s[6] = s2 >> 6;
+  s[7] = (s2 >> 14) | (s3 << 7);
+  s[8] = s3 >> 1;
+  s[9] = s3 >> 9;
+  s[10] = (s3 >> 17) | (s4 << 4);
+  s[11] = s4 >> 4;
+  s[12] = s4 >> 12;
+  s[13] = (s4 >> 20) | (s5 << 1);
+  s[14] = s5 >> 7;
+  s[15] = (s5 >> 15) | (s6 << 6);
+  s[16] = s6 >> 2;
+  s[17] = s6 >> 10;
+  s[18] = (s6 >> 18) | (s7 << 3);
+  s[19] = s7 >> 5;
+  s[20] = s7 >> 13;
+  s[21] = s8 >> 0;
+  s[22] = s8 >> 8;
+  s[23] = (s8 >> 16) | (s9 << 5);
+  s[24] = s9 >> 3;
+  s[25] = s9 >> 11;
+  s[26] = (s9 >> 19) | (s10 << 2);
+  s[27] = s10 >> 6;
+  s[28] = (s10 >> 14) | (s11 << 7);
+  s[29] = s11 >> 1;
+  s[30] = s11 >> 9;
+  s[31] = s11 >> 17;
+}
+
+/*
+Input:
+  a[0]+256*a[1]+...+256^31*a[31] = a
+  b[0]+256*b[1]+...+256^31*b[31] = b
+  c[0]+256*c[1]+...+256^31*c[31] = c
+
+Output:
+  s[0]+256*s[1]+...+256^31*s[31] = (ab+c) mod l
+  where l = 2^252 + 27742317777372353535851937790883648493.
+*/
+
+static void sc_muladd(unsigned char *s,const unsigned char *a,const unsigned char *b,const unsigned char *c)
+{
+  crypto_int64 a0 = 2097151 & load_3(a);
+  crypto_int64 a1 = 2097151 & (load_4(a + 2) >> 5);
+  crypto_int64 a2 = 2097151 & (load_3(a + 5) >> 2);
+  crypto_int64 a3 = 2097151 & (load_4(a + 7) >> 7);
+  crypto_int64 a4 = 2097151 & (load_4(a + 10) >> 4);
+  crypto_int64 a5 = 2097151 & (load_3(a + 13) >> 1);
+  crypto_int64 a6 = 2097151 & (load_4(a + 15) >> 6);
+  crypto_int64 a7 = 2097151 & (load_3(a + 18) >> 3);
+  crypto_int64 a8 = 2097151 & load_3(a + 21);
+  crypto_int64 a9 = 2097151 & (load_4(a + 23) >> 5);
+  crypto_int64 a10 = 2097151 & (load_3(a + 26) >> 2);
+  crypto_int64 a11 = (load_4(a + 28) >> 7);
+  crypto_int64 b0 = 2097151 & load_3(b);
+  crypto_int64 b1 = 2097151 & (load_4(b + 2) >> 5);
+  crypto_int64 b2 = 2097151 & (load_3(b + 5) >> 2);
+  crypto_int64 b3 = 2097151 & (load_4(b + 7) >> 7);
+  crypto_int64 b4 = 2097151 & (load_4(b + 10) >> 4);
+  crypto_int64 b5 = 2097151 & (load_3(b + 13) >> 1);
+  crypto_int64 b6 = 2097151 & (load_4(b + 15) >> 6);
+  crypto_int64 b7 = 2097151 & (load_3(b + 18) >> 3);
+  crypto_int64 b8 = 2097151 & load_3(b + 21);
+  crypto_int64 b9 = 2097151 & (load_4(b + 23) >> 5);
+  crypto_int64 b10 = 2097151 & (load_3(b + 26) >> 2);
+  crypto_int64 b11 = (load_4(b + 28) >> 7);
+  crypto_int64 c0 = 2097151 & load_3(c);
+  crypto_int64 c1 = 2097151 & (load_4(c + 2) >> 5);
+  crypto_int64 c2 = 2097151 & (load_3(c + 5) >> 2);
+  crypto_int64 c3 = 2097151 & (load_4(c + 7) >> 7);
+  crypto_int64 c4 = 2097151 & (load_4(c + 10) >> 4);
+  crypto_int64 c5 = 2097151 & (load_3(c + 13) >> 1);
+  crypto_int64 c6 = 2097151 & (load_4(c + 15) >> 6);
+  crypto_int64 c7 = 2097151 & (load_3(c + 18) >> 3);
+  crypto_int64 c8 = 2097151 & load_3(c + 21);
+  crypto_int64 c9 = 2097151 & (load_4(c + 23) >> 5);
+  crypto_int64 c10 = 2097151 & (load_3(c + 26) >> 2);
+  crypto_int64 c11 = (load_4(c + 28) >> 7);
+  crypto_int64 s0;
+  crypto_int64 s1;
+  crypto_int64 s2;
+  crypto_int64 s3;
+  crypto_int64 s4;
+  crypto_int64 s5;
+  crypto_int64 s6;
+  crypto_int64 s7;
+  crypto_int64 s8;
+  crypto_int64 s9;
+  crypto_int64 s10;
+  crypto_int64 s11;
+  crypto_int64 s12;
+  crypto_int64 s13;
+  crypto_int64 s14;
+  crypto_int64 s15;
+  crypto_int64 s16;
+  crypto_int64 s17;
+  crypto_int64 s18;
+  crypto_int64 s19;
+  crypto_int64 s20;
+  crypto_int64 s21;
+  crypto_int64 s22;
+  crypto_int64 s23;
+  crypto_int64 carry0;
+  crypto_int64 carry1;
+  crypto_int64 carry2;
+  crypto_int64 carry3;
+  crypto_int64 carry4;
+  crypto_int64 carry5;
+  crypto_int64 carry6;
+  crypto_int64 carry7;
+  crypto_int64 carry8;
+  crypto_int64 carry9;
+  crypto_int64 carry10;
+  crypto_int64 carry11;
+  crypto_int64 carry12;
+  crypto_int64 carry13;
+  crypto_int64 carry14;
+  crypto_int64 carry15;
+  crypto_int64 carry16;
+  crypto_int64 carry17;
+  crypto_int64 carry18;
+  crypto_int64 carry19;
+  crypto_int64 carry20;
+  crypto_int64 carry21;
+  crypto_int64 carry22;
+
+  s0 = c0 + a0*b0;
+  s1 = c1 + a0*b1 + a1*b0;
+  s2 = c2 + a0*b2 + a1*b1 + a2*b0;
+  s3 = c3 + a0*b3 + a1*b2 + a2*b1 + a3*b0;
+  s4 = c4 + a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0;
+  s5 = c5 + a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0;
+  s6 = c6 + a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0;
+  s7 = c7 + a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0;
+  s8 = c8 + a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0;
+  s9 = c9 + a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0;
+  s10 = c10 + a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0;
+  s11 = c11 + a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0;
+  s12 = a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1;
+  s13 = a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2;
+  s14 = a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3;
+  s15 = a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4;
+  s16 = a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5;
+  s17 = a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6;
+  s18 = a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7;
+  s19 = a8*b11 + a9*b10 + a10*b9 + a11*b8;
+  s20 = a9*b11 + a10*b10 + a11*b9;
+  s21 = a10*b11 + a11*b10;
+  s22 = a11*b11;
+  s23 = 0;
+
+  carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
+  carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
+  carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
+  carry18 = (s18 + (1<<20)) >> 21; s19 += carry18; s18 -= carry18 << 21;
+  carry20 = (s20 + (1<<20)) >> 21; s21 += carry20; s20 -= carry20 << 21;
+  carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= carry22 << 21;
+
+  carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+  carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
+  carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
+  carry17 = (s17 + (1<<20)) >> 21; s18 += carry17; s17 -= carry17 << 21;
+  carry19 = (s19 + (1<<20)) >> 21; s20 += carry19; s19 -= carry19 << 21;
+  carry21 = (s21 + (1<<20)) >> 21; s22 += carry21; s21 -= carry21 << 21;
+
+  s11 += s23 * 666643;
+  s12 += s23 * 470296;
+  s13 += s23 * 654183;
+  s14 -= s23 * 997805;
+  s15 += s23 * 136657;
+  s16 -= s23 * 683901;
+  s23 = 0;
+
+  s10 += s22 * 666643;
+  s11 += s22 * 470296;
+  s12 += s22 * 654183;
+  s13 -= s22 * 997805;
+  s14 += s22 * 136657;
+  s15 -= s22 * 683901;
+  s22 = 0;
+
+  s9 += s21 * 666643;
+  s10 += s21 * 470296;
+  s11 += s21 * 654183;
+  s12 -= s21 * 997805;
+  s13 += s21 * 136657;
+  s14 -= s21 * 683901;
+  s21 = 0;
+
+  s8 += s20 * 666643;
+  s9 += s20 * 470296;
+  s10 += s20 * 654183;
+  s11 -= s20 * 997805;
+  s12 += s20 * 136657;
+  s13 -= s20 * 683901;
+  s20 = 0;
+
+  s7 += s19 * 666643;
+  s8 += s19 * 470296;
+  s9 += s19 * 654183;
+  s10 -= s19 * 997805;
+  s11 += s19 * 136657;
+  s12 -= s19 * 683901;
+  s19 = 0;
+
+  s6 += s18 * 666643;
+  s7 += s18 * 470296;
+  s8 += s18 * 654183;
+  s9 -= s18 * 997805;
+  s10 += s18 * 136657;
+  s11 -= s18 * 683901;
+  s18 = 0;
+
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21;
+  carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21;
+  carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21;
+
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+  carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21;
+  carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21;
+
+  s5 += s17 * 666643;
+  s6 += s17 * 470296;
+  s7 += s17 * 654183;
+  s8 -= s17 * 997805;
+  s9 += s17 * 136657;
+  s10 -= s17 * 683901;
+  s17 = 0;
+
+  s4 += s16 * 666643;
+  s5 += s16 * 470296;
+  s6 += s16 * 654183;
+  s7 -= s16 * 997805;
+  s8 += s16 * 136657;
+  s9 -= s16 * 683901;
+  s16 = 0;
+
+  s3 += s15 * 666643;
+  s4 += s15 * 470296;
+  s5 += s15 * 654183;
+  s6 -= s15 * 997805;
+  s7 += s15 * 136657;
+  s8 -= s15 * 683901;
+  s15 = 0;
+
+  s2 += s14 * 666643;
+  s3 += s14 * 470296;
+  s4 += s14 * 654183;
+  s5 -= s14 * 997805;
+  s6 += s14 * 136657;
+  s7 -= s14 * 683901;
+  s14 = 0;
+
+  s1 += s13 * 666643;
+  s2 += s13 * 470296;
+  s3 += s13 * 654183;
+  s4 -= s13 * 997805;
+  s5 += s13 * 136657;
+  s6 -= s13 * 683901;
+  s13 = 0;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21;
+
+  carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
+  carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21;
+
+  s0 += s12 * 666643;
+  s1 += s12 * 470296;
+  s2 += s12 * 654183;
+  s3 -= s12 * 997805;
+  s4 += s12 * 136657;
+  s5 -= s12 * 683901;
+  s12 = 0;
+
+  carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21;
+  carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21;
+  carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21;
+  carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21;
+  carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21;
+  carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21;
+  carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21;
+  carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21;
+  carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21;
+  carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21;
+  carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21;
+
+  s[0] = s0 >> 0;
+  s[1] = s0 >> 8;
+  s[2] = (s0 >> 16) | (s1 << 5);
+  s[3] = s1 >> 3;
+  s[4] = s1 >> 11;
+  s[5] = (s1 >> 19) | (s2 << 2);
+  s[6] = s2 >> 6;
+  s[7] = (s2 >> 14) | (s3 << 7);
+  s[8] = s3 >> 1;
+  s[9] = s3 >> 9;
+  s[10] = (s3 >> 17) | (s4 << 4);
+  s[11] = s4 >> 4;
+  s[12] = s4 >> 12;
+  s[13] = (s4 >> 20) | (s5 << 1);
+  s[14] = s5 >> 7;
+  s[15] = (s5 >> 15) | (s6 << 6);
+  s[16] = s6 >> 2;
+  s[17] = s6 >> 10;
+  s[18] = (s6 >> 18) | (s7 << 3);
+  s[19] = s7 >> 5;
+  s[20] = s7 >> 13;
+  s[21] = s8 >> 0;
+  s[22] = s8 >> 8;
+  s[23] = (s8 >> 16) | (s9 << 5);
+  s[24] = s9 >> 3;
+  s[25] = s9 >> 11;
+  s[26] = (s9 >> 19) | (s10 << 2);
+  s[27] = s10 >> 6;
+  s[28] = (s10 >> 14) | (s11 << 7);
+  s[29] = s11 >> 1;
+  s[30] = s11 >> 9;
+  s[31] = s11 >> 17;
+}
+
+/*
+int crypto_sign_keypair(unsigned char *pk,unsigned char *sk)
+{
+  unsigned char h[64];
+  ge_p3 A;
+  int i;
+
+  randombytes(sk,32);
+  crypto_hash_sha512(h,sk,32);
+  h[0] &= 248;
+  h[31] &= 63;
+  h[31] |= 64;
+
+  ge_scalarmult_base(&A,h);
+  ge_p3_tobytes(pk,&A);
+
+  for (i = 0;i < 32;++i) sk[32 + i] = pk[i];
+  return 0;
+}
+*/
+
+int crypto_sign_pk_ref10(unsigned char *pk,unsigned char *sk)
+{
+  unsigned char h[64];
+  ge_p3 A;
+  int i;
+
+  crypto_hash_sha512(h,sk,32);
+  h[0] &= 248;
+  h[31] &= 63;
+  h[31] |= 64;
+
+  ge_scalarmult_base(&A,h);
+  ge_p3_tobytes(pk,&A);
+
+  for (i = 0;i < 32;++i) sk[32 + i] = pk[i];
+  return 0;
+}
+
+int crypto_sign_ref10(
+  unsigned char *sm,unsigned long long *smlen,
+  const unsigned char *m,unsigned long long mlen,
+  const unsigned char *sk
+)
+{
+  unsigned char az[64];
+  unsigned char r[64];
+  unsigned char hram[64];
+  ge_p3 R;
+  unsigned long long i;
+
+  crypto_hash_sha512(az,sk,32);
+  az[0] &= 248;
+  az[31] &= 63;
+  az[31] |= 64;
+
+  *smlen = mlen + 64;
+  for (i = 0;i < mlen;++i) sm[64 + i] = m[i];
+  for (i = 0;i < 32;++i) sm[32 + i] = az[32 + i];
+  crypto_hash_sha512(r,sm + 32,mlen + 32);
+  for (i = 0;i < 32;++i) sm[32 + i] = sk[32 + i];
+
+  sc_reduce(r);
+  ge_scalarmult_base(&R,r);
+  ge_p3_tobytes(sm,&R);
+
+  crypto_hash_sha512(hram,sm,mlen + 64);
+  sc_reduce(hram);
+  sc_muladd(sm + 32,hram,az,r);
+
+  return 0;
+}
+
+int crypto_sign_open_ref10(
+  unsigned char *m,unsigned long long *mlen,
+  const unsigned char *sm,unsigned long long smlen,
+  const unsigned char *pk
+)
+{
+  unsigned char h[64];
+  unsigned char checkr[32];
+  ge_p3 A;
+  ge_p2 R;
+  unsigned long long i;
+
+  *mlen = -1;
+  if (smlen < 64) return -1;
+  if (sm[63] & 224) return -1;
+  if (ge_frombytes_negate_vartime(&A,pk) != 0) return -1;
+
+  for (i = 0;i < smlen;++i) m[i] = sm[i];
+  for (i = 0;i < 32;++i) m[32 + i] = pk[i];
+  crypto_hash_sha512(h,m,smlen);
+  sc_reduce(h);
+
+  ge_double_scalarmult_vartime(&R,h,&A,sm + 32);
+  ge_tobytes(checkr,&R);
+  if (crypto_verify_32(checkr,sm) != 0) {
+    for (i = 0;i < smlen;++i) m[i] = 0;
+    return -1;
+  }
+
+  for (i = 0;i < smlen - 64;++i) m[i] = sm[64 + i];
+  for (i = smlen - 64;i < smlen;++i) m[i] = 0;
+  *mlen = smlen - 64;
+  return 0;
+}
+

diff --git a/crypto/ed25519-donna/src/fuzz/ed25519-ref10.h b/crypto/ed25519-donna/src/fuzz/ed25519-ref10.h
new file mode 100644 (file)
index 0000000..c8a0f69
--- /dev/null
+++ b/crypto/ed25519-donna/src/fuzz/ed25519-ref10.h
@@ -0,0 +1,9 @@
+#ifndef ED25519_REF10_H
+#define ED25519_REF10_H
+
+int crypto_sign_pk_ref10(unsigned char *pk,unsigned char *sk);
+int crypto_sign_ref10(unsigned char *sm,unsigned long long *smlen,const unsigned char *m,unsigned long long mlen,const unsigned char *sk);
+int crypto_sign_open_ref10(unsigned char *m,unsigned long long *mlen,const unsigned char *sm,unsigned long long smlen,const unsigned char *pk);
+
+#endif /* ED25519_REF10_H */
+

diff --git a/crypto/ed25519-donna/src/fuzz/fuzz-curve25519.c b/crypto/ed25519-donna/src/fuzz/fuzz-curve25519.c
new file mode 100644 (file)
index 0000000..4301701
--- /dev/null
+++ b/crypto/ed25519-donna/src/fuzz/fuzz-curve25519.c
@@ -0,0 +1,172 @@
+#if defined(_WIN32)
+       #include <windows.h>
+       #include <wincrypt.h>
+       typedef unsigned int uint32_t;
+       typedef unsigned __int64 uint64_t;
+#else
+       #include <stdint.h>
+#endif
+
+#include <string.h>
+#include <stdio.h>
+
+#include "ed25519-donna.h"
+#include "curve25519-ref10.h"
+
+static void
+print_diff(const char *desc, const unsigned char *a, const unsigned char *b, size_t len) {
+       size_t p = 0;
+       unsigned char diff;
+       printf("%s diff:\n", desc);
+       while (len--) {
+               diff = *a++ ^ *b++;
+               if (!diff)
+                       printf("____,");
+               else
+                       printf("0x%02x,", diff);
+               if ((++p & 15) == 0)
+                       printf("\n");
+       }
+       printf("\n\n");
+}
+
+static void
+print_bytes(const char *desc, const unsigned char *bytes, size_t len) {
+       size_t p = 0;
+       printf("%s:\n", desc);
+       while (len--) {
+               printf("0x%02x,", *bytes++);
+               if ((++p & 15) == 0)
+                       printf("\n");
+       }
+       printf("\n\n");
+}
+
+
+/* chacha20/12 prng */
+void
+prng(unsigned char *out, size_t bytes) {
+       static uint32_t state[16];
+       static int init = 0;
+       uint32_t x[16], t;
+       size_t i;
+
+       if (!init) {
+       #if defined(_WIN32)
+               HCRYPTPROV csp;
+               if (!CryptAcquireContext(&csp, 0, 0, PROV_RSA_FULL, CRYPT_VERIFYCONTEXT)) {
+                       printf("CryptAcquireContext failed\n");
+                       exit(1);
+               }
+               if (!CryptGenRandom(csp, (DWORD)sizeof(state), (BYTE*)state)) {
+                       printf("CryptGenRandom failed\n");
+                       exit(1);
+               }
+               CryptReleaseContext(csp, 0);
+       #else
+               FILE *f = NULL;
+               f = fopen("/dev/urandom", "rb");
+               if (!f) {
+                       printf("failed to open /dev/urandom\n");
+                       exit(1);
+               }
+               if (fread(state, sizeof(state), 1, f) != 1) {
+                       printf("read error on /dev/urandom\n");
+                       exit(1);
+               }
+       #endif
+               init = 1;
+       }
+
+       while (bytes) {
+               for (i = 0; i < 16; i++) x[i] = state[i];
+
+               #define rotl32(x,k) ((x << k) | (x >> (32 - k)))
+               #define quarter(a,b,c,d) \
+                       x[a] += x[b]; t = x[d]^x[a]; x[d] = rotl32(t,16); \
+                       x[c] += x[d]; t = x[b]^x[c]; x[b] = rotl32(t,12); \
+                       x[a] += x[b]; t = x[d]^x[a]; x[d] = rotl32(t, 8); \
+                       x[c] += x[d]; t = x[b]^x[c]; x[b] = rotl32(t, 7);
+
+               for (i = 0; i < 12; i += 2) {
+                       quarter( 0, 4, 8,12)
+                       quarter( 1, 5, 9,13)
+                       quarter( 2, 6,10,14)
+                       quarter( 3, 7,11,15)
+                       quarter( 0, 5,10,15)
+                       quarter( 1, 6,11,12)
+                       quarter( 2, 7, 8,13)
+                       quarter( 3, 4, 9,14)
+               };
+
+               if (bytes <= 64) {
+                       memcpy(out, x, bytes);
+                       bytes = 0;
+               } else {
+                       memcpy(out, x, 64);
+                       bytes -= 64;
+                       out += 64;
+               }
+
+               /* don't need a nonce, so last 4 words are the counter. 2^136 bytes can be generated */
+               if (!++state[12]) if (!++state[13]) if (!++state[14]) ++state[15];
+       }
+}
+
+
+
+int main() {
+       const size_t skmax = 1024;
+       static unsigned char sk[1024][32];
+       unsigned char pk[3][32];
+       unsigned char *skp;
+       size_t ski, pki, i;
+       uint64_t ctr;
+
+       printf("fuzzing: ");
+       printf(" ref10");
+       printf(" curved25519");
+#if defined(ED25519_SSE2)
+       printf(" curved25519-sse2");
+#endif
+       printf("\n\n");
+
+       for (ctr = 0, ski = skmax;;ctr++) {
+               if (ski == skmax) {
+                       prng((unsigned char *)sk, sizeof(sk));
+                       ski = 0;
+               }
+               skp = sk[ski++];
+
+               pki = 0;
+               crypto_scalarmult_base_ref10(pk[pki++], skp);
+               curved25519_scalarmult_basepoint(pk[pki++],  skp);
+               #if defined(ED25519_SSE2)
+                       curved25519_scalarmult_basepoint_sse2(pk[pki++], skp);
+               #endif
+
+               for (i = 1; i < pki; i++) {
+                       if (memcmp(pk[0], pk[i], 32) != 0) {
+                               printf("\n\n");
+                               print_bytes("sk",  skp, 32);
+                               print_bytes("ref10", pk[0], 32);
+                               print_diff("curved25519", pk[0], pk[1], 32);
+                               #if defined(ED25519_SSE2)
+                                       print_diff("curved25519-sse2", pk[0], pk[2], 32);
+                               #endif
+                               exit(1);
+                       }
+               }
+
+               if (ctr && (ctr % 0x1000 == 0)) {
+                       printf(".");
+                       if ((ctr % 0x20000) == 0) {
+                               printf(" [");
+                               for (i = 0; i < 8; i++)
+                                       printf("%02x", (unsigned char)(ctr >> ((7 - i) * 8)));
+                               printf("]\n");
+                       }
+               }
+       }
+}
+

diff --git a/crypto/ed25519-donna/src/fuzz/fuzz-ed25519.c b/crypto/ed25519-donna/src/fuzz/fuzz-ed25519.c
new file mode 100644 (file)
index 0000000..b242e8e
--- /dev/null
+++ b/crypto/ed25519-donna/src/fuzz/fuzz-ed25519.c
@@ -0,0 +1,219 @@
+#if defined(_WIN32)
+       #include <windows.h>
+       #include <wincrypt.h>
+       typedef unsigned int uint32_t;
+#else
+       #include <stdint.h>
+#endif
+
+#include <string.h>
+#include <stdio.h>
+
+#include "ed25519-donna.h"
+#include "ed25519-ref10.h"
+
+static void
+print_diff(const char *desc, const unsigned char *a, const unsigned char *b, size_t len) {
+       size_t p = 0;
+       unsigned char diff;
+       printf("%s diff:\n", desc);
+       while (len--) {
+               diff = *a++ ^ *b++;
+               if (!diff)
+                       printf("____,");
+               else
+                       printf("0x%02x,", diff);
+               if ((++p & 15) == 0)
+                       printf("\n");
+       }
+       printf("\n");
+}
+
+static void
+print_bytes(const char *desc, const unsigned char *bytes, size_t len) {
+       size_t p = 0;
+       printf("%s:\n", desc);
+       while (len--) {
+               printf("0x%02x,", *bytes++);
+               if ((++p & 15) == 0)
+                       printf("\n");
+       }
+       printf("\n");
+}
+
+
+/* chacha20/12 prng */
+void
+prng(unsigned char *out, size_t bytes) {
+       static uint32_t state[16];
+       static int init = 0;
+       uint32_t x[16], t;
+       size_t i;
+
+       if (!init) {
+       #if defined(_WIN32)
+               HCRYPTPROV csp = NULL;
+               if (!CryptAcquireContext(&csp, 0, 0, PROV_RSA_FULL, CRYPT_VERIFYCONTEXT)) {
+                       printf("CryptAcquireContext failed\n");
+                       exit(1);
+               }
+               if (!CryptGenRandom(csp, (DWORD)sizeof(state), (BYTE*)state)) {
+                       printf("CryptGenRandom failed\n");
+                       exit(1);
+               }
+               CryptReleaseContext(csp, 0);
+       #else
+               FILE *f = NULL;
+               f = fopen("/dev/urandom", "rb");
+               if (!f) {
+                       printf("failed to open /dev/urandom\n");
+                       exit(1);
+               }
+               if (fread(state, sizeof(state), 1, f) != 1) {
+                       printf("read error on /dev/urandom\n");
+                       exit(1);
+               }
+       #endif
+               init = 1;
+       }
+
+       while (bytes) {
+               for (i = 0; i < 16; i++) x[i] = state[i];
+
+               #define rotl32(x,k) ((x << k) | (x >> (32 - k)))
+               #define quarter(a,b,c,d) \
+                       x[a] += x[b]; t = x[d]^x[a]; x[d] = rotl32(t,16); \
+                       x[c] += x[d]; t = x[b]^x[c]; x[b] = rotl32(t,12); \
+                       x[a] += x[b]; t = x[d]^x[a]; x[d] = rotl32(t, 8); \
+                       x[c] += x[d]; t = x[b]^x[c]; x[b] = rotl32(t, 7);
+
+               for (i = 0; i < 12; i += 2) {
+                       quarter( 0, 4, 8,12)
+                       quarter( 1, 5, 9,13)
+                       quarter( 2, 6,10,14)
+                       quarter( 3, 7,11,15)
+                       quarter( 0, 5,10,15)
+                       quarter( 1, 6,11,12)
+                       quarter( 2, 7, 8,13)
+                       quarter( 3, 4, 9,14)
+               };
+
+               if (bytes <= 64) {
+                       memcpy(out, x, bytes);
+                       bytes = 0;
+               } else {
+                       memcpy(out, x, 64);
+                       bytes -= 64;
+                       out += 64;
+               }
+
+               /* don't need a nonce, so last 4 words are the counter. 2^136 bytes can be generated */
+               if (!++state[12]) if (!++state[13]) if (!++state[14]) ++state[15];
+       }
+}
+
+typedef struct random_data_t {
+       unsigned char sk[32];
+       unsigned char m[128];
+} random_data;
+
+typedef struct generated_data_t {
+       unsigned char pk[32];
+       unsigned char sig[64];
+       int valid;
+} generated_data;
+
+static void
+print_generated(const char *desc, generated_data *g) {
+       printf("%s:\n", desc);
+       print_bytes("pk", g->pk, 32);
+       print_bytes("sig", g->sig, 64);
+       printf("valid: %s\n\n", g->valid ? "no" : "yes");
+}
+
+static void
+print_generated_diff(const char *desc, const generated_data *base, generated_data *g) {
+       printf("%s:\n", desc);
+       print_diff("pk", base->pk, g->pk, 32);
+       print_diff("sig", base->sig, g->sig, 64);
+       printf("valid: %s\n\n", (base->valid == g->valid) ? "___" : (g->valid ? "no" : "yes"));
+}
+
+int main() {
+       const size_t rndmax = 128;
+       static random_data rnd[128];
+       static generated_data gen[3];
+       random_data *r;
+       generated_data *g;
+       unsigned long long dummylen;
+       unsigned char dummysk[64];
+       unsigned char dummymsg[2][128+64];
+       size_t rndi, geni, i, j;
+       uint64_t ctr;
+
+       printf("fuzzing: ");
+       printf(" ref10");
+       printf(" ed25519-donna");
+#if defined(ED25519_SSE2)
+       printf(" ed25519-donna-sse2");
+#endif
+       printf("\n\n");
+
+       for (ctr = 0, rndi = rndmax;;ctr++) {
+               if (rndi == rndmax) {
+                       prng((unsigned char *)rnd, sizeof(rnd));
+                       rndi = 0;
+               }
+               r = &rnd[rndi++];
+
+               /* ref10, lots of horrible gymnastics to work around the wonky api */
+               geni = 0;
+               g = &gen[geni++];
+               memcpy(dummysk, r->sk, 32); /* pk is appended to the sk, need to copy the sk to a larger buffer */
+               crypto_sign_pk_ref10(dummysk + 32, dummysk);
+               memcpy(g->pk, dummysk + 32, 32); 
+               crypto_sign_ref10(dummymsg[0], &dummylen, r->m, 128, dummysk);
+               memcpy(g->sig, dummymsg[0], 64); /* sig is placed in front of the signed message */
+               g->valid = crypto_sign_open_ref10(dummymsg[1], &dummylen, dummymsg[0], 128 + 64, g->pk);
+
+               /* ed25519-donna */
+               g = &gen[geni++];
+               ed25519_publickey(r->sk, g->pk);
+               ed25519_sign(r->m, 128, r->sk, g->pk, g->sig);
+               g->valid = ed25519_sign_open(r->m, 128, g->pk, g->sig);
+
+               #if defined(ED25519_SSE2)
+                       /* ed25519-donna-sse2 */
+                       g = &gen[geni++];
+                       ed25519_publickey_sse2(r->sk, g->pk);
+                       ed25519_sign_sse2(r->m, 128, r->sk, g->pk, g->sig);
+                       g->valid = ed25519_sign_open_sse2(r->m, 128, g->pk, g->sig);
+               #endif
+
+               /* compare implementations 1..geni against the reference */
+               for (i = 1; i < geni; i++) {
+                       if (memcmp(&gen[0], &gen[i], sizeof(generated_data)) != 0) {
+                               printf("\n\n");
+                               print_bytes("sk", r->sk, 32);
+                               print_bytes("m", r->m, 128);
+                               print_generated("ref10", &gen[0]);
+                               print_generated_diff("ed25519-donna", &gen[0], &gen[1]);
+                               #if defined(ED25519_SSE2)
+                                       print_generated_diff("ed25519-donna-sse2", &gen[0], &gen[2]);
+                               #endif
+                               exit(1);
+                       }
+               }
+
+               /* print out status */
+               if (ctr && (ctr % 0x1000 == 0)) {
+                       printf(".");
+                       if ((ctr % 0x20000) == 0) {
+                               printf(" [");
+                               for (i = 0; i < 8; i++)
+                                       printf("%02x", (unsigned char)(ctr >> ((7 - i) * 8)));
+                               printf("]\n");
+                       }
+               }
+       }
+}
\ No newline at end of file

diff --git a/crypto/ed25519-donna/src/modm-donna-32bit.h b/crypto/ed25519-donna/src/modm-donna-32bit.h
new file mode 100644 (file)
index 0000000..dfd76be
--- /dev/null
+++ b/crypto/ed25519-donna/src/modm-donna-32bit.h
@@ -0,0 +1,469 @@
+/*
+       Public domain by Andrew M. <liquidsun@gmail.com>
+*/
+
+
+/*
+       Arithmetic modulo the group order n = 2^252 +  27742317777372353535851937790883648493 = 7237005577332262213973186563042994240857116359379907606001950938285454250989
+
+       k = 32
+       b = 1 << 8 = 256
+       m = 2^252 + 27742317777372353535851937790883648493 = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed
+       mu = floor( b^(k*2) / m ) = 0xfffffffffffffffffffffffffffffffeb2106215d086329a7ed9ce5a30a2c131b
+*/
+
+#define bignum256modm_bits_per_limb 30
+#define bignum256modm_limb_size 9
+
+typedef uint32_t bignum256modm_element_t;
+typedef bignum256modm_element_t bignum256modm[9];
+
+static const bignum256modm modm_m = {
+       0x1cf5d3ed, 0x20498c69, 0x2f79cd65, 0x37be77a8,
+       0x00000014,     0x00000000, 0x00000000, 0x00000000,
+       0x00001000
+};
+
+static const bignum256modm modm_mu = {
+       0x0a2c131b, 0x3673968c, 0x06329a7e, 0x01885742,
+       0x3fffeb21, 0x3fffffff, 0x3fffffff, 0x3fffffff,
+       0x000fffff
+};
+
+static bignum256modm_element_t
+lt_modm(bignum256modm_element_t a, bignum256modm_element_t b) {
+       return (a - b) >> 31;
+}
+
+/* see HAC, Alg. 14.42 Step 4 */
+static void
+reduce256_modm(bignum256modm r) {
+       bignum256modm t;
+       bignum256modm_element_t b = 0, pb, mask;
+
+       /* t = r - m */
+       pb = 0;
+       pb += modm_m[0]; b = lt_modm(r[0], pb); t[0] = (r[0] - pb + (b << 30)); pb = b;
+       pb += modm_m[1]; b = lt_modm(r[1], pb); t[1] = (r[1] - pb + (b << 30)); pb = b;
+       pb += modm_m[2]; b = lt_modm(r[2], pb); t[2] = (r[2] - pb + (b << 30)); pb = b;
+       pb += modm_m[3]; b = lt_modm(r[3], pb); t[3] = (r[3] - pb + (b << 30)); pb = b;
+       pb += modm_m[4]; b = lt_modm(r[4], pb); t[4] = (r[4] - pb + (b << 30)); pb = b;
+       pb += modm_m[5]; b = lt_modm(r[5], pb); t[5] = (r[5] - pb + (b << 30)); pb = b;
+       pb += modm_m[6]; b = lt_modm(r[6], pb); t[6] = (r[6] - pb + (b << 30)); pb = b;
+       pb += modm_m[7]; b = lt_modm(r[7], pb); t[7] = (r[7] - pb + (b << 30)); pb = b;
+       pb += modm_m[8]; b = lt_modm(r[8], pb); t[8] = (r[8] - pb + (b << 16));
+
+       /* keep r if r was smaller than m */
+       mask = b - 1;
+       r[0] ^= mask & (r[0] ^ t[0]);
+       r[1] ^= mask & (r[1] ^ t[1]);
+       r[2] ^= mask & (r[2] ^ t[2]);
+       r[3] ^= mask & (r[3] ^ t[3]);
+       r[4] ^= mask & (r[4] ^ t[4]);
+       r[5] ^= mask & (r[5] ^ t[5]);
+       r[6] ^= mask & (r[6] ^ t[6]);
+       r[7] ^= mask & (r[7] ^ t[7]);
+       r[8] ^= mask & (r[8] ^ t[8]);
+}
+
+/*
+       Barrett reduction,  see HAC, Alg. 14.42
+
+       Instead of passing in x, pre-process in to q1 and r1 for efficiency
+*/
+static void
+barrett_reduce256_modm(bignum256modm r, const bignum256modm q1, const bignum256modm r1) {
+       bignum256modm q3, r2;
+       uint64_t c;
+       bignum256modm_element_t f, b, pb;
+
+       /* q1 = x >> 248 = 264 bits = 9 30 bit elements
+          q2 = mu * q1
+          q3 = (q2 / 256(32+1)) = q2 / (2^8)^(32+1) = q2 >> 264 */
+       c  = mul32x32_64(modm_mu[0], q1[7]) + mul32x32_64(modm_mu[1], q1[6]) + mul32x32_64(modm_mu[2], q1[5]) + mul32x32_64(modm_mu[3], q1[4]) + mul32x32_64(modm_mu[4], q1[3]) + mul32x32_64(modm_mu[5], q1[2]) + mul32x32_64(modm_mu[6], q1[1]) + mul32x32_64(modm_mu[7], q1[0]); 
+       c >>= 30;
+       c += mul32x32_64(modm_mu[0], q1[8]) + mul32x32_64(modm_mu[1], q1[7]) + mul32x32_64(modm_mu[2], q1[6]) + mul32x32_64(modm_mu[3], q1[5]) + mul32x32_64(modm_mu[4], q1[4]) + mul32x32_64(modm_mu[5], q1[3]) + mul32x32_64(modm_mu[6], q1[2]) + mul32x32_64(modm_mu[7], q1[1]) + mul32x32_64(modm_mu[8], q1[0]);
+       f = (bignum256modm_element_t)c; q3[0] = (f >> 24) & 0x3f; c >>= 30;
+       c += mul32x32_64(modm_mu[1], q1[8]) + mul32x32_64(modm_mu[2], q1[7]) + mul32x32_64(modm_mu[3], q1[6]) + mul32x32_64(modm_mu[4], q1[5]) + mul32x32_64(modm_mu[5], q1[4]) + mul32x32_64(modm_mu[6], q1[3]) + mul32x32_64(modm_mu[7], q1[2]) + mul32x32_64(modm_mu[8], q1[1]);
+       f = (bignum256modm_element_t)c; q3[0] |= (f << 6) & 0x3fffffff; q3[1] = (f >> 24) & 0x3f; c >>= 30;
+       c += mul32x32_64(modm_mu[2], q1[8]) + mul32x32_64(modm_mu[3], q1[7]) + mul32x32_64(modm_mu[4], q1[6]) + mul32x32_64(modm_mu[5], q1[5]) + mul32x32_64(modm_mu[6], q1[4]) + mul32x32_64(modm_mu[7], q1[3]) + mul32x32_64(modm_mu[8], q1[2]);
+       f = (bignum256modm_element_t)c; q3[1] |= (f << 6) & 0x3fffffff; q3[2] = (f >> 24) & 0x3f; c >>= 30;
+       c += mul32x32_64(modm_mu[3], q1[8]) + mul32x32_64(modm_mu[4], q1[7]) + mul32x32_64(modm_mu[5], q1[6]) + mul32x32_64(modm_mu[6], q1[5]) + mul32x32_64(modm_mu[7], q1[4]) + mul32x32_64(modm_mu[8], q1[3]);
+       f = (bignum256modm_element_t)c; q3[2] |= (f << 6) & 0x3fffffff; q3[3] = (f >> 24) & 0x3f; c >>= 30;
+       c += mul32x32_64(modm_mu[4], q1[8]) + mul32x32_64(modm_mu[5], q1[7]) + mul32x32_64(modm_mu[6], q1[6]) + mul32x32_64(modm_mu[7], q1[5]) + mul32x32_64(modm_mu[8], q1[4]);
+       f = (bignum256modm_element_t)c; q3[3] |= (f << 6) & 0x3fffffff; q3[4] = (f >> 24) & 0x3f; c >>= 30;
+       c += mul32x32_64(modm_mu[5], q1[8]) + mul32x32_64(modm_mu[6], q1[7]) + mul32x32_64(modm_mu[7], q1[6]) + mul32x32_64(modm_mu[8], q1[5]);
+       f = (bignum256modm_element_t)c; q3[4] |= (f << 6) & 0x3fffffff; q3[5] = (f >> 24) & 0x3f; c >>= 30;
+       c += mul32x32_64(modm_mu[6], q1[8]) + mul32x32_64(modm_mu[7], q1[7]) + mul32x32_64(modm_mu[8], q1[6]);
+       f = (bignum256modm_element_t)c; q3[5] |= (f << 6) & 0x3fffffff; q3[6] = (f >> 24) & 0x3f; c >>= 30;
+       c += mul32x32_64(modm_mu[7], q1[8]) + mul32x32_64(modm_mu[8], q1[7]);
+       f = (bignum256modm_element_t)c; q3[6] |= (f << 6) & 0x3fffffff; q3[7] = (f >> 24) & 0x3f; c >>= 30;
+       c += mul32x32_64(modm_mu[8], q1[8]);
+       f = (bignum256modm_element_t)c; q3[7] |= (f << 6) & 0x3fffffff; q3[8] = (bignum256modm_element_t)(c >> 24);
+
+       /* r1 = (x mod 256^(32+1)) = x mod (2^8)(31+1) = x & ((1 << 264) - 1)
+          r2 = (q3 * m) mod (256^(32+1)) = (q3 * m) & ((1 << 264) - 1) */
+       c = mul32x32_64(modm_m[0], q3[0]);
+       r2[0] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
+       c += mul32x32_64(modm_m[0], q3[1]) + mul32x32_64(modm_m[1], q3[0]);
+       r2[1] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
+       c += mul32x32_64(modm_m[0], q3[2]) + mul32x32_64(modm_m[1], q3[1]) + mul32x32_64(modm_m[2], q3[0]);
+       r2[2] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
+       c += mul32x32_64(modm_m[0], q3[3]) + mul32x32_64(modm_m[1], q3[2]) + mul32x32_64(modm_m[2], q3[1]) + mul32x32_64(modm_m[3], q3[0]);
+       r2[3] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
+       c += mul32x32_64(modm_m[0], q3[4]) + mul32x32_64(modm_m[1], q3[3]) + mul32x32_64(modm_m[2], q3[2]) + mul32x32_64(modm_m[3], q3[1]) + mul32x32_64(modm_m[4], q3[0]);
+       r2[4] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
+       c += mul32x32_64(modm_m[0], q3[5]) + mul32x32_64(modm_m[1], q3[4]) + mul32x32_64(modm_m[2], q3[3]) + mul32x32_64(modm_m[3], q3[2]) + mul32x32_64(modm_m[4], q3[1]) + mul32x32_64(modm_m[5], q3[0]);
+       r2[5] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
+       c += mul32x32_64(modm_m[0], q3[6]) + mul32x32_64(modm_m[1], q3[5]) + mul32x32_64(modm_m[2], q3[4]) + mul32x32_64(modm_m[3], q3[3]) + mul32x32_64(modm_m[4], q3[2]) + mul32x32_64(modm_m[5], q3[1]) + mul32x32_64(modm_m[6], q3[0]);
+       r2[6] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
+       c += mul32x32_64(modm_m[0], q3[7]) + mul32x32_64(modm_m[1], q3[6]) + mul32x32_64(modm_m[2], q3[5]) + mul32x32_64(modm_m[3], q3[4]) + mul32x32_64(modm_m[4], q3[3]) + mul32x32_64(modm_m[5], q3[2]) + mul32x32_64(modm_m[6], q3[1]) + mul32x32_64(modm_m[7], q3[0]);
+       r2[7] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
+       c += mul32x32_64(modm_m[0], q3[8]) + mul32x32_64(modm_m[1], q3[7]) + mul32x32_64(modm_m[2], q3[6]) + mul32x32_64(modm_m[3], q3[5]) + mul32x32_64(modm_m[4], q3[4]) + mul32x32_64(modm_m[5], q3[3]) + mul32x32_64(modm_m[6], q3[2]) + mul32x32_64(modm_m[7], q3[1]) + mul32x32_64(modm_m[8], q3[0]);
+       r2[8] = (bignum256modm_element_t)(c & 0xffffff);
+
+       /* r = r1 - r2
+          if (r < 0) r += (1 << 264) */
+       pb = 0;
+       pb += r2[0]; b = lt_modm(r1[0], pb); r[0] = (r1[0] - pb + (b << 30)); pb = b;
+       pb += r2[1]; b = lt_modm(r1[1], pb); r[1] = (r1[1] - pb + (b << 30)); pb = b;
+       pb += r2[2]; b = lt_modm(r1[2], pb); r[2] = (r1[2] - pb + (b << 30)); pb = b;
+       pb += r2[3]; b = lt_modm(r1[3], pb); r[3] = (r1[3] - pb + (b << 30)); pb = b;
+       pb += r2[4]; b = lt_modm(r1[4], pb); r[4] = (r1[4] - pb + (b << 30)); pb = b;
+       pb += r2[5]; b = lt_modm(r1[5], pb); r[5] = (r1[5] - pb + (b << 30)); pb = b;
+       pb += r2[6]; b = lt_modm(r1[6], pb); r[6] = (r1[6] - pb + (b << 30)); pb = b;
+       pb += r2[7]; b = lt_modm(r1[7], pb); r[7] = (r1[7] - pb + (b << 30)); pb = b;
+       pb += r2[8]; b = lt_modm(r1[8], pb); r[8] = (r1[8] - pb + (b << 24));
+
+       reduce256_modm(r);
+       reduce256_modm(r);
+}
+
+/* addition modulo m */
+static void
+add256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y) {
+       bignum256modm_element_t c;
+
+       c  = x[0] + y[0]; r[0] = c & 0x3fffffff; c >>= 30;
+       c += x[1] + y[1]; r[1] = c & 0x3fffffff; c >>= 30;
+       c += x[2] + y[2]; r[2] = c & 0x3fffffff; c >>= 30;
+       c += x[3] + y[3]; r[3] = c & 0x3fffffff; c >>= 30;
+       c += x[4] + y[4]; r[4] = c & 0x3fffffff; c >>= 30;
+       c += x[5] + y[5]; r[5] = c & 0x3fffffff; c >>= 30;
+       c += x[6] + y[6]; r[6] = c & 0x3fffffff; c >>= 30;
+       c += x[7] + y[7]; r[7] = c & 0x3fffffff; c >>= 30;
+       c += x[8] + y[8]; r[8] = c;
+
+       reduce256_modm(r);
+}
+
+/* multiplication modulo m */
+static void 
+mul256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y) {
+       bignum256modm r1, q1;
+       uint64_t c;
+       bignum256modm_element_t f;
+
+       /* r1 = (x mod 256^(32+1)) = x mod (2^8)(31+1) = x & ((1 << 264) - 1)
+          q1 = x >> 248 = 264 bits = 9 30 bit elements */
+       c = mul32x32_64(x[0], y[0]);
+       f = (bignum256modm_element_t)c; r1[0] = (f & 0x3fffffff); c >>= 30;
+       c += mul32x32_64(x[0], y[1]) + mul32x32_64(x[1], y[0]);
+       f = (bignum256modm_element_t)c; r1[1] = (f & 0x3fffffff); c >>= 30;
+       c += mul32x32_64(x[0], y[2]) + mul32x32_64(x[1], y[1]) + mul32x32_64(x[2], y[0]);
+       f = (bignum256modm_element_t)c; r1[2] = (f & 0x3fffffff); c >>= 30;
+       c += mul32x32_64(x[0], y[3]) + mul32x32_64(x[1], y[2]) + mul32x32_64(x[2], y[1]) + mul32x32_64(x[3], y[0]);
+       f = (bignum256modm_element_t)c; r1[3] = (f & 0x3fffffff); c >>= 30;
+       c += mul32x32_64(x[0], y[4]) + mul32x32_64(x[1], y[3]) + mul32x32_64(x[2], y[2]) + mul32x32_64(x[3], y[1]) + mul32x32_64(x[4], y[0]);
+       f = (bignum256modm_element_t)c; r1[4] = (f & 0x3fffffff); c >>= 30;
+       c += mul32x32_64(x[0], y[5]) + mul32x32_64(x[1], y[4]) + mul32x32_64(x[2], y[3]) + mul32x32_64(x[3], y[2]) + mul32x32_64(x[4], y[1]) + mul32x32_64(x[5], y[0]);
+       f = (bignum256modm_element_t)c; r1[5] = (f & 0x3fffffff); c >>= 30;
+       c += mul32x32_64(x[0], y[6]) + mul32x32_64(x[1], y[5]) + mul32x32_64(x[2], y[4]) + mul32x32_64(x[3], y[3]) + mul32x32_64(x[4], y[2]) + mul32x32_64(x[5], y[1]) + mul32x32_64(x[6], y[0]);
+       f = (bignum256modm_element_t)c; r1[6] = (f & 0x3fffffff); c >>= 30;
+       c += mul32x32_64(x[0], y[7]) + mul32x32_64(x[1], y[6]) + mul32x32_64(x[2], y[5]) + mul32x32_64(x[3], y[4]) + mul32x32_64(x[4], y[3]) + mul32x32_64(x[5], y[2]) + mul32x32_64(x[6], y[1]) + mul32x32_64(x[7], y[0]);
+       f = (bignum256modm_element_t)c; r1[7] = (f & 0x3fffffff); c >>= 30;
+       c += mul32x32_64(x[0], y[8]) + mul32x32_64(x[1], y[7]) + mul32x32_64(x[2], y[6]) + mul32x32_64(x[3], y[5]) + mul32x32_64(x[4], y[4]) + mul32x32_64(x[5], y[3]) + mul32x32_64(x[6], y[2]) + mul32x32_64(x[7], y[1]) + mul32x32_64(x[8], y[0]);
+       f = (bignum256modm_element_t)c; r1[8] = (f & 0x00ffffff); q1[0] = (f >> 8) & 0x3fffff; c >>= 30;
+       c += mul32x32_64(x[1], y[8]) + mul32x32_64(x[2], y[7]) + mul32x32_64(x[3], y[6]) + mul32x32_64(x[4], y[5]) + mul32x32_64(x[5], y[4]) + mul32x32_64(x[6], y[3]) + mul32x32_64(x[7], y[2]) + mul32x32_64(x[8], y[1]);
+       f = (bignum256modm_element_t)c; q1[0] = (q1[0] | (f << 22)) & 0x3fffffff; q1[1] = (f >> 8) & 0x3fffff; c >>= 30;        
+       c += mul32x32_64(x[2], y[8]) + mul32x32_64(x[3], y[7]) + mul32x32_64(x[4], y[6]) + mul32x32_64(x[5], y[5]) + mul32x32_64(x[6], y[4]) + mul32x32_64(x[7], y[3]) + mul32x32_64(x[8], y[2]);
+       f = (bignum256modm_element_t)c; q1[1] = (q1[1] | (f << 22)) & 0x3fffffff; q1[2] = (f >> 8) & 0x3fffff; c >>= 30;        
+       c += mul32x32_64(x[3], y[8]) + mul32x32_64(x[4], y[7]) + mul32x32_64(x[5], y[6]) + mul32x32_64(x[6], y[5]) + mul32x32_64(x[7], y[4]) + mul32x32_64(x[8], y[3]);
+       f = (bignum256modm_element_t)c; q1[2] = (q1[2] | (f << 22)) & 0x3fffffff; q1[3] = (f >> 8) & 0x3fffff; c >>= 30;        
+       c += mul32x32_64(x[4], y[8]) + mul32x32_64(x[5], y[7]) + mul32x32_64(x[6], y[6]) + mul32x32_64(x[7], y[5]) + mul32x32_64(x[8], y[4]);
+       f = (bignum256modm_element_t)c; q1[3] = (q1[3] | (f << 22)) & 0x3fffffff; q1[4] = (f >> 8) & 0x3fffff; c >>= 30;        
+       c += mul32x32_64(x[5], y[8]) + mul32x32_64(x[6], y[7]) + mul32x32_64(x[7], y[6]) + mul32x32_64(x[8], y[5]);
+       f = (bignum256modm_element_t)c; q1[4] = (q1[4] | (f << 22)) & 0x3fffffff; q1[5] = (f >> 8) & 0x3fffff; c >>= 30;
+       c += mul32x32_64(x[6], y[8]) + mul32x32_64(x[7], y[7]) + mul32x32_64(x[8], y[6]);
+       f = (bignum256modm_element_t)c; q1[5] = (q1[5] | (f << 22)) & 0x3fffffff; q1[6] = (f >> 8) & 0x3fffff; c >>= 30;
+       c += mul32x32_64(x[7], y[8]) + mul32x32_64(x[8], y[7]);
+       f = (bignum256modm_element_t)c; q1[6] = (q1[6] | (f << 22)) & 0x3fffffff; q1[7] = (f >> 8) & 0x3fffff; c >>= 30;
+       c += mul32x32_64(x[8], y[8]);
+       f = (bignum256modm_element_t)c; q1[7] = (q1[7] | (f << 22)) & 0x3fffffff; q1[8] = (f >> 8) & 0x3fffff;
+
+       barrett_reduce256_modm(r, q1, r1);
+}
+
+static void
+expand256_modm(bignum256modm out, const unsigned char *in, size_t len) {
+       unsigned char work[64] = {0};
+       bignum256modm_element_t x[16];
+       bignum256modm q1;
+
+       memcpy(work, in, len);
+       x[0] = U8TO32_LE(work +  0);
+       x[1] = U8TO32_LE(work +  4);
+       x[2] = U8TO32_LE(work +  8);
+       x[3] = U8TO32_LE(work + 12);
+       x[4] = U8TO32_LE(work + 16);
+       x[5] = U8TO32_LE(work + 20);
+       x[6] = U8TO32_LE(work + 24);
+       x[7] = U8TO32_LE(work + 28);
+       x[8] = U8TO32_LE(work + 32);
+       x[9] = U8TO32_LE(work + 36);
+       x[10] = U8TO32_LE(work + 40);
+       x[11] = U8TO32_LE(work + 44);
+       x[12] = U8TO32_LE(work + 48);
+       x[13] = U8TO32_LE(work + 52);
+       x[14] = U8TO32_LE(work + 56);
+       x[15] = U8TO32_LE(work + 60);
+
+       /* r1 = (x mod 256^(32+1)) = x mod (2^8)(31+1) = x & ((1 << 264) - 1) */
+       out[0] = (                         x[0]) & 0x3fffffff;
+       out[1] = ((x[ 0] >> 30) | (x[ 1] <<  2)) & 0x3fffffff;
+       out[2] = ((x[ 1] >> 28) | (x[ 2] <<  4)) & 0x3fffffff;
+       out[3] = ((x[ 2] >> 26) | (x[ 3] <<  6)) & 0x3fffffff;
+       out[4] = ((x[ 3] >> 24) | (x[ 4] <<  8)) & 0x3fffffff;
+       out[5] = ((x[ 4] >> 22) | (x[ 5] << 10)) & 0x3fffffff;
+       out[6] = ((x[ 5] >> 20) | (x[ 6] << 12)) & 0x3fffffff;
+       out[7] = ((x[ 6] >> 18) | (x[ 7] << 14)) & 0x3fffffff;
+       out[8] = ((x[ 7] >> 16) | (x[ 8] << 16)) & 0x00ffffff;
+
+       /* 8*31 = 248 bits, no need to reduce */
+       if (len < 32)
+               return;
+
+       /* q1 = x >> 248 = 264 bits = 9 30 bit elements */
+       q1[0] = ((x[ 7] >> 24) | (x[ 8] <<  8)) & 0x3fffffff;
+       q1[1] = ((x[ 8] >> 22) | (x[ 9] << 10)) & 0x3fffffff;
+       q1[2] = ((x[ 9] >> 20) | (x[10] << 12)) & 0x3fffffff;
+       q1[3] = ((x[10] >> 18) | (x[11] << 14)) & 0x3fffffff;
+       q1[4] = ((x[11] >> 16) | (x[12] << 16)) & 0x3fffffff;
+       q1[5] = ((x[12] >> 14) | (x[13] << 18)) & 0x3fffffff;
+       q1[6] = ((x[13] >> 12) | (x[14] << 20)) & 0x3fffffff;
+       q1[7] = ((x[14] >> 10) | (x[15] << 22)) & 0x3fffffff;
+       q1[8] = ((x[15] >>  8)                );        
+
+       barrett_reduce256_modm(out, q1, out);
+}
+
+static void
+expand_raw256_modm(bignum256modm out, const unsigned char in[32]) {
+       bignum256modm_element_t x[8];
+
+       x[0] = U8TO32_LE(in +  0);
+       x[1] = U8TO32_LE(in +  4);
+       x[2] = U8TO32_LE(in +  8);
+       x[3] = U8TO32_LE(in + 12);
+       x[4] = U8TO32_LE(in + 16);
+       x[5] = U8TO32_LE(in + 20);
+       x[6] = U8TO32_LE(in + 24);
+       x[7] = U8TO32_LE(in + 28);
+
+       out[0] = (                         x[0]) & 0x3fffffff;
+       out[1] = ((x[ 0] >> 30) | (x[ 1] <<  2)) & 0x3fffffff;
+       out[2] = ((x[ 1] >> 28) | (x[ 2] <<  4)) & 0x3fffffff;
+       out[3] = ((x[ 2] >> 26) | (x[ 3] <<  6)) & 0x3fffffff;
+       out[4] = ((x[ 3] >> 24) | (x[ 4] <<  8)) & 0x3fffffff;
+       out[5] = ((x[ 4] >> 22) | (x[ 5] << 10)) & 0x3fffffff;
+       out[6] = ((x[ 5] >> 20) | (x[ 6] << 12)) & 0x3fffffff;
+       out[7] = ((x[ 6] >> 18) | (x[ 7] << 14)) & 0x3fffffff;
+       out[8] = ((x[ 7] >> 16)                ) & 0x0000ffff;
+}
+
+static void
+contract256_modm(unsigned char out[32], const bignum256modm in) {
+       U32TO8_LE(out +  0, (in[0]      ) | (in[1] << 30));
+       U32TO8_LE(out +  4, (in[1] >>  2) | (in[2] << 28));
+       U32TO8_LE(out +  8, (in[2] >>  4) | (in[3] << 26));
+       U32TO8_LE(out + 12, (in[3] >>  6) | (in[4] << 24));
+       U32TO8_LE(out + 16, (in[4] >>  8) | (in[5] << 22));
+       U32TO8_LE(out + 20, (in[5] >> 10) | (in[6] << 20));
+       U32TO8_LE(out + 24, (in[6] >> 12) | (in[7] << 18));
+       U32TO8_LE(out + 28, (in[7] >> 14) | (in[8] << 16));
+}
+
+
+
+static void
+contract256_window4_modm(signed char r[64], const bignum256modm in) {
+       char carry;
+       signed char *quads = r;
+       bignum256modm_element_t i, j, v;
+
+       for (i = 0; i < 8; i += 2) {
+               v = in[i];
+               for (j = 0; j < 7; j++) {
+                       *quads++ = (v & 15);
+                       v >>= 4;
+               }
+               v |= (in[i+1] << 2);
+               for (j = 0; j < 8; j++) {
+                       *quads++ = (v & 15);
+                       v >>= 4;
+               }
+       }
+       v = in[8];
+       *quads++ = (v & 15); v >>= 4;
+       *quads++ = (v & 15); v >>= 4;
+       *quads++ = (v & 15); v >>= 4;
+       *quads++ = (v & 15); v >>= 4;
+
+       /* making it signed */
+       carry = 0;
+       for(i = 0; i < 63; i++) {
+               r[i] += carry;
+               r[i+1] += (r[i] >> 4);
+               r[i] &= 15;
+               carry = (r[i] >> 3);
+               r[i] -= (carry << 4);
+       }
+       r[63] += carry;
+}
+
+static void
+contract256_slidingwindow_modm(signed char r[256], const bignum256modm s, int windowsize) {
+       int i,j,k,b;
+       int m = (1 << (windowsize - 1)) - 1, soplen = 256;
+       signed char *bits = r;
+       bignum256modm_element_t v;
+
+       /* first put the binary expansion into r  */
+       for (i = 0; i < 8; i++) {
+               v = s[i];
+               for (j = 0; j < 30; j++, v >>= 1)
+                       *bits++ = (v & 1);
+       }
+       v = s[8];
+       for (j = 0; j < 16; j++, v >>= 1)
+               *bits++ = (v & 1);
+
+       /* Making it sliding window */
+       for (j = 0; j < soplen; j++) {
+               if (!r[j])
+                       continue;
+
+               for (b = 1; (b < (soplen - j)) && (b <= 6); b++) {
+                       if ((r[j] + (r[j + b] << b)) <= m) {
+                               r[j] += r[j + b] << b;
+                               r[j + b] = 0;
+                       } else if ((r[j] - (r[j + b] << b)) >= -m) {
+                               r[j] -= r[j + b] << b;
+                               for (k = j + b; k < soplen; k++) {
+                                       if (!r[k]) {
+                                               r[k] = 1;
+                                               break;
+                                       }
+                                       r[k] = 0;
+                               }
+                       } else if (r[j + b]) {
+                               break;
+                       }
+               }
+       }
+}
+
+
+/*
+       helpers for batch verifcation, are allowed to be vartime
+*/
+
+/* out = a - b, a must be larger than b */
+static void
+sub256_modm_batch(bignum256modm out, const bignum256modm a, const bignum256modm b, size_t limbsize) {
+       size_t i = 0;
+       bignum256modm_element_t carry = 0;
+       switch (limbsize) {
+               case 8: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 31); out[i] &= 0x3fffffff; i++;
+               case 7: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 31); out[i] &= 0x3fffffff; i++;
+               case 6: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 31); out[i] &= 0x3fffffff; i++;
+               case 5: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 31); out[i] &= 0x3fffffff; i++;
+               case 4: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 31); out[i] &= 0x3fffffff; i++;
+               case 3: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 31); out[i] &= 0x3fffffff; i++;
+               case 2: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 31); out[i] &= 0x3fffffff; i++;
+               case 1: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 31); out[i] &= 0x3fffffff; i++;
+               case 0: 
+               default: out[i] = (a[i] - b[i]) - carry;
+       }
+}
+
+
+/* is a < b */
+static int
+lt256_modm_batch(const bignum256modm a, const bignum256modm b, size_t limbsize) {
+       switch (limbsize) {
+               case 8: if (a[8] > b[8]) return 0; if (a[8] < b[8]) return 1;
+               case 7: if (a[7] > b[7]) return 0; if (a[7] < b[7]) return 1;
+               case 6: if (a[6] > b[6]) return 0; if (a[6] < b[6]) return 1;
+               case 5: if (a[5] > b[5]) return 0; if (a[5] < b[5]) return 1;
+               case 4: if (a[4] > b[4]) return 0; if (a[4] < b[4]) return 1;
+               case 3: if (a[3] > b[3]) return 0; if (a[3] < b[3]) return 1;
+               case 2: if (a[2] > b[2]) return 0; if (a[2] < b[2]) return 1;
+               case 1: if (a[1] > b[1]) return 0; if (a[1] < b[1]) return 1;
+               case 0: if (a[0] > b[0]) return 0; if (a[0] < b[0]) return 1;
+       }
+       return 0;
+}
+
+/* is a <= b */
+static int
+lte256_modm_batch(const bignum256modm a, const bignum256modm b, size_t limbsize) {
+       switch (limbsize) {
+               case 8: if (a[8] > b[8]) return 0; if (a[8] < b[8]) return 1;
+               case 7: if (a[7] > b[7]) return 0; if (a[7] < b[7]) return 1;
+               case 6: if (a[6] > b[6]) return 0; if (a[6] < b[6]) return 1;
+               case 5: if (a[5] > b[5]) return 0; if (a[5] < b[5]) return 1;
+               case 4: if (a[4] > b[4]) return 0; if (a[4] < b[4]) return 1;
+               case 3: if (a[3] > b[3]) return 0; if (a[3] < b[3]) return 1;
+               case 2: if (a[2] > b[2]) return 0; if (a[2] < b[2]) return 1;
+               case 1: if (a[1] > b[1]) return 0; if (a[1] < b[1]) return 1;
+               case 0: if (a[0] > b[0]) return 0; if (a[0] < b[0]) return 1;
+       }
+       return 1;
+}
+
+
+/* is a == 0 */
+static int
+iszero256_modm_batch(const bignum256modm a) {
+       size_t i;
+       for (i = 0; i < 9; i++)
+               if (a[i])
+                       return 0;
+       return 1;
+}
+
+/* is a == 1 */
+static int
+isone256_modm_batch(const bignum256modm a) {
+       size_t i;
+       if (a[0] != 1)
+               return 0;
+       for (i = 1; i < 9; i++)
+               if (a[i])
+                       return 0;
+       return 1;
+}
+
+/* can a fit in to (at most) 128 bits */
+static int
+isatmost128bits256_modm_batch(const bignum256modm a) {
+       uint32_t mask =
+               ((a[8]             )  | /*  16 */
+                (a[7]             )  | /*  46 */
+                (a[6]             )  | /*  76 */
+                (a[5]             )  | /* 106 */
+                (a[4] & 0x3fffff00));  /* 128 */
+
+       return (mask == 0);
+}

diff --git a/crypto/ed25519-donna/src/modm-donna-64bit.h b/crypto/ed25519-donna/src/modm-donna-64bit.h
new file mode 100644 (file)
index 0000000..a47a38a
--- /dev/null
+++ b/crypto/ed25519-donna/src/modm-donna-64bit.h
@@ -0,0 +1,361 @@
+/*
+       Public domain by Andrew M. <liquidsun@gmail.com>
+*/
+
+
+/*
+       Arithmetic modulo the group order n = 2^252 +  27742317777372353535851937790883648493 = 7237005577332262213973186563042994240857116359379907606001950938285454250989
+
+       k = 32
+       b = 1 << 8 = 256
+       m = 2^252 + 27742317777372353535851937790883648493 = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed
+       mu = floor( b^(k*2) / m ) = 0xfffffffffffffffffffffffffffffffeb2106215d086329a7ed9ce5a30a2c131b
+*/
+
+#define bignum256modm_bits_per_limb 56
+#define bignum256modm_limb_size 5
+
+typedef uint64_t bignum256modm_element_t;
+typedef bignum256modm_element_t bignum256modm[5];
+
+static const bignum256modm modm_m = {
+       0x12631a5cf5d3ed, 
+       0xf9dea2f79cd658, 
+       0x000000000014de, 
+       0x00000000000000, 
+       0x00000010000000
+};
+
+static const bignum256modm modm_mu = {
+       0x9ce5a30a2c131b,
+       0x215d086329a7ed,
+       0xffffffffeb2106,
+       0xffffffffffffff,
+       0x00000fffffffff
+};
+
+static bignum256modm_element_t
+lt_modm(bignum256modm_element_t a, bignum256modm_element_t b) {
+       return (a - b) >> 63;
+}
+
+static void
+reduce256_modm(bignum256modm r) {
+       bignum256modm t;
+       bignum256modm_element_t b = 0, pb, mask;
+
+       /* t = r - m */
+       pb = 0;
+       pb += modm_m[0]; b = lt_modm(r[0], pb); t[0] = (r[0] - pb + (b << 56)); pb = b;
+       pb += modm_m[1]; b = lt_modm(r[1], pb); t[1] = (r[1] - pb + (b << 56)); pb = b;
+       pb += modm_m[2]; b = lt_modm(r[2], pb); t[2] = (r[2] - pb + (b << 56)); pb = b;
+       pb += modm_m[3]; b = lt_modm(r[3], pb); t[3] = (r[3] - pb + (b << 56)); pb = b;
+       pb += modm_m[4]; b = lt_modm(r[4], pb); t[4] = (r[4] - pb + (b << 32)); 
+
+       /* keep r if r was smaller than m */
+       mask = b - 1;
+
+       r[0] ^= mask & (r[0] ^ t[0]);
+       r[1] ^= mask & (r[1] ^ t[1]);
+       r[2] ^= mask & (r[2] ^ t[2]);
+       r[3] ^= mask & (r[3] ^ t[3]);
+       r[4] ^= mask & (r[4] ^ t[4]);
+}
+
+static void
+barrett_reduce256_modm(bignum256modm r, const bignum256modm q1, const bignum256modm r1) {
+       bignum256modm q3, r2;
+       uint128_t c, mul;
+       bignum256modm_element_t f, b, pb;
+
+       /* q1 = x >> 248 = 264 bits = 5 56 bit elements
+          q2 = mu * q1
+          q3 = (q2 / 256(32+1)) = q2 / (2^8)^(32+1) = q2 >> 264 */
+       mul64x64_128(c, modm_mu[0], q1[3])                 mul64x64_128(mul, modm_mu[3], q1[0]) add128(c, mul) mul64x64_128(mul, modm_mu[1], q1[2]) add128(c, mul) mul64x64_128(mul, modm_mu[2], q1[1]) add128(c, mul) shr128(f, c, 56);
+       mul64x64_128(c, modm_mu[0], q1[4]) add128_64(c, f) mul64x64_128(mul, modm_mu[4], q1[0]) add128(c, mul) mul64x64_128(mul, modm_mu[3], q1[1]) add128(c, mul) mul64x64_128(mul, modm_mu[1], q1[3]) add128(c, mul) mul64x64_128(mul, modm_mu[2], q1[2]) add128(c, mul)
+       f = lo128(c); q3[0] = (f >> 40) & 0xffff; shr128(f, c, 56);
+       mul64x64_128(c, modm_mu[4], q1[1]) add128_64(c, f) mul64x64_128(mul, modm_mu[1], q1[4]) add128(c, mul) mul64x64_128(mul, modm_mu[2], q1[3]) add128(c, mul) mul64x64_128(mul, modm_mu[3], q1[2]) add128(c, mul)
+       f = lo128(c); q3[0] |= (f << 16) & 0xffffffffffffff; q3[1] = (f >> 40) & 0xffff; shr128(f, c, 56);
+       mul64x64_128(c, modm_mu[4], q1[2]) add128_64(c, f) mul64x64_128(mul, modm_mu[2], q1[4]) add128(c, mul) mul64x64_128(mul, modm_mu[3], q1[3]) add128(c, mul)
+       f = lo128(c); q3[1] |= (f << 16) & 0xffffffffffffff; q3[2] = (f >> 40) & 0xffff; shr128(f, c, 56);
+       mul64x64_128(c, modm_mu[4], q1[3]) add128_64(c, f) mul64x64_128(mul, modm_mu[3], q1[4]) add128(c, mul)
+       f = lo128(c); q3[2] |= (f << 16) & 0xffffffffffffff; q3[3] = (f >> 40) & 0xffff; shr128(f, c, 56);
+       mul64x64_128(c, modm_mu[4], q1[4]) add128_64(c, f)
+       f = lo128(c); q3[3] |= (f << 16) & 0xffffffffffffff; q3[4] = (f >> 40) & 0xffff; shr128(f, c, 56);
+       q3[4] |= (f << 16);
+
+       mul64x64_128(c, modm_m[0], q3[0]) 
+       r2[0] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
+       mul64x64_128(c, modm_m[0], q3[1]) add128_64(c, f) mul64x64_128(mul, modm_m[1], q3[0]) add128(c, mul)
+       r2[1] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
+       mul64x64_128(c, modm_m[0], q3[2]) add128_64(c, f) mul64x64_128(mul, modm_m[2], q3[0]) add128(c, mul) mul64x64_128(mul, modm_m[1], q3[1]) add128(c, mul)
+       r2[2] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
+       mul64x64_128(c, modm_m[0], q3[3]) add128_64(c, f) mul64x64_128(mul, modm_m[3], q3[0]) add128(c, mul) mul64x64_128(mul, modm_m[1], q3[2]) add128(c, mul) mul64x64_128(mul, modm_m[2], q3[1]) add128(c, mul)
+       r2[3] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
+       mul64x64_128(c, modm_m[0], q3[4]) add128_64(c, f) mul64x64_128(mul, modm_m[4], q3[0]) add128(c, mul) mul64x64_128(mul, modm_m[3], q3[1]) add128(c, mul) mul64x64_128(mul, modm_m[1], q3[3]) add128(c, mul) mul64x64_128(mul, modm_m[2], q3[2]) add128(c, mul)
+       r2[4] = lo128(c) & 0x0000ffffffffff;
+
+       pb = 0;
+       pb += r2[0]; b = lt_modm(r1[0], pb); r[0] = (r1[0] - pb + (b << 56)); pb = b;
+       pb += r2[1]; b = lt_modm(r1[1], pb); r[1] = (r1[1] - pb + (b << 56)); pb = b;
+       pb += r2[2]; b = lt_modm(r1[2], pb); r[2] = (r1[2] - pb + (b << 56)); pb = b;
+       pb += r2[3]; b = lt_modm(r1[3], pb); r[3] = (r1[3] - pb + (b << 56)); pb = b;
+       pb += r2[4]; b = lt_modm(r1[4], pb); r[4] = (r1[4] - pb + (b << 40)); 
+
+       reduce256_modm(r);
+       reduce256_modm(r);
+}
+
+
+static void
+add256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y) {
+       bignum256modm_element_t c;
+
+       c  = x[0] + y[0]; r[0] = c & 0xffffffffffffff; c >>= 56;
+       c += x[1] + y[1]; r[1] = c & 0xffffffffffffff; c >>= 56;
+       c += x[2] + y[2]; r[2] = c & 0xffffffffffffff; c >>= 56;
+       c += x[3] + y[3]; r[3] = c & 0xffffffffffffff; c >>= 56;
+       c += x[4] + y[4]; r[4] = c;
+
+       reduce256_modm(r);
+}
+
+static void
+mul256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y) {
+       bignum256modm q1, r1;
+       uint128_t c, mul;
+       bignum256modm_element_t f;
+
+       mul64x64_128(c, x[0], y[0])
+       f = lo128(c); r1[0] = f & 0xffffffffffffff; shr128(f, c, 56);
+       mul64x64_128(c, x[0], y[1]) add128_64(c, f) mul64x64_128(mul, x[1], y[0]) add128(c, mul) 
+       f = lo128(c); r1[1] = f & 0xffffffffffffff; shr128(f, c, 56);
+       mul64x64_128(c, x[0], y[2]) add128_64(c, f) mul64x64_128(mul, x[2], y[0]) add128(c, mul) mul64x64_128(mul, x[1], y[1]) add128(c, mul) 
+       f = lo128(c); r1[2] = f & 0xffffffffffffff; shr128(f, c, 56);
+       mul64x64_128(c, x[0], y[3]) add128_64(c, f) mul64x64_128(mul, x[3], y[0]) add128(c, mul) mul64x64_128(mul, x[1], y[2]) add128(c, mul) mul64x64_128(mul, x[2], y[1]) add128(c, mul) 
+       f = lo128(c); r1[3] = f & 0xffffffffffffff; shr128(f, c, 56);
+       mul64x64_128(c, x[0], y[4]) add128_64(c, f) mul64x64_128(mul, x[4], y[0]) add128(c, mul) mul64x64_128(mul, x[3], y[1]) add128(c, mul) mul64x64_128(mul, x[1], y[3]) add128(c, mul) mul64x64_128(mul, x[2], y[2]) add128(c, mul) 
+       f = lo128(c); r1[4] = f & 0x0000ffffffffff; q1[0] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
+       mul64x64_128(c, x[4], y[1]) add128_64(c, f) mul64x64_128(mul, x[1], y[4]) add128(c, mul) mul64x64_128(mul, x[2], y[3]) add128(c, mul) mul64x64_128(mul, x[3], y[2]) add128(c, mul) 
+       f = lo128(c); q1[0] |= (f << 32) & 0xffffffffffffff; q1[1] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
+       mul64x64_128(c, x[4], y[2]) add128_64(c, f) mul64x64_128(mul, x[2], y[4]) add128(c, mul) mul64x64_128(mul, x[3], y[3]) add128(c, mul) 
+       f = lo128(c); q1[1] |= (f << 32) & 0xffffffffffffff; q1[2] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
+       mul64x64_128(c, x[4], y[3]) add128_64(c, f) mul64x64_128(mul, x[3], y[4]) add128(c, mul) 
+       f = lo128(c); q1[2] |= (f << 32) & 0xffffffffffffff; q1[3] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
+       mul64x64_128(c, x[4], y[4]) add128_64(c, f)
+       f = lo128(c); q1[3] |= (f << 32) & 0xffffffffffffff; q1[4] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
+       q1[4] |= (f << 32);
+
+       barrett_reduce256_modm(r, q1, r1);
+}
+
+static void
+expand256_modm(bignum256modm out, const unsigned char *in, size_t len) {
+       unsigned char work[64] = {0};
+       bignum256modm_element_t x[16];
+       bignum256modm q1;
+
+       memcpy(work, in, len);
+       x[0] = U8TO64_LE(work +  0);
+       x[1] = U8TO64_LE(work +  8);
+       x[2] = U8TO64_LE(work + 16);
+       x[3] = U8TO64_LE(work + 24);
+       x[4] = U8TO64_LE(work + 32);
+       x[5] = U8TO64_LE(work + 40);
+       x[6] = U8TO64_LE(work + 48);
+       x[7] = U8TO64_LE(work + 56);
+
+       /* r1 = (x mod 256^(32+1)) = x mod (2^8)(31+1) = x & ((1 << 264) - 1) */
+       out[0] = (                         x[0]) & 0xffffffffffffff;
+       out[1] = ((x[ 0] >> 56) | (x[ 1] <<  8)) & 0xffffffffffffff;
+       out[2] = ((x[ 1] >> 48) | (x[ 2] << 16)) & 0xffffffffffffff;
+       out[3] = ((x[ 2] >> 40) | (x[ 3] << 24)) & 0xffffffffffffff;
+       out[4] = ((x[ 3] >> 32) | (x[ 4] << 32)) & 0x0000ffffffffff;
+
+       /* under 252 bits, no need to reduce */
+       if (len < 32)
+               return;
+
+       /* q1 = x >> 248 = 264 bits */
+       q1[0] = ((x[ 3] >> 56) | (x[ 4] <<  8)) & 0xffffffffffffff;
+       q1[1] = ((x[ 4] >> 48) | (x[ 5] << 16)) & 0xffffffffffffff;
+       q1[2] = ((x[ 5] >> 40) | (x[ 6] << 24)) & 0xffffffffffffff;
+       q1[3] = ((x[ 6] >> 32) | (x[ 7] << 32)) & 0xffffffffffffff;
+       q1[4] = ((x[ 7] >> 24)                );
+
+       barrett_reduce256_modm(out, q1, out);
+}
+
+static void
+expand_raw256_modm(bignum256modm out, const unsigned char in[32]) {
+       bignum256modm_element_t x[4];
+
+       x[0] = U8TO64_LE(in +  0);
+       x[1] = U8TO64_LE(in +  8);
+       x[2] = U8TO64_LE(in + 16);
+       x[3] = U8TO64_LE(in + 24);
+
+       out[0] = (                         x[0]) & 0xffffffffffffff;
+       out[1] = ((x[ 0] >> 56) | (x[ 1] <<  8)) & 0xffffffffffffff;
+       out[2] = ((x[ 1] >> 48) | (x[ 2] << 16)) & 0xffffffffffffff;
+       out[3] = ((x[ 2] >> 40) | (x[ 3] << 24)) & 0xffffffffffffff;
+       out[4] = ((x[ 3] >> 32)                ) & 0x000000ffffffff;
+}
+
+static void
+contract256_modm(unsigned char out[32], const bignum256modm in) {
+       U64TO8_LE(out +  0, (in[0]      ) | (in[1] << 56));
+       U64TO8_LE(out +  8, (in[1] >>  8) | (in[2] << 48));
+       U64TO8_LE(out + 16, (in[2] >> 16) | (in[3] << 40));
+       U64TO8_LE(out + 24, (in[3] >> 24) | (in[4] << 32));
+}
+
+static void
+contract256_window4_modm(signed char r[64], const bignum256modm in) {
+       char carry;
+       signed char *quads = r;
+       bignum256modm_element_t i, j, v, m;
+
+       for (i = 0; i < 5; i++) {
+               v = in[i];
+               m = (i == 4) ? 8 : 14;
+               for (j = 0; j < m; j++) {
+                       *quads++ = (v & 15);
+                       v >>= 4;
+               }
+       }
+
+       /* making it signed */
+       carry = 0;
+       for(i = 0; i < 63; i++) {
+               r[i] += carry;
+               r[i+1] += (r[i] >> 4);
+               r[i] &= 15;
+               carry = (r[i] >> 3);
+               r[i] -= (carry << 4);
+       }
+       r[63] += carry;
+}
+
+static void
+contract256_slidingwindow_modm(signed char r[256], const bignum256modm s, int windowsize) {
+       int i,j,k,b;
+       int m = (1 << (windowsize - 1)) - 1, soplen = 256;
+       signed char *bits = r;
+       bignum256modm_element_t v;
+
+       /* first put the binary expansion into r  */
+       for (i = 0; i < 4; i++) {
+               v = s[i];
+               for (j = 0; j < 56; j++, v >>= 1)
+                       *bits++ = (v & 1);
+       }
+       v = s[4];
+       for (j = 0; j < 32; j++, v >>= 1)
+               *bits++ = (v & 1);
+
+       /* Making it sliding window */
+       for (j = 0; j < soplen; j++) {
+               if (!r[j])
+                       continue;
+
+               for (b = 1; (b < (soplen - j)) && (b <= 6); b++) {
+                       if ((r[j] + (r[j + b] << b)) <= m) {
+                               r[j] += r[j + b] << b;
+                               r[j + b] = 0;
+                       } else if ((r[j] - (r[j + b] << b)) >= -m) {
+                               r[j] -= r[j + b] << b;
+                               for (k = j + b; k < soplen; k++) {
+                                       if (!r[k]) {
+                                               r[k] = 1;
+                                               break;
+                                       }
+                                       r[k] = 0;
+                               }
+                       } else if (r[j + b]) {
+                               break;
+                       }
+               }
+       }
+}
+
+/*
+       helpers for batch verifcation, are allowed to be vartime
+*/
+
+/* out = a - b, a must be larger than b */
+static void
+sub256_modm_batch(bignum256modm out, const bignum256modm a, const bignum256modm b, size_t limbsize) {
+       size_t i = 0;
+       bignum256modm_element_t carry = 0;
+       switch (limbsize) {
+               case 4: out[i] = (a[i] - b[i])        ; carry = (out[i] >> 63); out[i] &= 0xffffffffffffff; i++;
+               case 3: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 63); out[i] &= 0xffffffffffffff; i++;
+               case 2: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 63); out[i] &= 0xffffffffffffff; i++;
+               case 1: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 63); out[i] &= 0xffffffffffffff; i++;
+               case 0: 
+               default: out[i] = (a[i] - b[i]) - carry;
+       }
+}
+
+
+/* is a < b */
+static int
+lt256_modm_batch(const bignum256modm a, const bignum256modm b, size_t limbsize) {
+       size_t i = 0;
+       bignum256modm_element_t t, carry = 0;
+       switch (limbsize) {
+               case 4: t = (a[i] - b[i])        ; carry = (t >> 63); i++;
+               case 3: t = (a[i] - b[i]) - carry; carry = (t >> 63); i++;
+               case 2: t = (a[i] - b[i]) - carry; carry = (t >> 63); i++;
+               case 1: t = (a[i] - b[i]) - carry; carry = (t >> 63); i++;
+               case 0: t = (a[i] - b[i]) - carry; carry = (t >> 63);
+       }
+       return (int)carry;
+}
+
+/* is a <= b */
+static int
+lte256_modm_batch(const bignum256modm a, const bignum256modm b, size_t limbsize) {
+       size_t i = 0;
+       bignum256modm_element_t t, carry = 0;
+       switch (limbsize) {
+               case 4: t = (b[i] - a[i])        ; carry = (t >> 63); i++;
+               case 3: t = (b[i] - a[i]) - carry; carry = (t >> 63); i++;
+               case 2: t = (b[i] - a[i]) - carry; carry = (t >> 63); i++;
+               case 1: t = (b[i] - a[i]) - carry; carry = (t >> 63); i++;
+               case 0: t = (b[i] - a[i]) - carry; carry = (t >> 63);
+       }
+       return (int)!carry;
+}
+
+/* is a == 0 */
+static int
+iszero256_modm_batch(const bignum256modm a) {
+       size_t i;
+       for (i = 0; i < 5; i++)
+               if (a[i])
+                       return 0;
+       return 1;
+}
+
+/* is a == 1 */
+static int
+isone256_modm_batch(const bignum256modm a) {
+       size_t i;
+       for (i = 0; i < 5; i++)
+               if (a[i] != ((i) ? 0 : 1))
+                       return 0;
+       return 1;
+}
+
+/* can a fit in to (at most) 128 bits */
+static int
+isatmost128bits256_modm_batch(const bignum256modm a) {
+       uint64_t mask =
+               ((a[4]                   )  | /*  32 */
+                (a[3]                   )  | /*  88 */
+                (a[2] & 0xffffffffff0000));
+
+       return (mask == 0);
+}

diff --git a/crypto/ed25519-donna/src/regression.h b/crypto/ed25519-donna/src/regression.h
new file mode 100644 (file)
index 0000000..b4c2e62
--- /dev/null
+++ b/crypto/ed25519-donna/src/regression.h
@@ -0,0 +1,1024 @@
+{{0x9d,0x61,0xb1,0x9d,0xef,0xfd,0x5a,0x60,0xba,0x84,0x4a,0xf4,0x92,0xec,0x2c,0xc4,0x44,0x49,0xc5,0x69,0x7b,0x32,0x69,0x19,0x70,0x3b,0xac,0x03,0x1c,0xae,0x7f,0x60,},{0xd7,0x5a,0x98,0x01,0x82,0xb1,0x0a,0xb7,0xd5,0x4b,0xfe,0xd3,0xc9,0x64,0x07,0x3a,0x0e,0xe1,0x72,0xf3,0xda,0xa6,0x23,0x25,0xaf,0x02,0x1a,0x68,0xf7,0x07,0x51,0x1a,},{0xe5,0x56,0x43,0x00,0xc3,0x60,0xac,0x72,0x90,0x86,0xe2,0xcc,0x80,0x6e,0x82,0x8a,0x84,0x87,0x7f,0x1e,0xb8,0xe5,0xd9,0x74,0xd8,0x73,0xe0,0x65,0x22,0x49,0x01,0x55,0x5f,0xb8,0x82,0x15,0x90,0xa3,0x3b,0xac,0xc6,0x1e,0x39,0x70,0x1c,0xf9,0xb4,0x6b,0xd2,0x5b,0xf5,0xf0,0x59,0x5b,0xbe,0x24,0x65,0x51,0x41,0x43,0x8e,0x7a,0x10,0x0b,},""},
+{{0x4c,0xcd,0x08,0x9b,0x28,0xff,0x96,0xda,0x9d,0xb6,0xc3,0x46,0xec,0x11,0x4e,0x0f,0x5b,0x8a,0x31,0x9f,0x35,0xab,0xa6,0x24,0xda,0x8c,0xf6,0xed,0x4f,0xb8,0xa6,0xfb,},{0x3d,0x40,0x17,0xc3,0xe8,0x43,0x89,0x5a,0x92,0xb7,0x0a,0xa7,0x4d,0x1b,0x7e,0xbc,0x9c,0x98,0x2c,0xcf,0x2e,0xc4,0x96,0x8c,0xc0,0xcd,0x55,0xf1,0x2a,0xf4,0x66,0x0c,},{0x92,0xa0,0x09,0xa9,0xf0,0xd4,0xca,0xb8,0x72,0x0e,0x82,0x0b,0x5f,0x64,0x25,0x40,0xa2,0xb2,0x7b,0x54,0x16,0x50,0x3f,0x8f,0xb3,0x76,0x22,0x23,0xeb,0xdb,0x69,0xda,0x08,0x5a,0xc1,0xe4,0x3e,0x15,0x99,0x6e,0x45,0x8f,0x36,0x13,0xd0,0xf1,0x1d,0x8c,0x38,0x7b,0x2e,0xae,0xb4,0x30,0x2a,0xee,0xb0,0x0d,0x29,0x16,0x12,0xbb,0x0c,0x00,},"\x72"},
+{{0xc5,0xaa,0x8d,0xf4,0x3f,0x9f,0x83,0x7b,0xed,0xb7,0x44,0x2f,0x31,0xdc,0xb7,0xb1,0x66,0xd3,0x85,0x35,0x07,0x6f,0x09,0x4b,0x85,0xce,0x3a,0x2e,0x0b,0x44,0x58,0xf7,},{0xfc,0x51,0xcd,0x8e,0x62,0x18,0xa1,0xa3,0x8d,0xa4,0x7e,0xd0,0x02,0x30,0xf0,0x58,0x08,0x16,0xed,0x13,0xba,0x33,0x03,0xac,0x5d,0xeb,0x91,0x15,0x48,0x90,0x80,0x25,},{0x62,0x91,0xd6,0x57,0xde,0xec,0x24,0x02,0x48,0x27,0xe6,0x9c,0x3a,0xbe,0x01,0xa3,0x0c,0xe5,0x48,0xa2,0x84,0x74,0x3a,0x44,0x5e,0x36,0x80,0xd7,0xdb,0x5a,0xc3,0xac,0x18,0xff,0x9b,0x53,0x8d,0x16,0xf2,0x90,0xae,0x67,0xf7,0x60,0x98,0x4d,0xc6,0x59,0x4a,0x7c,0x15,0xe9,0x71,0x6e,0xd2,0x8d,0xc0,0x27,0xbe,0xce,0xea,0x1e,0xc4,0x0a,},"\xaf\x82"},
+{{0x0d,0x4a,0x05,0xb0,0x73,0x52,0xa5,0x43,0x6e,0x18,0x03,0x56,0xda,0x0a,0xe6,0xef,0xa0,0x34,0x5f,0xf7,0xfb,0x15,0x72,0x57,0x57,0x72,0xe8,0x00,0x5e,0xd9,0x78,0xe9,},{0xe6,0x1a,0x18,0x5b,0xce,0xf2,0x61,0x3a,0x6c,0x7c,0xb7,0x97,0x63,0xce,0x94,0x5d,0x3b,0x24,0x5d,0x76,0x11,0x4d,0xd4,0x40,0xbc,0xf5,0xf2,0xdc,0x1a,0xa5,0x70,0x57,},{0xd9,0x86,0x8d,0x52,0xc2,0xbe,0xbc,0xe5,0xf3,0xfa,0x5a,0x79,0x89,0x19,0x70,0xf3,0x09,0xcb,0x65,0x91,0xe3,0xe1,0x70,0x2a,0x70,0x27,0x6f,0xa9,0x7c,0x24,0xb3,0xa8,0xe5,0x86,0x06,0xc3,0x8c,0x97,0x58,0x52,0x9d,0xa5,0x0e,0xe3,0x1b,0x82,0x19,0xcb,0xa4,0x52,0x71,0xc6,0x89,0xaf,0xa6,0x0b,0x0e,0xa2,0x6c,0x99,0xdb,0x19,0xb0,0x0c,},"\xcb\xc7\x7b"},
+{{0x6d,0xf9,0x34,0x0c,0x13,0x8c,0xc1,0x88,0xb5,0xfe,0x44,0x64,0xeb,0xaa,0x3f,0x7f,0xc2,0x06,0xa2,0xd5,0x5c,0x34,0x34,0x70,0x7e,0x74,0xc9,0xfc,0x04,0xe2,0x0e,0xbb,},{0xc0,0xda,0xc1,0x02,0xc4,0x53,0x31,0x86,0xe2,0x5d,0xc4,0x31,0x28,0x47,0x23,0x53,0xea,0xab,0xdb,0x87,0x8b,0x15,0x2a,0xeb,0x8e,0x00,0x1f,0x92,0xd9,0x02,0x33,0xa7,},{0x12,0x4f,0x6f,0xc6,0xb0,0xd1,0x00,0x84,0x27,0x69,0xe7,0x1b,0xd5,0x30,0x66,0x4d,0x88,0x8d,0xf8,0x50,0x7d,0xf6,0xc5,0x6d,0xed,0xfd,0xb5,0x09,0xae,0xb9,0x34,0x16,0xe2,0x6b,0x91,0x8d,0x38,0xaa,0x06,0x30,0x5d,0xf3,0x09,0x56,0x97,0xc1,0x8b,0x2a,0xa8,0x32,0xea,0xa5,0x2e,0xdc,0x0a,0xe4,0x9f,0xba,0xe5,0xa8,0x5e,0x15,0x0c,0x07,},"\x5f\x4c\x89\x89"},
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+{{0xf5,0xe5,0x76,0x7c,0xf1,0x53,0x31,0x95,0x17,0x63,0x0f,0x22,0x68,0x76,0xb8,0x6c,0x81,0x60,0xcc,0x58,0x3b,0xc0,0x13,0x74,0x4c,0x6b,0xf2,0x55,0xf5,0xcc,0x0e,0xe5,},{0x27,0x81,0x17,0xfc,0x14,0x4c,0x72,0x34,0x0f,0x67,0xd0,0xf2,0x31,0x6e,0x83,0x86,0xce,0xff,0xbf,0x2b,0x24,0x28,0xc9,0xc5,0x1f,0xef,0x7c,0x59,0x7f,0x1d,0x42,0x6e,},{0x0a,0xab,0x4c,0x90,0x05,0x01,0xb3,0xe2,0x4d,0x7c,0xdf,0x46,0x63,0x32,0x6a,0x3a,0x87,0xdf,0x5e,0x48,0x43,0xb2,0xcb,0xdb,0x67,0xcb,0xf6,0xe4,0x60,0xfe,0xc3,0x50,0xaa,0x53,0x71,0xb1,0x50,0x8f,0x9f,0x45,0x28,0xec,0xea,0x23,0xc4,0x36,0xd9,0x4b,0x5e,0x8f,0xcd,0x4f,0x68,0x1e,0x30,0xa6,0xac,0x00,0xa9,0x70,0x4a,0x18,0x8a,0x03,},"\x08\xb8\xb2\xb7\x33\x42\x42\x43\x76\x0f\xe4\x26\xa4\xb5\x49\x08\x63\x21\x10\xa6\x6c\x2f\x65\x91\xea\xbd\x33\x45\xe3\xe4\xeb\x98\xfa\x6e\x26\x4b\xf0\x9e\xfe\x12\xee\x50\xf8\xf5\x4e\x9f\x77\xb1\xe3\x55\xf6\xc5\x05\x44\xe2\x3f\xb1\x43\x3d\xdf\x73\xbe\x84\xd8\x79\xde\x7c\x00\x46\xdc\x49\x96\xd9\xe7\x73\xf4\xbc\x9e\xfe\x57\x38\x82\x9a\xdb\x26\xc8\x1b\x37\xc9\x3a\x1b\x27\x0b\x20\x32\x9d\x65\x86\x75\xfc\x6e\xa5\x34\xe0\x81\x0a\x44\x32\x82\x6b\xf5\x8c\x94\x1e\xfb\x65\xd5\x7a\x33\x8b\xbd\x2e\x26\x64\x0f\x89\xff\xbc\x1a\x85\x8e\xfc\xb8\x55\x0e\xe3\xa5\xe1\x99\x8b\xd1\x77\xe9\x3a\x73\x63\xc3\x44\xfe\x6b\x19\x9e\xe5\xd0\x2e\x82\xd5\x22\xc4\xfe\xba\x15\x45\x2f\x80\x28\x8a\x82\x1a\x57\x91\x16\xec\x6d\xad\x2b\x3b\x31\x0d\xa9\x03\x40\x1a\xa6\x21\x00\xab\x5d\x1a\x36\x55\x3e\x06\x20\x3b\x33\x89\x0c\xc9\xb8\x32\xf7\x9e\xf8\x05\x60\xcc\xb9\xa3\x9c\xe7\x67\x96\x7e\xd6\x28\xc6\xad\x57\x3c\xb1\x16\xdb\xef\xef\xd7\x54\x99\xda\x96\xbd\x68\xa8\xa9\x7b\x92\x8a\x8b\xbc\x10\x3b\x66\x21\xfc\xde\x2b\xec\xa1\x23\x1d\x20\x6b\xe6\xcd\x9e\xc7\xaf\xf6\xf6\xc9\x4f\xcd\x72\x04\xed\x34\x55\xc6\x8c\x83\xf4\xa4\x1d\xa4\xaf\x2b\x74\xef\x5c\x53\xf1\xd8\xac\x70\xbd\xcb\x7e\xd1\x85\xce\x81\xbd\x84\x35\x9d\x44\x25\x4d\x95\x62\x9e\x98\x55\xa9\x4a\x7c\x19\x58\xd1\xf8\xad\xa5\xd0\x53\x2e\xd8\xa5\xaa\x3f\xb2\xd1\x7b\xa7\x0e\xb6\x24\x8e\x59\x4e\x1a\x22\x97\xac\xbb\xb3\x9d\x50\x2f\x1a\x8c\x6e\xb6\xf1\xce\x22\xb3\xde\x1a\x1f\x40\xcc\x24\x55\x41\x19\xa8\x31\xa9\xaa\xd6\x07\x9c\xad\x88\x42\x5d\xe6\xbd\xe1\xa9\x18\x7e\xbb\x60\x92\xcf\x67\xbf\x2b\x13\xfd\x65\xf2\x70\x88\xd7\x8b\x7e\x88\x3c\x87\x59\xd2\xc4\xf5\xc6\x5a\xdb\x75\x53\x87\x8a\xd5\x75\xf9\xfa\xd8\x78\xe8\x0a\x0c\x9b\xa6\x3b\xcb\xcc\x27\x32\xe6\x94\x85\xbb\xc9\xc9\x0b\xfb\xd6\x24\x81\xd9\x08\x9b\xec\xcf\x80\xcf\xe2\xdf\x16\xa2\xcf\x65\xbd\x92\xdd\x59\x7b\x07\x07\xe0\x91\x7a\xf4\x8b\xbb\x75\xfe\xd4\x13\xd2\x38\xf5\x55\x5a\x7a\x56\x9d\x80\xc3\x41\x4a\x8d\x08\x59\xdc\x65\xa4\x61\x28\xba\xb2\x7a\xf8\x7a\x71\x31\x4f\x31\x8c\x78\x2b\x23\xeb\xfe\x80\x8b\x82\xb0\xce\x26\x40\x1d\x2e\x22\xf0\x4d\x83\xd1\x25\x5d\xc5\x1a\xdd\xd3\xb7\x5a\x2b\x1a\xe0\x78\x45\x04\xdf\x54\x3a\xf8\x96\x9b\xe3\xea\x70\x82\xff\x7f\xc9\x88\x8c\x14\x4d\xa2\xaf\x58\x42\x9e\xc9\x60\x31\xdb\xca\xd3\xda\xd9\xaf\x0d\xcb\xaa\xaf\x26\x8c\xb8\xfc\xff\xea\xd9\x4f\x3c\x7c\xa4\x95\xe0\x56\xa9\xb4\x7a\xcd\xb7\x51\xfb\x73\xe6\x66\xc6\xc6\x55\xad\xe8\x29\x72\x97\xd0\x7a\xd1\xba\x5e\x43\xf1\xbc\xa3\x23\x01\x65\x13\x39\xe2\x29\x04\xcc\x8c\x42\xf5\x8c\x30\xc0\x4a\xaf\xdb\x03\x8d\xda\x08\x47\xdd\x98\x8d\xcd\xa6\xf3\xbf\xd1\x5c\x4b\x4c\x45\x25\x00\x4a\xa0\x6e\xef\xf8\xca\x61\x78\x3a\xac\xec\x57\xfb\x3d\x1f\x92\xb0\xfe\x2f\xd1\xa8\x5f\x67\x24\x51\x7b\x65\xe6\x14\xad\x68\x08\xd6\xf6\xee\x34\xdf\xf7\x31\x0f\xdc\x82\xae\xbf\xd9\x04\xb0\x1e\x1d\xc5\x4b\x29\x27\x09\x4b\x2d\xb6\x8d\x6f\x90\x3b\x68\x40\x1a\xde\xbf\x5a\x7e\x08\xd7\x8f\xf4\xef\x5d\x63\x65\x3a\x65\x04\x0c\xf9\xbf\xd4\xac\xa7\x98\x4a\x74\xd3\x71\x45\x98\x67\x80\xfc\x0b\x16\xac\x45\x16\x49\xde\x61\x88\xa7\xdb\xdf\x19\x1f\x64\xb5\xfc\x5e\x2a\xb4\x7b\x57\xf7\xf7\x27\x6c\xd4\x19\xc1\x7a\x3c\xa8\xe1\xb9\x39\xae\x49\xe4\x88\xac\xba\x6b\x96\x56\x10\xb5\x48\x01\x09\xc8\xb1\x7b\x80\xe1\xb7\xb7\x50\xdf\xc7\x59\x8d\x5d\x50\x11\xfd\x2d\xcc\x56\x00\xa3\x2e\xf5\xb5\x2a\x1e\xcc\x82\x0e\x30\x8a\xa3\x42\x72\x1a\xac\x09\x43\xbf\x66\x86\xb6\x4b\x25\x79\x37\x65\x04\xcc\xc4\x93\xd9\x7e\x6a\xed\x3f\xb0\xf9\xcd\x71\xa4\x3d\xd4\x97\xf0\x1f\x17\xc0\xe2\xcb\x37\x97\xaa\x2a\x2f\x25\x66\x56\x16\x8e\x6c\x49\x6a\xfc\x5f\xb9\x32\x46\xf6\xb1\x11\x63\x98\xa3\x46\xf1\xa6\x41\xf3\xb0\x41\xe9\x89\xf7\x91\x4f\x90\xcc\x2c\x7f\xff\x35\x78\x76\xe5\x06\xb5\x0d\x33\x4b\xa7\x7c\x22\x5b\xc3\x07\xba\x53\x71\x52\xf3\xf1\x61\x0e\x4e\xaf\xe5\x95\xf6\xd9\xd9\x0d\x11\xfa\xa9\x33\xa1\x5e\xf1\x36\x95\x46\x86\x8a\x7f\x3a\x45\xa9\x67\x68\xd4\x0f\xd9\xd0\x34\x12\xc0\x91\xc6\x31\x5c\xf4\xfd\xe7\xcb\x68\x60\x69\x37\x38\x0d\xb2\xea\xaa\x70\x7b\x4c\x41\x85\xc3\x2e\xdd\xcd\xd3\x06\x70\x5e\x4d\xc1\xff\xc8\x72\xee\xee\x47\x5a\x64\xdf\xac\x86\xab\xa4\x1c\x06\x18\x98\x3f\x87\x41\xc5\xef\x68\xd3\xa1\x01\xe8\xa3\xb8\xca\xc6\x0c\x90\x5c\x15\xfc\x91\x08\x40\xb9\x4c\x00\xa0\xb9\xd0"},

diff --git a/crypto/ed25519-donna/src/test-internals.c b/crypto/ed25519-donna/src/test-internals.c
new file mode 100644 (file)
index 0000000..3c67df5
--- /dev/null
+++ b/crypto/ed25519-donna/src/test-internals.c
@@ -0,0 +1,176 @@
+#include <stdio.h>
+#include "ed25519-donna.h"
+
+static int
+test_adds() {
+#if defined(HAVE_UINT128) && !defined(ED25519_SSE2)
+       /* largest result for each limb from a mult or square: all elements except r1 reduced, r1 overflowed as far as possible */
+       static const bignum25519 max_bignum = {
+               0x7ffffffffffff,0x8000000001230,0x7ffffffffffff,0x7ffffffffffff,0x7ffffffffffff
+       };
+
+       /* what max_bignum should fully reduce to */
+       static const unsigned char max_bignum_raw[32] = {
+               0x12,0x00,0x00,0x00,0x00,0x00,0x88,0x91,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
+               0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00
+       };
+
+       /* (max_bignum + max_bignum)^2 */
+       static const unsigned char max_bignum2_squared_raw[32] = {
+               0x10,0x05,0x00,0x00,0x00,0x00,0x80,0xdc,0x51,0x00,0x00,0x00,0x00,0x61,0xed,0x4a,
+               0x01,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
+       };
+
+       /* ((max_bignum + max_bignum) + max_bignum)^2 */
+       static const unsigned char max_bignum3_squared_raw[32] = {
+               0x64,0x0b,0x00,0x00,0x00,0x00,0x20,0x30,0xb8,0x00,0x00,0x00,0x40,0x1a,0x96,0xe8,
+               0x02,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
+       };
+#else
+       /* largest result for each limb from a mult or square: all elements except r1 reduced, r1 overflowed as far as possible */
+       static const bignum25519 ALIGN(16) max_bignum = {
+               0x3ffffff,0x2000300,0x3ffffff,0x1ffffff,0x3ffffff,
+               0x1ffffff,0x3ffffff,0x1ffffff,0x3ffffff,0x1ffffff
+       };
+
+       /* what max_bignum should fully reduce to */
+       static const unsigned char max_bignum2_squared_raw[32] = {
+               0x10,0x05,0x00,0x40,0xc2,0x06,0x40,0x80,0x41,0x02,0x00,0x00,0x00,0x00,0x00,0x00,
+               0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
+       };
+
+       /* (max_bignum * max_bignum) */
+       static const unsigned char max_bignum3_squared_raw[32] = {
+               0x64,0x0b,0x00,0x10,0x35,0x0f,0x90,0x60,0x13,0x05,0x00,0x00,0x00,0x00,0x00,0x00,
+               0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
+       };
+#endif
+       unsigned char result[32];
+       static const bignum25519 ALIGN(16) zero = {0};
+       bignum25519 ALIGN(16) a, b, c;
+       size_t i;
+
+       /* a = (max_bignum + max_bignum) */
+       curve25519_add(a, max_bignum, max_bignum);
+
+       /* b = ((max_bignum + max_bignum) * (max_bignum + max_bignum)) */
+       curve25519_mul(b, a, a);
+       curve25519_contract(result, b);
+       if (memcmp(result, max_bignum2_squared_raw, 32) != 0)
+               return -1;
+       curve25519_square(b, a);
+       curve25519_contract(result, b);
+       if (memcmp(result, max_bignum2_squared_raw, 32) != 0)
+               return -1;
+
+       /* b = (max_bignum + max_bignum + max_bignum) */
+       curve25519_add_after_basic(b, a, max_bignum);
+
+       /* a = ((max_bignum + max_bignum + max_bignum) * (max_bignum + max_bignum + max_bignum)) */
+       curve25519_mul(a, b, b);
+       curve25519_contract(result, a);
+       if (memcmp(result, max_bignum3_squared_raw, 32) != 0)
+               return -1;
+       curve25519_square(a, b);
+       curve25519_contract(result, a);
+       if (memcmp(result, max_bignum3_squared_raw, 32) != 0)
+               return -1;
+
+       return 0;
+}
+
+static int
+test_subs() {
+#if defined(HAVE_UINT128) && !defined(ED25519_SSE2)
+       /* largest result for each limb from a mult or square: all elements except r1 reduced, r1 overflowed as far as possible */
+       static const bignum25519 max_bignum = {
+               0x7ffffffffffff,0x8000000001230,0x7ffffffffffff,0x7ffffffffffff,0x7ffffffffffff
+       };
+
+       /* what max_bignum should fully reduce to */
+       static const unsigned char max_bignum_raw[32] = {
+               0x12,0x00,0x00,0x00,0x00,0x00,0x88,0x91,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
+               0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00
+       };
+
+       /* (max_bignum * max_bignum) */
+       static const unsigned char max_bignum_squared_raw[32] = {
+               0x44,0x01,0x00,0x00,0x00,0x00,0x20,0x77,0x14,0x00,0x00,0x00,0x40,0x58,0xbb,0x52,
+               0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00
+       };
+#else
+       /* largest result for each limb from a mult or square: all elements except r1 reduced, r1 overflowed as far as possible */
+       static const bignum25519 ALIGN(16) max_bignum = {
+               0x3ffffff,0x2000300,0x3ffffff,0x1ffffff,0x3ffffff,
+               0x1ffffff,0x3ffffff,0x1ffffff,0x3ffffff,0x1ffffff
+       };
+
+       /* what max_bignum should fully reduce to */
+       static const unsigned char max_bignum_raw[32] = {
+               0x12,0x00,0x00,0x04,0x0c,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
+               0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
+       };
+
+       /* (max_bignum * max_bignum) */
+       static const unsigned char max_bignum_squared_raw[32] = {
+               0x44,0x01,0x00,0x90,0xb0,0x01,0x10,0x60,0x90,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
+               0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
+       };
+#endif
+       unsigned char result[32];
+       static const bignum25519 ALIGN(16) zero = {0};
+       bignum25519 ALIGN(16) a, b, c;
+       size_t i;
+
+       /* a = max_bignum - 0, which expands to 2p + max_bignum - 0 */
+       curve25519_sub(a, max_bignum, zero);
+       curve25519_contract(result, a);
+       if (memcmp(result, max_bignum_raw, 32) != 0)
+               return -1;
+
+       /* b = (max_bignum * max_bignum) */
+       curve25519_mul(b, a, a);
+       curve25519_contract(result, b);
+       if (memcmp(result, max_bignum_squared_raw, 32) != 0)
+               return -1;
+       curve25519_square(b, a);
+       curve25519_contract(result, b);
+       if (memcmp(result, max_bignum_squared_raw, 32) != 0)
+               return -1;
+
+       /* b = ((a - 0) - 0) */
+       curve25519_sub_after_basic(b, a, zero);
+       curve25519_contract(result, b);
+       if (memcmp(result, max_bignum_raw, 32) != 0)
+               return -1;
+
+       /* a = (max_bignum * max_bignum) */
+       curve25519_mul(a, b, b);
+       curve25519_contract(result, a);
+       if (memcmp(result, max_bignum_squared_raw, 32) != 0)
+               return -1;
+       curve25519_square(a, b);
+       curve25519_contract(result, a);
+       if (memcmp(result, max_bignum_squared_raw, 32) != 0)
+               return -1;
+
+
+       return 0;
+}
+
+
+int
+main() {
+       int ret = 0;
+       int single;
+       single = test_adds();
+       if (single) printf("test_adds: FAILED\n");
+       ret |= single;
+       single = test_subs();
+       if (single) printf("test_subs: FAILED\n");
+       ret |= single;
+       if (!ret) printf("success\n");
+       return ret;
+}
+
+

diff --git a/crypto/ed25519-donna/src/test-ticks.h b/crypto/ed25519-donna/src/test-ticks.h
new file mode 100644 (file)
index 0000000..0103e03
--- /dev/null
+++ b/crypto/ed25519-donna/src/test-ticks.h
@@ -0,0 +1,50 @@
+#include "ed25519-donna-portable-identify.h"
+
+/* ticks - not tested on anything other than x86 */
+static uint64_t
+get_ticks(void) {
+#if defined(CPU_X86) || defined(CPU_X86_64)
+       #if defined(COMPILER_INTEL)
+               return _rdtsc();
+       #elif defined(COMPILER_MSVC)
+               return __rdtsc();
+       #elif defined(COMPILER_GCC)
+               uint32_t lo, hi;
+               __asm__ __volatile__("rdtsc" : "=a" (lo), "=d" (hi));
+               return ((uint64_t)lo | ((uint64_t)hi << 32));
+       #else
+               need rdtsc for this compiler
+       #endif
+#elif defined(OS_SOLARIS)
+       return (uint64_t)gethrtime();
+#elif defined(CPU_SPARC) && !defined(OS_OPENBSD)
+       uint64_t t;
+       __asm__ __volatile__("rd %%tick, %0" : "=r" (t));
+       return t;
+#elif defined(CPU_PPC)
+       uint32_t lo = 0, hi = 0;
+       __asm__ __volatile__("mftbu %0; mftb %1" : "=r" (hi), "=r" (lo));
+       return ((uint64_t)lo | ((uint64_t)hi << 32));
+#elif defined(CPU_IA64)
+       uint64_t t;
+       __asm__ __volatile__("mov %0=ar.itc" : "=r" (t));
+       return t;
+#elif defined(OS_NIX)
+       timeval t2;
+       gettimeofday(&t2, NULL);
+       t = ((uint64_t)t2.tv_usec << 32) | (uint64_t)t2.tv_sec;
+       return t;
+#else
+       need ticks for this platform
+#endif
+}
+
+#define timeit(x,minvar)         \
+       ticks = get_ticks();         \
+       x;                           \
+       ticks = get_ticks() - ticks; \
+       if (ticks < minvar)          \
+               minvar = ticks;
+
+#define maxticks 0xffffffffffffffffull
+

diff --git a/crypto/ed25519-donna/src/test.c b/crypto/ed25519-donna/src/test.c
new file mode 100644 (file)
index 0000000..8af3afc
--- /dev/null
+++ b/crypto/ed25519-donna/src/test.c
@@ -0,0 +1,273 @@
+/*
+       Validate ed25519 implementation against the official test vectors from 
+       http://ed25519.cr.yp.to/software.html
+*/
+
+#include <stdio.h>
+#include <string.h>
+#include "ed25519.h"
+
+#include "test-ticks.h"
+
+static void
+edassert(int check, int round, const char *failreason) {
+       if (check)
+               return;
+       printf("round %d, %s\n", round, failreason);
+       exit(1);
+}
+
+static void
+edassert_die(const unsigned char *a, const unsigned char *b, size_t len, int round, const char *failreason) {
+       size_t i;
+       if (round > 0)
+               printf("round %d, %s\n", round, failreason);
+       else
+               printf("%s\n", failreason);
+       printf("want: "); for (i = 0; i < len; i++) printf("%02x,", a[i]); printf("\n");
+       printf("got : "); for (i = 0; i < len; i++) printf("%02x,", b[i]); printf("\n");
+       printf("diff: "); for (i = 0; i < len; i++) if (a[i] ^ b[i]) printf("%02x,", a[i] ^ b[i]); else printf("  ,"); printf("\n\n");
+       exit(1);
+}
+
+static void
+edassert_equal(const unsigned char *a, const unsigned char *b, size_t len, const char *failreason) {
+       if (memcmp(a, b, len) == 0)
+               return;
+       edassert_die(a, b, len, -1, failreason);
+}
+
+static void
+edassert_equal_round(const unsigned char *a, const unsigned char *b, size_t len, int round, const char *failreason) {
+       if (memcmp(a, b, len) == 0)
+               return;
+       edassert_die(a, b, len, round, failreason);
+}
+
+
+/* test data */
+typedef struct test_data_t {
+       unsigned char sk[32], pk[32], sig[64];
+       const char *m;
+} test_data;
+
+
+test_data dataset[] = {
+#include "regression.h"
+};
+
+/* result of the curve25519 scalarmult ((|255| * basepoint) * basepoint)... 1024 times */
+const curved25519_key curved25519_expected = {
+       0xac,0xce,0x24,0xb1,0xd4,0xa2,0x36,0x21,
+       0x15,0xe2,0x3e,0x84,0x3c,0x23,0x2b,0x5f,
+       0x95,0x6c,0xc0,0x7b,0x95,0x82,0xd7,0x93,
+       0xd5,0x19,0xb6,0xf1,0xfb,0x96,0xd6,0x04
+};
+
+
+/* from ed25519-donna-batchverify.h */
+extern unsigned char batch_point_buffer[3][32];
+
+/* y coordinate of the final point from 'amd64-51-30k' with the same random generator */
+static const unsigned char batch_verify_y[32] = {
+       0x51,0xe7,0x68,0xe0,0xf7,0xa1,0x88,0x45,
+       0xde,0xa1,0xcb,0xd9,0x37,0xd4,0x78,0x53,
+       0x1b,0x95,0xdb,0xbe,0x66,0x59,0x29,0x3b,
+       0x94,0x51,0x2f,0xbc,0x0d,0x66,0xba,0x3f
+};
+
+/*
+static const unsigned char batch_verify_y[32] = {
+       0x5c,0x63,0x96,0x26,0xca,0xfe,0xfd,0xc4,
+       0x2d,0x11,0xa8,0xe4,0xc4,0x46,0x42,0x97,
+       0x97,0x92,0xbe,0xe0,0x3c,0xef,0x96,0x01,
+       0x50,0xa1,0xcc,0x8f,0x50,0x85,0x76,0x7d
+};
+
+Introducing the 128 bit r scalars to the heap _before_ the largest scalar
+fits in to 128 bits alters the heap shape and produces a different,
+yet still neutral/valid y/z value.
+
+This was the value of introducing the r scalars when the largest scalar fit
+in to 135-256 bits. You can produce it with amd64-64-24k / amd64-51-32k
+with the random sequence used in the first pass by changing
+
+    unsigned long long hlen=((npoints+1)/2)|1;
+
+to
+
+    unsigned long long hlen=npoints;
+
+in ge25519_multi_scalarmult.c
+
+ed25519-donna-batchverify.h has been modified to match the 
+default amd64-64-24k / amd64-51-32k behaviour
+*/
+
+
+
+/* batch test */
+#ifndef ED25519_SVP64
+#define test_batch_count 64
+#define test_batch_rounds 96
+#else
+#define test_batch_count 1
+#define test_batch_rounds 1
+#endif
+
+typedef enum batch_test_t {
+       batch_no_errors = 0,
+       batch_wrong_message = 1,
+       batch_wrong_pk = 2,
+       batch_wrong_sig = 3
+} batch_test;
+
+static int
+test_batch_instance(batch_test type, uint64_t *ticks) {
+       ed25519_secret_key sks[test_batch_count];
+       ed25519_public_key pks[test_batch_count];
+       ed25519_signature sigs[test_batch_count];
+       unsigned char messages[test_batch_count][128];
+       size_t message_lengths[test_batch_count];
+       const unsigned char *message_pointers[test_batch_count];
+       const unsigned char *pk_pointers[test_batch_count];
+       const unsigned char *sig_pointers[test_batch_count];
+       int valid[test_batch_count], ret, validret;
+       size_t i;
+       uint64_t t;
+
+       /* generate keys */
+       for (i = 0; i < test_batch_count; i++) {
+               ed25519_randombytes_unsafe(sks[i], sizeof(sks[i]));
+               ed25519_publickey(sks[i], pks[i]);
+               pk_pointers[i] = pks[i];
+       }
+
+       /* generate messages */
+       ed25519_randombytes_unsafe(messages, sizeof(messages));
+       for (i = 0; i < test_batch_count; i++) {
+               message_pointers[i] = messages[i];
+               message_lengths[i] = (i & 127) + 1;
+       }
+
+       /* sign messages */
+       for (i = 0; i < test_batch_count; i++) {
+               ed25519_sign(message_pointers[i], message_lengths[i], sks[i], pks[i], sigs[i]);
+               sig_pointers[i] = sigs[i];
+       }
+
+       validret = 0;
+       if (type == batch_wrong_message) {
+               message_pointers[0] = message_pointers[1];
+               validret = 1|2;
+       } else if (type == batch_wrong_pk) {
+               pk_pointers[0] = pk_pointers[1];
+               validret = 1|2;
+       } else if (type == batch_wrong_sig) {
+               sig_pointers[0] = sig_pointers[1];
+               validret = 1|2;
+       }
+
+       /* batch verify */
+       t = get_ticks();
+       ret = ed25519_sign_open_batch(message_pointers, message_lengths, pk_pointers, sig_pointers, test_batch_count, valid);
+       *ticks = get_ticks() - t;
+       edassert_equal((unsigned char *)&validret, (unsigned char *)&ret, sizeof(int), "batch return code");
+       for (i = 0; i < test_batch_count; i++) {
+               validret = ((type == batch_no_errors) || (i != 0)) ? 1 : 0;
+               edassert_equal((unsigned char *)&validret, (unsigned char *)&valid[i], sizeof(int), "individual batch return code");
+       }
+       return ret;
+}
+
+static void
+test_batch(void) {
+       uint64_t dummy_ticks, ticks[test_batch_rounds], best = maxticks, sum;
+       size_t i, count;
+
+       /* check the first pass for the expected result */
+       test_batch_instance(batch_no_errors, &dummy_ticks);
+       edassert_equal(batch_verify_y, batch_point_buffer[1], 32, "failed to generate expected result");
+
+       /* make sure ge25519_multi_scalarmult_vartime throws an error on the entire batch with wrong data */
+       for (i = 0; i < 4; i++) {
+               test_batch_instance(batch_wrong_message, &dummy_ticks);
+               test_batch_instance(batch_wrong_pk, &dummy_ticks);
+               test_batch_instance(batch_wrong_sig, &dummy_ticks);
+       }
+
+       /* speed test */
+       for (i = 0; i < test_batch_rounds; i++) {
+               test_batch_instance(batch_no_errors, &ticks[i]);
+               if (ticks[i] < best)
+                       best = ticks[i];
+       }
+
+       /* take anything within 1% of the best time */
+       for (i = 0, sum = 0, count = 0; i < test_batch_rounds; i++) {
+               if (ticks[i] < (best * 1.01)) {
+                       sum += ticks[i];
+                       count++;
+               }
+       }
+       printf("%.0f ticks/verification\n", (double)sum / (count * test_batch_count));
+}
+
+static void
+test_main(void) {
+       int i, res;
+       ed25519_public_key pk;
+       ed25519_signature sig;
+       unsigned char forge[1024] = {'x'};
+       curved25519_key csk[2] = {{255}};
+       uint64_t ticks, pkticks = maxticks, signticks = maxticks, openticks = maxticks, curvedticks = maxticks;
+
+#ifndef ED25519_SVP64
+       for (i = 0; i < 1024; i++) {
+#else
+       for (i = 0; i < 2; i++) {
+#endif
+               ed25519_publickey(dataset[i].sk, pk);
+               edassert_equal_round(dataset[i].pk, pk, sizeof(pk), i, "public key didn't match");
+               ed25519_sign((unsigned char *)dataset[i].m, i, dataset[i].sk, pk, sig);
+               edassert_equal_round(dataset[i].sig, sig, sizeof(sig), i, "signature didn't match");
+               edassert(!ed25519_sign_open((unsigned char *)dataset[i].m, i, pk, sig), i, "failed to open message");
+
+               memcpy(forge, dataset[i].m, i);
+               if (i)
+                       forge[i - 1] += 1;
+
+               edassert(ed25519_sign_open(forge, (i) ? i : 1, pk, sig), i, "opened forged message");
+       }
+
+       for (i = 0; i < 1024; i++)
+               curved25519_scalarmult_basepoint(csk[(i & 1) ^ 1], csk[i & 1]);
+       edassert_equal(curved25519_expected, csk[0], sizeof(curved25519_key), "curve25519 failed to generate correct value");
+
+#ifndef ED25519_SVP64
+       for (i = 0; i < 2048; i++) {
+#else
+       for (i = 0; i < 2; i++) {
+#endif
+               timeit(ed25519_publickey(dataset[0].sk, pk), pkticks)
+               edassert_equal_round(dataset[0].pk, pk, sizeof(pk), i, "public key didn't match");
+               timeit(ed25519_sign((unsigned char *)dataset[0].m, 0, dataset[0].sk, pk, sig), signticks)
+               edassert_equal_round(dataset[0].sig, sig, sizeof(sig), i, "signature didn't match");
+               timeit(res = ed25519_sign_open((unsigned char *)dataset[0].m, 0, pk, sig), openticks)
+               edassert(!res, 0, "failed to open message");
+               timeit(curved25519_scalarmult_basepoint(csk[1], csk[0]), curvedticks);
+       }
+
+       printf("%.0f ticks/public key generation\n", (double)pkticks);
+       printf("%.0f ticks/signature\n", (double)signticks);
+       printf("%.0f ticks/signature verification\n", (double)openticks);
+       printf("%.0f ticks/curve25519 basepoint scalarmult\n", (double)curvedticks);
+}
+
+int
+main(void) {
+       test_main();
+       test_batch();
+       return 0;
+}
+