Import Andrew Moon's ed25519-donna.

This is a clean copy of ed25519-donna as of commit:

  8757bd4cd209cb032853ece0ce413f122eef212c

https://github.com/floodyberry/ed25519-donna
This commit is contained in:
Yawning Angel 2015-06-24 14:51:00 +00:00
parent 19440b9e58
commit 7b10741be4
42 changed files with 15370 additions and 0 deletions

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@ -60,6 +60,11 @@ ed25519/ref10/*
Daniel Bernsten's portable ref10 implementation of ed25519.
Public domain.
ed25519/donna/*
Andrew Moon's semi-portable ed25519-donna implementation of
ed25519. Public domain.
readpassphrase.[ch]
Portable readpassphrase implementation from OpenSSH portable, version

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@ -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)

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/*
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;
}

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@ -0,0 +1,413 @@
/*
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;
/* 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 = 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

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/*
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);
}

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#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) */

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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}}
};

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@ -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) */

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@ -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}}
};

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@ -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) */

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@ -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) */

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

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@ -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;
}

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/*
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);
}
}

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/*
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);
}
}

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/* 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

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#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>

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/*
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

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/*
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);
*/

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#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

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/*
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
*/

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#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

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/*
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);
}

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#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

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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.

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<?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();
?>

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#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 */

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#define ED25519_SUFFIX _sse2
#define ED25519_SSE2
#include "../ed25519.c"

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#include "../ed25519.c"

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#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

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#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 */

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#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");
}
}
}
}

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#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");
}
}
}
}

View File

@ -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);
}

View File

@ -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);
}

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#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;
}

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#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

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/*
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 */
#define test_batch_count 64
#define test_batch_rounds 96
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;
for (i = 0; i < 1024; i++) {
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");
for (i = 0; i < 2048; i++) {
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;
}