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Fixed carry propagation bug in m64 impl for P-256.

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This commit is contained in:
Thomas Pornin 2020-11-18 09:53:11 -05:00
parent dda1f8a0c4
commit b2ec2030e4
1 changed files with 59 additions and 8 deletions
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67
src/ec/ec_p256_m64.c
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@ -99,6 +99,9 @@ f256_add(uint64_t *d, const uint64_t *a, const uint64_t *b)
unsigned __int128 w; unsigned __int128 w;
uint64_t t; uint64_t t;
/*
* Do the addition, with an extra carry in t.
*/
w = (unsigned __int128)a[0] + b[0]; w = (unsigned __int128)a[0] + b[0];
d[0] = (uint64_t)w; d[0] = (uint64_t)w;
w = (unsigned __int128)a[1] + b[1] + (w >> 64); w = (unsigned __int128)a[1] + b[1] + (w >> 64);
@ -110,7 +113,7 @@ f256_add(uint64_t *d, const uint64_t *a, const uint64_t *b)
t = (uint64_t)(w >> 64); t = (uint64_t)(w >> 64);
/* /*
* 2^256 = 2^224 - 2^192 - 2^96 + 1 in the field. * Fold carry t, using: 2^256 = 2^224 - 2^192 - 2^96 + 1 mod p.
*/ */
w = (unsigned __int128)d[0] + t; w = (unsigned __int128)d[0] + t;
d[0] = (uint64_t)w; d[0] = (uint64_t)w;
@ -119,8 +122,22 @@ f256_add(uint64_t *d, const uint64_t *a, const uint64_t *b)
/* Here, carry "w >> 64" can only be 0 or -1 */ /* Here, carry "w >> 64" can only be 0 or -1 */
w = (unsigned __int128)d[2] - ((w >> 64) & 1); w = (unsigned __int128)d[2] - ((w >> 64) & 1);
d[2] = (uint64_t)w; d[2] = (uint64_t)w;
/* Again, carry is 0 or -1 */ /* Again, carry is 0 or -1. But there can be carry only if t = 1,
d[3] += (uint64_t)(w >> 64) + (t << 32) - t; in which case the addition of (t << 32) - t is positive. */
w = (unsigned __int128)d[3] - ((w >> 64) & 1) + (t << 32) - t;
d[3] = (uint64_t)w;
t = (uint64_t)(w >> 64);
/*
* There can be an extra carry here, which we must fold again.
*/
w = (unsigned __int128)d[0] + t;
d[0] = (uint64_t)w;
w = (unsigned __int128)d[1] + (w >> 64) - (t << 32);
d[1] = (uint64_t)w;
w = (unsigned __int128)d[2] - ((w >> 64) & 1);
d[2] = (uint64_t)w;
d[3] += (t << 32) - t - (uint64_t)((w >> 64) & 1);
#elif BR_UMUL128 #elif BR_UMUL128
@ -140,6 +157,15 @@ f256_add(uint64_t *d, const uint64_t *a, const uint64_t *b)
cc = _addcarry_u64(cc, d[0], 0, &d[0]); cc = _addcarry_u64(cc, d[0], 0, &d[0]);
cc = _addcarry_u64(cc, d[1], -(t << 32), &d[1]); cc = _addcarry_u64(cc, d[1], -(t << 32), &d[1]);
cc = _addcarry_u64(cc, d[2], -t, &d[2]); cc = _addcarry_u64(cc, d[2], -t, &d[2]);
cc = _addcarry_u64(cc, d[3], (t << 32) - (t << 1), &d[3]);
/*
* We have to do it again if there still is a carry.
*/
t = cc;
cc = _addcarry_u64(cc, d[0], 0, &d[0]);
cc = _addcarry_u64(cc, d[1], -(t << 32), &d[1]);
cc = _addcarry_u64(cc, d[2], -t, &d[2]);
(void)_addcarry_u64(cc, d[3], (t << 32) - (t << 1), &d[3]); (void)_addcarry_u64(cc, d[3], (t << 32) - (t << 1), &d[3]);
#endif #endif
@ -167,6 +193,7 @@ f256_sub(uint64_t *d, const uint64_t *a, const uint64_t *b)
t = (uint64_t)(w >> 64) & 1; t = (uint64_t)(w >> 64) & 1;
/* /*
* If there is a borrow (t = 1), then we must add the modulus
* p = 2^256 - 2^224 + 2^192 + 2^96 - 1. * p = 2^256 - 2^224 + 2^192 + 2^96 - 1.
*/ */
w = (unsigned __int128)d[0] - t; w = (unsigned __int128)d[0] - t;
@ -177,6 +204,20 @@ f256_sub(uint64_t *d, const uint64_t *a, const uint64_t *b)
w = (unsigned __int128)d[2] + (w >> 64); w = (unsigned __int128)d[2] + (w >> 64);
d[2] = (uint64_t)w; d[2] = (uint64_t)w;
/* Again, carry is 0 or +1 */ /* Again, carry is 0 or +1 */
w = (unsigned __int128)d[3] + (w >> 64) - (t << 32) + t;
d[3] = (uint64_t)w;
t = (uint64_t)(w >> 64) & 1;
/*
* There may be again a borrow, in which case we must add the
* modulus again.
*/
w = (unsigned __int128)d[0] - t;
d[0] = (uint64_t)w;
w = (unsigned __int128)d[1] + (t << 32) - ((w >> 64) & 1);
d[1] = (uint64_t)w;
w = (unsigned __int128)d[2] + (w >> 64);
d[2] = (uint64_t)w;
d[3] += (uint64_t)(w >> 64) - (t << 32) + t; d[3] += (uint64_t)(w >> 64) - (t << 32) + t;
#elif BR_UMUL128 #elif BR_UMUL128
@ -190,13 +231,23 @@ f256_sub(uint64_t *d, const uint64_t *a, const uint64_t *b)
cc = _subborrow_u64(cc, a[3], b[3], &d[3]); cc = _subborrow_u64(cc, a[3], b[3], &d[3]);
/* /*
* If there is a carry, then we need to add p. * If there is a borrow, then we need to add p. We (virtually)
* add 2^256, then subtract 2^256 - p.
*/ */
t = cc; t = cc;
cc = _addcarry_u64(0, d[0], -t, &d[0]); cc = _subborrow_u64(0, d[0], t, &d[0]);
cc = _addcarry_u64(cc, d[1], (-t) >> 32, &d[1]); cc = _subborrow_u64(cc, d[1], -(t << 32), &d[1]);
cc = _addcarry_u64(cc, d[2], 0, &d[2]); cc = _subborrow_u64(cc, d[2], -t, &d[2]);
(void)_addcarry_u64(cc, d[3], t - (t << 32), &d[3]); cc = _subborrow_u64(cc, d[3], (t << 32) - (t << 1), &d[3]);
/*
* If there still is a borrow, then we need to add p again.
*/
t = cc;
cc = _subborrow_u64(0, d[0], t, &d[0]);
cc = _subborrow_u64(cc, d[1], -(t << 32), &d[1]);
cc = _subborrow_u64(cc, d[2], -t, &d[2]);
(void)_subborrow_u64(cc, d[3], (t << 32) - (t << 1), &d[3]);
#endif #endif
} }