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Make secp256k1_fe_mul_inner use the r != property

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Suggested by Peter Dettman.
This commit is contained in:
Pieter Wuille 2014-11-30 19:38:07 +01:00
parent be82e92fc4
commit 4d4eeea4ac
1 changed files with 52 additions and 55 deletions
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107
src/field_5x52_int128_impl.h
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@ -34,15 +34,17 @@ SECP256K1_INLINE static void secp256k1_fe_mul_inner(const uint64_t *a, const uin
* Note that [x 0 0 0 0 0] = [x*R].
*/
uint64_t a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4];
__int128 c, d;
d = (__int128)a[0] * b[3]
+ (__int128)a[1] * b[2]
+ (__int128)a[2] * b[1]
+ (__int128)a[3] * b[0];
d = (__int128)a0 * b[3]
+ (__int128)a1 * b[2]
+ (__int128)a2 * b[1]
+ (__int128)a3 * b[0];
VERIFY_BITS(d, 114);
/* [d 0 0 0] = [p3 0 0 0] */
c = (__int128)a[4] * b[4];
c = (__int128)a4 * b[4];
VERIFY_BITS(c, 112);
/* [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
d += (c & M) * R; c >>= 52;
@ -54,11 +56,11 @@ SECP256K1_INLINE static void secp256k1_fe_mul_inner(const uint64_t *a, const uin
VERIFY_BITS(d, 63);
/* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0] */
d += (__int128)a[0] * b[4]
+ (__int128)a[1] * b[3]
+ (__int128)a[2] * b[2]
+ (__int128)a[3] * b[1]
+ (__int128)a[4] * b[0];
d += (__int128)a0 * b[4]
+ (__int128)a1 * b[3]
+ (__int128)a2 * b[2]
+ (__int128)a3 * b[1]
+ (__int128)a4 * b[0];
VERIFY_BITS(d, 115);
/* [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
d += c * R;
@ -73,13 +75,13 @@ SECP256K1_INLINE static void secp256k1_fe_mul_inner(const uint64_t *a, const uin
VERIFY_BITS(t4, 48);
/* [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0] */
c = (__int128)a[0] * b[0];
c = (__int128)a0 * b[0];
VERIFY_BITS(c, 112);
/* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0] */
d += (__int128)a[1] * b[4]
+ (__int128)a[2] * b[3]
+ (__int128)a[3] * b[2]
+ (__int128)a[4] * b[1];
d += (__int128)a1 * b[4]
+ (__int128)a2 * b[3]
+ (__int128)a3 * b[2]
+ (__int128)a4 * b[1];
VERIFY_BITS(d, 115);
/* [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
uint64_t u0 = d & M; d >>= 52;
@ -93,48 +95,43 @@ SECP256K1_INLINE static void secp256k1_fe_mul_inner(const uint64_t *a, const uin
c += (__int128)u0 * (R >> 4);
VERIFY_BITS(c, 115);
/* [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0] */
uint64_t t0 = c & M; c >>= 52;
VERIFY_BITS(t0, 52);
VERIFY_BITS(c, 61);
/* [d 0 t4 t3 0 c t0] = [p8 0 0 p5 p4 p3 0 0 p0] */
c += (__int128)a[0] * b[1]
+ (__int128)a[1] * b[0];
VERIFY_BITS(c, 114);
/* [d 0 t4 t3 0 c t0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
d += (__int128)a[2] * b[4]
+ (__int128)a[3] * b[3]
+ (__int128)a[4] * b[2];
VERIFY_BITS(d, 114);
/* [d 0 t4 t3 0 c t0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
c += (d & M) * R; d >>= 52;
VERIFY_BITS(c, 115);
VERIFY_BITS(d, 62);
/* [d 0 0 t4 t3 0 c t0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
uint64_t t1 = c & M; c >>= 52;
VERIFY_BITS(t1, 52);
VERIFY_BITS(c, 63);
/* [d 0 0 t4 t3 c t1 t0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
c += (__int128)a[0] * b[2]
+ (__int128)a[1] * b[1]
+ (__int128)a[2] * b[0];
VERIFY_BITS(c, 114);
/* [d 0 0 t4 t3 c t1 t0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
d += (__int128)a[3] * b[4]
+ (__int128)a[4] * b[3];
VERIFY_BITS(d, 114);
/* [d 0 0 t4 t3 c t1 t0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
c += (d & M) * R; d >>= 52;
VERIFY_BITS(c, 115);
VERIFY_BITS(d, 62);
/* [d 0 0 0 t4 t3 c t1 t0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
r[0] = t0;
r[0] = c & M; c >>= 52;
VERIFY_BITS(r[0], 52);
/* [d 0 0 0 t4 t3 c t1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
r[1] = t1;
VERIFY_BITS(c, 61);
/* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0] */
c += (__int128)a0 * b[1]
+ (__int128)a1 * b[0];
VERIFY_BITS(c, 114);
/* [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0] */
d += (__int128)a2 * b[4]
+ (__int128)a3 * b[3]
+ (__int128)a4 * b[2];
VERIFY_BITS(d, 114);
/* [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
c += (d & M) * R; d >>= 52;
VERIFY_BITS(c, 115);
VERIFY_BITS(d, 62);
/* [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
r[1] = c & M; c >>= 52;
VERIFY_BITS(r[1], 52);
VERIFY_BITS(c, 63);
/* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0] */
c += (__int128)a0 * b[2]
+ (__int128)a1 * b[1]
+ (__int128)a2 * b[0];
VERIFY_BITS(c, 114);
/* [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0] */
d += (__int128)a3 * b[4]
+ (__int128)a4 * b[3];
VERIFY_BITS(d, 114);
/* [d 0 0 t4 t3 c t1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
c += (d & M) * R; d >>= 52;
VERIFY_BITS(c, 115);
VERIFY_BITS(d, 62);
/* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
/* [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0] */
r[2] = c & M; c >>= 52;
VERIFY_BITS(r[2], 52);