frost/secp256k1-zkp
3
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Add equalities relating input and output variables

Browse Source
This commit is contained in:
Pieter Wuille
2014-11-13 07:00:44 -08:00
parent 5dd421bab5
commit fa0d620668
2 changed files with 194 additions and 0 deletions
Download Patch File Download Diff File Expand all files Collapse all files

62
src/field_5x52_int128_impl.h
View File

@@ -10,6 +10,9 @@
SECP256K1_INLINE static void secp256k1_fe_mul_inner(const uint64_t *a, const uint64_t *b, uint64_t *r) {
const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
// [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n.
// px is a shorthand for sum(a[i]*b[x-i], i=0..x).
// Note that [x 0 0 0 0 0] = [x*R].
__int128 c, d;
@@ -17,56 +20,88 @@ SECP256K1_INLINE static void secp256k1_fe_mul_inner(const uint64_t *a, const uin
+ (__int128)a[1] * b[2]
+ (__int128)a[2] * b[1]
+ (__int128)a[3] * b[0];
// [d 0 0 0] = [p3 0 0 0]
c = (__int128)a[4] * b[4];
// [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0]
d += (c & M) * R; c >>= 52;
// [c 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0]
uint64_t t3 = d & M; d >>= 52;
// [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];
// [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0]
d += c * R;
// [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0]
uint64_t t4 = d & M; d >>= 52;
// [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0]
uint64_t tx = (t4 >> 48); t4 &= (M >> 4);
// [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0]
c = (__int128)a[0] * b[0];
// [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 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0]
uint64_t u0 = d & M; d >>= 52;
// [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0]
// [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0]
u0 = (u0 << 4) | tx;
// [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0]
c += (__int128)u0 * (R >> 4);
// [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0]
uint64_t t0 = c & M; c >>= 52;
// [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];
// [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];
// [d 0 t4 t3 0 c t0] = [p8 0 p6 p5 p4 p3 0 p1 p0]
c += (d & M) * R; d >>= 52;
// [d 0 0 t4 t3 0 c t0] = [p8 0 p6 p5 p4 p3 0 p1 p0]
uint64_t t1 = c & M; c >>= 52;
// [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];
// [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];
// [d 0 0 t4 t3 c t1 t0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0]
c += (d & M) * R; d >>= 52;
// [d 0 0 0 t4 t3 c t1 t0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0]
r[0] = t0;
// [d 0 0 0 t4 t3 c t1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0]
r[1] = t1;
// [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0]
r[2] = c & M; c >>= 52;
// [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0]
c += d * R + t3;;
// [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0]
r[3] = c & M; c >>= 52;
// [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0]
c += t4;
// [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0]
r[4] = c;
// [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0]
}
SECP256K1_INLINE static void secp256k1_fe_sqr_inner(const uint64_t *a, uint64_t *r) {
const uint64_t M = 0xFFFFFFFFFFFFFULL, R = 0x1000003D10ULL;
// [... a b c] is a shorthand for ... + a<<104 + b<<52 + c<<0 mod n.
// px is a shorthand for sum(a[i]*a[x-i], i=0..x).
// Note that [x 0 0 0 0 0] = [x*R].
__int128 c, d;
@@ -74,43 +109,70 @@ SECP256K1_INLINE static void secp256k1_fe_sqr_inner(const uint64_t *a, uint64_t
d = (__int128)(a0*2) * a3
+ (__int128)(a1*2) * a2;
// [d 0 0 0] = [p3 0 0 0]
c = (__int128)a4 * a4;
// [c 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0]
d += (c & M) * R; c >>= 52;
// [c 0 0 0 0 0 d 0 0 0] = [p8 0 0 0 0 p3 0 0 0]
uint64_t t3 = d & M; d >>= 52;
// [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 0 p3 0 0 0]
a4 *= 2;
d += (__int128)a0 * a4
+ (__int128)(a1*2) * a3
+ (__int128)a2 * a2;
// [c 0 0 0 0 d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0]
d += c * R;
// [d t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0]
uint64_t t4 = d & M; d >>= 52;
// [d t4 t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0]
uint64_t tx = (t4 >> 48); t4 &= (M >> 4);
// [d t4+(tx<<48) t3 0 0 0] = [p8 0 0 0 p4 p3 0 0 0]
c = (__int128)a0 * a0;
// [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 0 p4 p3 0 0 p0]
d += (__int128)a1 * a4
+ (__int128)(a2*2) * a3;
// [d t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0]
uint64_t u0 = d & M; d >>= 52;
// [d u0 t4+(tx<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0]
// [d 0 t4+(tx<<48)+(u0<<52) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0]
u0 = (u0 << 4) | tx;
// [d 0 t4+(u0<<48) t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0]
c += (__int128)u0 * (R >> 4);
// [d 0 t4 t3 0 0 c] = [p8 0 0 p5 p4 p3 0 0 p0]
r[0] = c & M; c >>= 52;
// [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 0 p0]
a0 *= 2;
c += (__int128)a0 * a1;
// [d 0 t4 t3 0 c r0] = [p8 0 0 p5 p4 p3 0 p1 p0]
d += (__int128)a2 * a4
+ (__int128)a3 * a3;
// [d 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0]
c += (d & M) * R; d >>= 52;
// [d 0 0 t4 t3 0 c r0] = [p8 0 p6 p5 p4 p3 0 p1 p0]
r[1] = c & M; c >>= 52;
// [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 0 p1 p0]
c += (__int128)a0 * a2
+ (__int128)a1 * a1;
// [d 0 0 t4 t3 c r1 r0] = [p8 0 p6 p5 p4 p3 p2 p1 p0]
d += (__int128)a3 * a4;
// [d 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0]
c += (d & M) * R; d >>= 52;
// [d 0 0 0 t4 t3 c r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0]
r[2] = c & M; c >>= 52;
// [d 0 0 0 t4 t3+c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0]
c += d * R + t3;;
// [t4 c r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0]
r[3] = c & M; c >>= 52;
// [t4+c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0]
c += t4;
// [c r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0]
r[4] = c;
// [r4 r3 r2 r1 r0] = [p8 p7 p6 p5 p4 p3 p2 p1 p0]
}
#endif