mirror of
https://github.com/trezor/trezor-firmware.git
synced 2024-12-18 12:28:09 +00:00
362 lines
13 KiB
C
362 lines
13 KiB
C
/*
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Public domain by Andrew M. <liquidsun@gmail.com>
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*/
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/*
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Arithmetic modulo the group order n = 2^252 + 27742317777372353535851937790883648493 = 7237005577332262213973186563042994240857116359379907606001950938285454250989
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k = 32
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b = 1 << 8 = 256
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m = 2^252 + 27742317777372353535851937790883648493 = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed
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mu = floor( b^(k*2) / m ) = 0xfffffffffffffffffffffffffffffffeb2106215d086329a7ed9ce5a30a2c131b
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*/
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#define bignum256modm_bits_per_limb 56
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#define bignum256modm_limb_size 5
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typedef uint64_t bignum256modm_element_t;
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typedef bignum256modm_element_t bignum256modm[5];
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static const bignum256modm modm_m = {
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0x12631a5cf5d3ed,
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0xf9dea2f79cd658,
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0x000000000014de,
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0x00000000000000,
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0x00000010000000
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};
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static const bignum256modm modm_mu = {
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0x9ce5a30a2c131b,
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0x215d086329a7ed,
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0xffffffffeb2106,
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0xffffffffffffff,
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0x00000fffffffff
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};
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static bignum256modm_element_t
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lt_modm(bignum256modm_element_t a, bignum256modm_element_t b) {
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return (a - b) >> 63;
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}
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static void
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reduce256_modm(bignum256modm r) {
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bignum256modm t;
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bignum256modm_element_t b = 0, pb, mask;
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/* t = r - m */
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pb = 0;
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pb += modm_m[0]; b = lt_modm(r[0], pb); t[0] = (r[0] - pb + (b << 56)); pb = b;
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pb += modm_m[1]; b = lt_modm(r[1], pb); t[1] = (r[1] - pb + (b << 56)); pb = b;
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pb += modm_m[2]; b = lt_modm(r[2], pb); t[2] = (r[2] - pb + (b << 56)); pb = b;
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pb += modm_m[3]; b = lt_modm(r[3], pb); t[3] = (r[3] - pb + (b << 56)); pb = b;
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pb += modm_m[4]; b = lt_modm(r[4], pb); t[4] = (r[4] - pb + (b << 32));
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/* keep r if r was smaller than m */
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mask = b - 1;
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r[0] ^= mask & (r[0] ^ t[0]);
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r[1] ^= mask & (r[1] ^ t[1]);
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r[2] ^= mask & (r[2] ^ t[2]);
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r[3] ^= mask & (r[3] ^ t[3]);
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r[4] ^= mask & (r[4] ^ t[4]);
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}
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static void
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barrett_reduce256_modm(bignum256modm r, const bignum256modm q1, const bignum256modm r1) {
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bignum256modm q3, r2;
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uint128_t c, mul;
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bignum256modm_element_t f, b, pb;
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/* q1 = x >> 248 = 264 bits = 5 56 bit elements
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q2 = mu * q1
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q3 = (q2 / 256(32+1)) = q2 / (2^8)^(32+1) = q2 >> 264 */
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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);
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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)
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f = lo128(c); q3[0] = (f >> 40) & 0xffff; shr128(f, c, 56);
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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)
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f = lo128(c); q3[0] |= (f << 16) & 0xffffffffffffff; q3[1] = (f >> 40) & 0xffff; shr128(f, c, 56);
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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)
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f = lo128(c); q3[1] |= (f << 16) & 0xffffffffffffff; q3[2] = (f >> 40) & 0xffff; shr128(f, c, 56);
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mul64x64_128(c, modm_mu[4], q1[3]) add128_64(c, f) mul64x64_128(mul, modm_mu[3], q1[4]) add128(c, mul)
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f = lo128(c); q3[2] |= (f << 16) & 0xffffffffffffff; q3[3] = (f >> 40) & 0xffff; shr128(f, c, 56);
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mul64x64_128(c, modm_mu[4], q1[4]) add128_64(c, f)
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f = lo128(c); q3[3] |= (f << 16) & 0xffffffffffffff; q3[4] = (f >> 40) & 0xffff; shr128(f, c, 56);
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q3[4] |= (f << 16);
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mul64x64_128(c, modm_m[0], q3[0])
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r2[0] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
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mul64x64_128(c, modm_m[0], q3[1]) add128_64(c, f) mul64x64_128(mul, modm_m[1], q3[0]) add128(c, mul)
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r2[1] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
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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)
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r2[2] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
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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)
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r2[3] = lo128(c) & 0xffffffffffffff; shr128(f, c, 56);
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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)
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r2[4] = lo128(c) & 0x0000ffffffffff;
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pb = 0;
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pb += r2[0]; b = lt_modm(r1[0], pb); r[0] = (r1[0] - pb + (b << 56)); pb = b;
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pb += r2[1]; b = lt_modm(r1[1], pb); r[1] = (r1[1] - pb + (b << 56)); pb = b;
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pb += r2[2]; b = lt_modm(r1[2], pb); r[2] = (r1[2] - pb + (b << 56)); pb = b;
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pb += r2[3]; b = lt_modm(r1[3], pb); r[3] = (r1[3] - pb + (b << 56)); pb = b;
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pb += r2[4]; b = lt_modm(r1[4], pb); r[4] = (r1[4] - pb + (b << 40));
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reduce256_modm(r);
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reduce256_modm(r);
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}
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static void
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add256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y) {
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bignum256modm_element_t c;
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c = x[0] + y[0]; r[0] = c & 0xffffffffffffff; c >>= 56;
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c += x[1] + y[1]; r[1] = c & 0xffffffffffffff; c >>= 56;
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c += x[2] + y[2]; r[2] = c & 0xffffffffffffff; c >>= 56;
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c += x[3] + y[3]; r[3] = c & 0xffffffffffffff; c >>= 56;
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c += x[4] + y[4]; r[4] = c;
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reduce256_modm(r);
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}
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static void
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mul256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y) {
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bignum256modm q1, r1;
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uint128_t c, mul;
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bignum256modm_element_t f;
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mul64x64_128(c, x[0], y[0])
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f = lo128(c); r1[0] = f & 0xffffffffffffff; shr128(f, c, 56);
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mul64x64_128(c, x[0], y[1]) add128_64(c, f) mul64x64_128(mul, x[1], y[0]) add128(c, mul)
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f = lo128(c); r1[1] = f & 0xffffffffffffff; shr128(f, c, 56);
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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)
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f = lo128(c); r1[2] = f & 0xffffffffffffff; shr128(f, c, 56);
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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)
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f = lo128(c); r1[3] = f & 0xffffffffffffff; shr128(f, c, 56);
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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)
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f = lo128(c); r1[4] = f & 0x0000ffffffffff; q1[0] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
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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)
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f = lo128(c); q1[0] |= (f << 32) & 0xffffffffffffff; q1[1] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
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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)
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f = lo128(c); q1[1] |= (f << 32) & 0xffffffffffffff; q1[2] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
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mul64x64_128(c, x[4], y[3]) add128_64(c, f) mul64x64_128(mul, x[3], y[4]) add128(c, mul)
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f = lo128(c); q1[2] |= (f << 32) & 0xffffffffffffff; q1[3] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
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mul64x64_128(c, x[4], y[4]) add128_64(c, f)
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f = lo128(c); q1[3] |= (f << 32) & 0xffffffffffffff; q1[4] = (f >> 24) & 0xffffffff; shr128(f, c, 56);
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q1[4] |= (f << 32);
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barrett_reduce256_modm(r, q1, r1);
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}
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static void
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expand256_modm(bignum256modm out, const unsigned char *in, size_t len) {
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unsigned char work[64] = {0};
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bignum256modm_element_t x[16];
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bignum256modm q1;
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memcpy(work, in, len);
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x[0] = U8TO64_LE(work + 0);
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x[1] = U8TO64_LE(work + 8);
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x[2] = U8TO64_LE(work + 16);
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x[3] = U8TO64_LE(work + 24);
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x[4] = U8TO64_LE(work + 32);
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x[5] = U8TO64_LE(work + 40);
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x[6] = U8TO64_LE(work + 48);
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x[7] = U8TO64_LE(work + 56);
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/* r1 = (x mod 256^(32+1)) = x mod (2^8)(31+1) = x & ((1 << 264) - 1) */
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out[0] = ( x[0]) & 0xffffffffffffff;
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out[1] = ((x[ 0] >> 56) | (x[ 1] << 8)) & 0xffffffffffffff;
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out[2] = ((x[ 1] >> 48) | (x[ 2] << 16)) & 0xffffffffffffff;
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out[3] = ((x[ 2] >> 40) | (x[ 3] << 24)) & 0xffffffffffffff;
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out[4] = ((x[ 3] >> 32) | (x[ 4] << 32)) & 0x0000ffffffffff;
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/* under 252 bits, no need to reduce */
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if (len < 32)
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return;
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/* q1 = x >> 248 = 264 bits */
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q1[0] = ((x[ 3] >> 56) | (x[ 4] << 8)) & 0xffffffffffffff;
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q1[1] = ((x[ 4] >> 48) | (x[ 5] << 16)) & 0xffffffffffffff;
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q1[2] = ((x[ 5] >> 40) | (x[ 6] << 24)) & 0xffffffffffffff;
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q1[3] = ((x[ 6] >> 32) | (x[ 7] << 32)) & 0xffffffffffffff;
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q1[4] = ((x[ 7] >> 24) );
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barrett_reduce256_modm(out, q1, out);
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}
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static void
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expand_raw256_modm(bignum256modm out, const unsigned char in[32]) {
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bignum256modm_element_t x[4];
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x[0] = U8TO64_LE(in + 0);
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x[1] = U8TO64_LE(in + 8);
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x[2] = U8TO64_LE(in + 16);
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x[3] = U8TO64_LE(in + 24);
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out[0] = ( x[0]) & 0xffffffffffffff;
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out[1] = ((x[ 0] >> 56) | (x[ 1] << 8)) & 0xffffffffffffff;
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out[2] = ((x[ 1] >> 48) | (x[ 2] << 16)) & 0xffffffffffffff;
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out[3] = ((x[ 2] >> 40) | (x[ 3] << 24)) & 0xffffffffffffff;
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out[4] = ((x[ 3] >> 32) ) & 0x000000ffffffff;
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}
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static void
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contract256_modm(unsigned char out[32], const bignum256modm in) {
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U64TO8_LE(out + 0, (in[0] ) | (in[1] << 56));
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U64TO8_LE(out + 8, (in[1] >> 8) | (in[2] << 48));
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U64TO8_LE(out + 16, (in[2] >> 16) | (in[3] << 40));
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U64TO8_LE(out + 24, (in[3] >> 24) | (in[4] << 32));
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}
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static void
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contract256_window4_modm(signed char r[64], const bignum256modm in) {
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char carry;
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signed char *quads = r;
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bignum256modm_element_t i, j, v, m;
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for (i = 0; i < 5; i++) {
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v = in[i];
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m = (i == 4) ? 8 : 14;
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for (j = 0; j < m; j++) {
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*quads++ = (v & 15);
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v >>= 4;
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}
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}
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/* making it signed */
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carry = 0;
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for(i = 0; i < 63; i++) {
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r[i] += carry;
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r[i+1] += (r[i] >> 4);
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r[i] &= 15;
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carry = (r[i] >> 3);
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r[i] -= (carry << 4);
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}
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r[63] += carry;
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}
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static void
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contract256_slidingwindow_modm(signed char r[256], const bignum256modm s, int windowsize) {
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int i,j,k,b;
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int m = (1 << (windowsize - 1)) - 1, soplen = 256;
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signed char *bits = r;
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bignum256modm_element_t v;
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/* first put the binary expansion into r */
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for (i = 0; i < 4; i++) {
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v = s[i];
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for (j = 0; j < 56; j++, v >>= 1)
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*bits++ = (v & 1);
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}
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v = s[4];
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for (j = 0; j < 32; j++, v >>= 1)
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*bits++ = (v & 1);
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/* Making it sliding window */
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for (j = 0; j < soplen; j++) {
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if (!r[j])
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continue;
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for (b = 1; (b < (soplen - j)) && (b <= 6); b++) {
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if ((r[j] + (r[j + b] << b)) <= m) {
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r[j] += r[j + b] << b;
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r[j + b] = 0;
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} else if ((r[j] - (r[j + b] << b)) >= -m) {
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r[j] -= r[j + b] << b;
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for (k = j + b; k < soplen; k++) {
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if (!r[k]) {
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r[k] = 1;
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break;
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}
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r[k] = 0;
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}
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} else if (r[j + b]) {
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break;
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}
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}
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}
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}
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/*
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helpers for batch verifcation, are allowed to be vartime
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*/
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/* out = a - b, a must be larger than b */
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static void
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sub256_modm_batch(bignum256modm out, const bignum256modm a, const bignum256modm b, size_t limbsize) {
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size_t i = 0;
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bignum256modm_element_t carry = 0;
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switch (limbsize) {
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case 4: out[i] = (a[i] - b[i]) ; carry = (out[i] >> 63); out[i] &= 0xffffffffffffff; i++;
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case 3: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 63); out[i] &= 0xffffffffffffff; i++;
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case 2: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 63); out[i] &= 0xffffffffffffff; i++;
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case 1: out[i] = (a[i] - b[i]) - carry; carry = (out[i] >> 63); out[i] &= 0xffffffffffffff; i++;
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case 0:
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default: out[i] = (a[i] - b[i]) - carry;
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}
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}
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/* is a < b */
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static int
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lt256_modm_batch(const bignum256modm a, const bignum256modm b, size_t limbsize) {
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size_t i = 0;
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bignum256modm_element_t t, carry = 0;
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switch (limbsize) {
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case 4: t = (a[i] - b[i]) ; carry = (t >> 63); i++;
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case 3: t = (a[i] - b[i]) - carry; carry = (t >> 63); i++;
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case 2: t = (a[i] - b[i]) - carry; carry = (t >> 63); i++;
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case 1: t = (a[i] - b[i]) - carry; carry = (t >> 63); i++;
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case 0: t = (a[i] - b[i]) - carry; carry = (t >> 63);
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}
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return (int)carry;
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}
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/* is a <= b */
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static int
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lte256_modm_batch(const bignum256modm a, const bignum256modm b, size_t limbsize) {
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size_t i = 0;
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bignum256modm_element_t t, carry = 0;
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switch (limbsize) {
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case 4: t = (b[i] - a[i]) ; carry = (t >> 63); i++;
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case 3: t = (b[i] - a[i]) - carry; carry = (t >> 63); i++;
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case 2: t = (b[i] - a[i]) - carry; carry = (t >> 63); i++;
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case 1: t = (b[i] - a[i]) - carry; carry = (t >> 63); i++;
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case 0: t = (b[i] - a[i]) - carry; carry = (t >> 63);
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}
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return (int)!carry;
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}
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|
|
|
/* is a == 0 */
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|
static int
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|
iszero256_modm_batch(const bignum256modm a) {
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|
size_t i;
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|
for (i = 0; i < 5; i++)
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|
if (a[i])
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|
return 0;
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|
return 1;
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|
}
|
|
|
|
/* 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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|
}
|