/* Public domain by Andrew M. */ /* 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); }