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518 lines
22 KiB
518 lines
22 KiB
/*
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Public domain by Andrew M. <liquidsun@gmail.com>
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*/
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#include "ed25519-donna.h"
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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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static const bignum256modm modm_m = {
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0x1cf5d3ed, 0x20498c69, 0x2f79cd65, 0x37be77a8,
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0x00000014, 0x00000000, 0x00000000, 0x00000000,
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0x00001000
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};
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static const bignum256modm modm_mu = {
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0x0a2c131b, 0x3673968c, 0x06329a7e, 0x01885742,
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0x3fffeb21, 0x3fffffff, 0x3fffffff, 0x3fffffff,
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0x000fffff
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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) >> 31;
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}
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/* see HAC, Alg. 14.42 Step 4 */
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void reduce256_modm(bignum256modm r) {
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bignum256modm t = {0};
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bignum256modm_element_t b = 0, pb = 0, mask = 0;
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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 << 30)); pb = b;
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pb += modm_m[1]; b = lt_modm(r[1], pb); t[1] = (r[1] - pb + (b << 30)); pb = b;
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pb += modm_m[2]; b = lt_modm(r[2], pb); t[2] = (r[2] - pb + (b << 30)); pb = b;
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pb += modm_m[3]; b = lt_modm(r[3], pb); t[3] = (r[3] - pb + (b << 30)); pb = b;
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pb += modm_m[4]; b = lt_modm(r[4], pb); t[4] = (r[4] - pb + (b << 30)); pb = b;
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pb += modm_m[5]; b = lt_modm(r[5], pb); t[5] = (r[5] - pb + (b << 30)); pb = b;
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pb += modm_m[6]; b = lt_modm(r[6], pb); t[6] = (r[6] - pb + (b << 30)); pb = b;
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pb += modm_m[7]; b = lt_modm(r[7], pb); t[7] = (r[7] - pb + (b << 30)); pb = b;
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pb += modm_m[8]; b = lt_modm(r[8], pb); t[8] = (r[8] - pb + (b << 16));
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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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r[5] ^= mask & (r[5] ^ t[5]);
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r[6] ^= mask & (r[6] ^ t[6]);
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r[7] ^= mask & (r[7] ^ t[7]);
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r[8] ^= mask & (r[8] ^ t[8]);
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}
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/*
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Barrett reduction, see HAC, Alg. 14.42
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Instead of passing in x, pre-process in to q1 and r1 for efficiency
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*/
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void barrett_reduce256_modm(bignum256modm r, const bignum256modm q1, const bignum256modm r1) {
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bignum256modm q3 = {0}, r2 = {0};
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uint64_t c = 0;
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bignum256modm_element_t f = 0, b = 0, pb = 0;
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/* q1 = x >> 248 = 264 bits = 9 30 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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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]);
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c >>= 30;
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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]);
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f = (bignum256modm_element_t)c; q3[0] = (f >> 24) & 0x3f; c >>= 30;
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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]);
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f = (bignum256modm_element_t)c; q3[0] |= (f << 6) & 0x3fffffff; q3[1] = (f >> 24) & 0x3f; c >>= 30;
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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]);
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f = (bignum256modm_element_t)c; q3[1] |= (f << 6) & 0x3fffffff; q3[2] = (f >> 24) & 0x3f; c >>= 30;
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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]);
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f = (bignum256modm_element_t)c; q3[2] |= (f << 6) & 0x3fffffff; q3[3] = (f >> 24) & 0x3f; c >>= 30;
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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]);
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f = (bignum256modm_element_t)c; q3[3] |= (f << 6) & 0x3fffffff; q3[4] = (f >> 24) & 0x3f; c >>= 30;
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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]);
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f = (bignum256modm_element_t)c; q3[4] |= (f << 6) & 0x3fffffff; q3[5] = (f >> 24) & 0x3f; c >>= 30;
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c += mul32x32_64(modm_mu[6], q1[8]) + mul32x32_64(modm_mu[7], q1[7]) + mul32x32_64(modm_mu[8], q1[6]);
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f = (bignum256modm_element_t)c; q3[5] |= (f << 6) & 0x3fffffff; q3[6] = (f >> 24) & 0x3f; c >>= 30;
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c += mul32x32_64(modm_mu[7], q1[8]) + mul32x32_64(modm_mu[8], q1[7]);
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f = (bignum256modm_element_t)c; q3[6] |= (f << 6) & 0x3fffffff; q3[7] = (f >> 24) & 0x3f; c >>= 30;
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c += mul32x32_64(modm_mu[8], q1[8]);
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f = (bignum256modm_element_t)c; q3[7] |= (f << 6) & 0x3fffffff; q3[8] = (bignum256modm_element_t)(c >> 24);
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/* r1 = (x mod 256^(32+1)) = x mod (2^8)(32+1) = x & ((1 << 264) - 1)
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r2 = (q3 * m) mod (256^(32+1)) = (q3 * m) & ((1 << 264) - 1) */
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c = mul32x32_64(modm_m[0], q3[0]);
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r2[0] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
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c += mul32x32_64(modm_m[0], q3[1]) + mul32x32_64(modm_m[1], q3[0]);
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r2[1] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
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c += mul32x32_64(modm_m[0], q3[2]) + mul32x32_64(modm_m[1], q3[1]) + mul32x32_64(modm_m[2], q3[0]);
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r2[2] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
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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]);
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r2[3] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
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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]);
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r2[4] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
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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]);
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r2[5] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
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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]);
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r2[6] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
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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]);
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r2[7] = (bignum256modm_element_t)(c & 0x3fffffff); c >>= 30;
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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]);
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r2[8] = (bignum256modm_element_t)(c & 0xffffff);
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/* r = r1 - r2
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if (r < 0) r += (1 << 264) */
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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 << 30)); pb = b;
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pb += r2[1]; b = lt_modm(r1[1], pb); r[1] = (r1[1] - pb + (b << 30)); pb = b;
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pb += r2[2]; b = lt_modm(r1[2], pb); r[2] = (r1[2] - pb + (b << 30)); pb = b;
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pb += r2[3]; b = lt_modm(r1[3], pb); r[3] = (r1[3] - pb + (b << 30)); pb = b;
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pb += r2[4]; b = lt_modm(r1[4], pb); r[4] = (r1[4] - pb + (b << 30)); pb = b;
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pb += r2[5]; b = lt_modm(r1[5], pb); r[5] = (r1[5] - pb + (b << 30)); pb = b;
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pb += r2[6]; b = lt_modm(r1[6], pb); r[6] = (r1[6] - pb + (b << 30)); pb = b;
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pb += r2[7]; b = lt_modm(r1[7], pb); r[7] = (r1[7] - pb + (b << 30)); pb = b;
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pb += r2[8]; b = lt_modm(r1[8], pb); r[8] = (r1[8] - pb + (b << 24));
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reduce256_modm(r);
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reduce256_modm(r);
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}
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/* addition modulo m */
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void add256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y) {
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bignum256modm_element_t c = 0;
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c = x[0] + y[0]; r[0] = c & 0x3fffffff; c >>= 30;
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c += x[1] + y[1]; r[1] = c & 0x3fffffff; c >>= 30;
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c += x[2] + y[2]; r[2] = c & 0x3fffffff; c >>= 30;
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c += x[3] + y[3]; r[3] = c & 0x3fffffff; c >>= 30;
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c += x[4] + y[4]; r[4] = c & 0x3fffffff; c >>= 30;
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c += x[5] + y[5]; r[5] = c & 0x3fffffff; c >>= 30;
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c += x[6] + y[6]; r[6] = c & 0x3fffffff; c >>= 30;
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c += x[7] + y[7]; r[7] = c & 0x3fffffff; c >>= 30;
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c += x[8] + y[8]; r[8] = c;
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reduce256_modm(r);
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}
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/* -x modulo m */
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void neg256_modm(bignum256modm r, const bignum256modm x) {
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bignum256modm_element_t b = 0, pb = 0;
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/* r = m - x */
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pb = 0;
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pb += x[0]; b = lt_modm(modm_m[0], pb); r[0] = (modm_m[0] - pb + (b << 30)); pb = b;
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pb += x[1]; b = lt_modm(modm_m[1], pb); r[1] = (modm_m[1] - pb + (b << 30)); pb = b;
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pb += x[2]; b = lt_modm(modm_m[2], pb); r[2] = (modm_m[2] - pb + (b << 30)); pb = b;
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pb += x[3]; b = lt_modm(modm_m[3], pb); r[3] = (modm_m[3] - pb + (b << 30)); pb = b;
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pb += x[4]; b = lt_modm(modm_m[4], pb); r[4] = (modm_m[4] - pb + (b << 30)); pb = b;
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pb += x[5]; b = lt_modm(modm_m[5], pb); r[5] = (modm_m[5] - pb + (b << 30)); pb = b;
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pb += x[6]; b = lt_modm(modm_m[6], pb); r[6] = (modm_m[6] - pb + (b << 30)); pb = b;
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pb += x[7]; b = lt_modm(modm_m[7], pb); r[7] = (modm_m[7] - pb + (b << 30)); pb = b;
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pb += x[8]; b = lt_modm(modm_m[8], pb); r[8] = (modm_m[8] - pb + (b << 16));
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// if x==0, reduction is required
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reduce256_modm(r);
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}
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/* consts for subtraction, > p */
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/* Emilia Kasper trick, https://www.imperialviolet.org/2010/12/04/ecc.html */
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static const uint32_t twoP[] = {
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0x5cf5d3ed, 0x60498c68, 0x6f79cd64, 0x77be77a7, 0x40000013, 0x3fffffff, 0x3fffffff, 0x3fffffff, 0xfff};
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/* subtraction x-y % m */
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void sub256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y) {
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bignum256modm_element_t c = 0;
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c = twoP[0] + x[0] - y[0]; r[0] = c & 0x3fffffff; c >>= 30;
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c += twoP[1] + x[1] - y[1]; r[1] = c & 0x3fffffff; c >>= 30;
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c += twoP[2] + x[2] - y[2]; r[2] = c & 0x3fffffff; c >>= 30;
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c += twoP[3] + x[3] - y[3]; r[3] = c & 0x3fffffff; c >>= 30;
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c += twoP[4] + x[4] - y[4]; r[4] = c & 0x3fffffff; c >>= 30;
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c += twoP[5] + x[5] - y[5]; r[5] = c & 0x3fffffff; c >>= 30;
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c += twoP[6] + x[6] - y[6]; r[6] = c & 0x3fffffff; c >>= 30;
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c += twoP[7] + x[7] - y[7]; r[7] = c & 0x3fffffff; c >>= 30;
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c += twoP[8] + x[8] - y[8]; r[8] = c;
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reduce256_modm(r);
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}
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/* multiplication modulo m */
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void mul256_modm(bignum256modm r, const bignum256modm x, const bignum256modm y) {
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bignum256modm r1 = {0}, q1 = {0};
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uint64_t c = 0;
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bignum256modm_element_t f = 0;
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/* r1 = (x mod 256^(32+1)) = x mod (2^8)(31+1) = x & ((1 << 264) - 1)
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q1 = x >> 248 = 264 bits = 9 30 bit elements */
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c = mul32x32_64(x[0], y[0]);
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f = (bignum256modm_element_t)c; r1[0] = (f & 0x3fffffff); c >>= 30;
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c += mul32x32_64(x[0], y[1]) + mul32x32_64(x[1], y[0]);
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f = (bignum256modm_element_t)c; r1[1] = (f & 0x3fffffff); c >>= 30;
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c += mul32x32_64(x[0], y[2]) + mul32x32_64(x[1], y[1]) + mul32x32_64(x[2], y[0]);
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f = (bignum256modm_element_t)c; r1[2] = (f & 0x3fffffff); c >>= 30;
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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]);
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f = (bignum256modm_element_t)c; r1[3] = (f & 0x3fffffff); c >>= 30;
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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]);
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f = (bignum256modm_element_t)c; r1[4] = (f & 0x3fffffff); c >>= 30;
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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]);
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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);
|
|
}
|
|
|
|
void expand256_modm(bignum256modm out, const unsigned char *in, size_t len) {
|
|
unsigned char work[64] = {0};
|
|
bignum256modm_element_t x[16] = {0};
|
|
bignum256modm q1 = {0};
|
|
|
|
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);
|
|
}
|
|
|
|
void expand_raw256_modm(bignum256modm out, const unsigned char in[32]) {
|
|
bignum256modm_element_t x[8] = {0};
|
|
|
|
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;
|
|
}
|
|
|
|
int is_reduced256_modm(const bignum256modm in)
|
|
{
|
|
int i = 0;
|
|
uint32_t res1 = 0;
|
|
uint32_t res2 = 0;
|
|
for (i = 8; i >= 0; i--) {
|
|
res1 = (res1 << 1) | (in[i] < modm_m[i]);
|
|
res2 = (res2 << 1) | (in[i] > modm_m[i]);
|
|
}
|
|
return res1 > res2;
|
|
}
|
|
|
|
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));
|
|
}
|
|
|
|
void contract256_window4_modm(signed char r[64], const bignum256modm in) {
|
|
char carry = 0;
|
|
signed char *quads = r;
|
|
bignum256modm_element_t i = 0, j = 0, v = 0;
|
|
|
|
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;
|
|
}
|
|
|
|
void contract256_slidingwindow_modm(signed char r[256], const bignum256modm s, int windowsize) {
|
|
int i = 0, j = 0, k = 0, b = 0;
|
|
int m = (1 << (windowsize - 1)) - 1, soplen = 256;
|
|
signed char *bits = r;
|
|
bignum256modm_element_t v = 0;
|
|
|
|
/* 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;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
void set256_modm(bignum256modm r, uint64_t v) {
|
|
r[0] = (bignum256modm_element_t) (v & 0x3fffffff); v >>= 30;
|
|
r[1] = (bignum256modm_element_t) (v & 0x3fffffff); v >>= 30;
|
|
r[2] = (bignum256modm_element_t) (v & 0x3fffffff);
|
|
r[3] = 0;
|
|
r[4] = 0;
|
|
r[5] = 0;
|
|
r[6] = 0;
|
|
r[7] = 0;
|
|
r[8] = 0;
|
|
}
|
|
|
|
int get256_modm(uint64_t * v, const bignum256modm r){
|
|
*v = 0;
|
|
int con1 = 0;
|
|
|
|
#define NONZ(x) ((((((int64_t)(x)) - 1) >> 32) + 1) & 1)
|
|
bignum256modm_element_t c = 0;
|
|
c = r[0]; *v += (uint64_t)c & 0x3fffffff; c >>= 30; // 30
|
|
c += r[1]; *v += ((uint64_t)c & 0x3fffffff) << 30; c >>= 30; // 60
|
|
c += r[2]; *v += ((uint64_t)c & 0xf) << 60; con1 |= NONZ(c>>4); c >>= 30; // 64 bits
|
|
c += r[3]; con1 |= NONZ(c); c >>= 30;
|
|
c += r[4]; con1 |= NONZ(c); c >>= 30;
|
|
c += r[5]; con1 |= NONZ(c); c >>= 30;
|
|
c += r[6]; con1 |= NONZ(c); c >>= 30;
|
|
c += r[7]; con1 |= NONZ(c); c >>= 30;
|
|
c += r[8]; con1 |= NONZ(c); c >>= 30;
|
|
con1 |= NONZ(c);
|
|
#undef NONZ
|
|
|
|
return con1 ^ 1;
|
|
}
|
|
|
|
int eq256_modm(const bignum256modm x, const bignum256modm y){
|
|
size_t differentbits = 0;
|
|
int len = bignum256modm_limb_size;
|
|
while (len--) {
|
|
differentbits |= (*x++ ^ *y++);
|
|
}
|
|
return (int) (1 & ((differentbits - 1) >> bignum256modm_bits_per_limb));
|
|
}
|
|
|
|
int cmp256_modm(const bignum256modm x, const bignum256modm y){
|
|
int len = 2*bignum256modm_limb_size;
|
|
uint32_t a_gt = 0;
|
|
uint32_t b_gt = 0;
|
|
|
|
// 16B chunks
|
|
while (len--) {
|
|
const uint32_t ln = (const uint32_t) len;
|
|
const uint32_t a = (x[ln>>1] >> 16*(ln & 1)) & 0xffff;
|
|
const uint32_t b = (y[ln>>1] >> 16*(ln & 1)) & 0xffff;
|
|
|
|
const uint32_t limb_a_gt = ((b - a) >> 16) & 1;
|
|
const uint32_t limb_b_gt = ((a - b) >> 16) & 1;
|
|
a_gt |= limb_a_gt & ~b_gt;
|
|
b_gt |= limb_b_gt & ~a_gt;
|
|
}
|
|
|
|
return a_gt - b_gt;
|
|
}
|
|
|
|
int iszero256_modm(const bignum256modm x){
|
|
size_t differentbits = 0;
|
|
int len = bignum256modm_limb_size;
|
|
while (len--) {
|
|
differentbits |= (*x++);
|
|
}
|
|
return (int) (1 & ((differentbits - 1) >> bignum256modm_bits_per_limb));
|
|
}
|
|
|
|
void copy256_modm(bignum256modm r, const bignum256modm x){
|
|
r[0] = x[0];
|
|
r[1] = x[1];
|
|
r[2] = x[2];
|
|
r[3] = x[3];
|
|
r[4] = x[4];
|
|
r[5] = x[5];
|
|
r[6] = x[6];
|
|
r[7] = x[7];
|
|
r[8] = x[8];
|
|
}
|
|
|
|
int check256_modm(const bignum256modm x){
|
|
int ok = 1;
|
|
bignum256modm t={0}, z={0};
|
|
|
|
ok &= iszero256_modm(x) ^ 1;
|
|
barrett_reduce256_modm(t, z, x);
|
|
ok &= eq256_modm(t, x);
|
|
return ok;
|
|
}
|
|
|
|
void mulsub256_modm(bignum256modm r, const bignum256modm a, const bignum256modm b, const bignum256modm c){
|
|
//(cc - aa * bb) % l
|
|
bignum256modm t={0};
|
|
mul256_modm(t, a, b);
|
|
sub256_modm(r, c, t);
|
|
}
|
|
|
|
void muladd256_modm(bignum256modm r, const bignum256modm a, const bignum256modm b, const bignum256modm c){
|
|
//(cc + aa * bb) % l
|
|
bignum256modm t={0};
|
|
mul256_modm(t, a, b);
|
|
add256_modm(r, c, t);
|
|
}
|