X-Git-Url: https://www.bearssl.org/gitweb//home/git/?p=BearSSL;a=blobdiff_plain;f=src%2Fint%2Fi15_core.c;fp=src%2Fint%2Fi15_core.c;h=5ae3b314e8636d35b2240a7919ac88a2220f88e7;hp=0000000000000000000000000000000000000000;hb=28e4e120b84dacdf53963639f1a8a6fec2793662;hpb=6dd8c51ba7e8ca106ede7ff58b5c507042bbf6eb diff --git a/src/int/i15_core.c b/src/int/i15_core.c new file mode 100644 index 0000000..5ae3b31 --- /dev/null +++ b/src/int/i15_core.c @@ -0,0 +1,479 @@ +/* + * Copyright (c) 2017 Thomas Pornin + * + * Permission is hereby granted, free of charge, to any person obtaining + * a copy of this software and associated documentation files (the + * "Software"), to deal in the Software without restriction, including + * without limitation the rights to use, copy, modify, merge, publish, + * distribute, sublicense, and/or sell copies of the Software, and to + * permit persons to whom the Software is furnished to do so, subject to + * the following conditions: + * + * The above copyright notice and this permission notice shall be + * included in all copies or substantial portions of the Software. + * + * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, + * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF + * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND + * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS + * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN + * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN + * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE + * SOFTWARE. + */ + +#include "inner.h" + +/* + * This file contains the core "big integer" functions for the i15 + * implementation, that represents integers as sequences of 15-bit + * words. + */ + +/* see inner.h */ +uint32_t +br_i15_iszero(const uint16_t *x) +{ + uint32_t z; + size_t u; + + z = 0; + for (u = (x[0] + 15) >> 4; u > 0; u --) { + z |= x[u]; + } + return ~(z | -z) >> 31; +} + +/* see inner.h */ +uint16_t +br_i15_ninv15(uint16_t x) +{ + uint32_t y; + + y = 2 - x; + y = MUL15(y, 2 - MUL15(x, y)); + y = MUL15(y, 2 - MUL15(x, y)); + y = MUL15(y, 2 - MUL15(x, y)); + return MUX(x & 1, -y, 0) & 0x7FFF; +} + +/* see inner.h */ +uint32_t +br_i15_add(uint16_t *a, const uint16_t *b, uint32_t ctl) +{ + uint32_t cc; + size_t u, m; + + cc = 0; + m = (a[0] + 31) >> 4; + for (u = 1; u < m; u ++) { + uint32_t aw, bw, naw; + + aw = a[u]; + bw = b[u]; + naw = aw + bw + cc; + cc = naw >> 15; + a[u] = MUX(ctl, naw & 0x7FFF, aw); + } + return cc; +} + +/* see inner.h */ +uint32_t +br_i15_sub(uint16_t *a, const uint16_t *b, uint32_t ctl) +{ + uint32_t cc; + size_t u, m; + + cc = 0; + m = (a[0] + 31) >> 4; + for (u = 1; u < m; u ++) { + uint32_t aw, bw, naw; + + aw = a[u]; + bw = b[u]; + naw = aw - bw - cc; + cc = naw >> 31; + a[u] = MUX(ctl, naw & 0x7FFF, aw); + } + return cc; +} + +/* + * Constant-time division. The divisor must not be larger than 16 bits, + * and the quotient must fit on 17 bits. + */ +static uint32_t +divrem16(uint32_t x, uint32_t d, uint32_t *r) +{ + int i; + uint32_t q; + + q = 0; + d <<= 16; + for (i = 16; i >= 0; i --) { + uint32_t ctl; + + ctl = LE(d, x); + q |= ctl << i; + x -= (-ctl) & d; + d >>= 1; + } + if (r != NULL) { + *r = x; + } + return q; +} + +/* see inner.h */ +void +br_i15_muladd_small(uint16_t *x, uint16_t z, const uint16_t *m) +{ + /* + * Constant-time: we accept to leak the exact bit length of the + * modulus m. + */ + unsigned m_bitlen, mblr; + size_t u, mlen; + uint32_t hi, a0, a, b, q; + uint32_t cc, tb, over, under; + + /* + * Simple case: the modulus fits on one word. + */ + m_bitlen = m[0]; + if (m_bitlen == 0) { + return; + } + if (m_bitlen <= 15) { + uint32_t rem; + + divrem16(((uint32_t)x[1] << 15) | z, m[1], &rem); + x[1] = rem; + return; + } + mlen = (m_bitlen + 15) >> 4; + mblr = m_bitlen & 15; + + /* + * Principle: we estimate the quotient (x*2^15+z)/m by + * doing a 30/15 division with the high words. + * + * Let: + * w = 2^15 + * a = (w*a0 + a1) * w^N + a2 + * b = b0 * w^N + b2 + * such that: + * 0 <= a0 < w + * 0 <= a1 < w + * 0 <= a2 < w^N + * w/2 <= b0 < w + * 0 <= b2 < w^N + * a < w*b + * I.e. the two top words of a are a0:a1, the top word of b is + * b0, we ensured that b0 is "full" (high bit set), and a is + * such that the quotient q = a/b fits on one word (0 <= q < w). + * + * If a = b*q + r (with 0 <= r < q), then we can estimate q by + * using a division on the top words: + * a0*w + a1 = b0*u + v (with 0 <= v < b0) + * Then the following holds: + * 0 <= u <= w + * u-2 <= q <= u + */ + hi = x[mlen]; + if (mblr == 0) { + a0 = x[mlen]; + memmove(x + 2, x + 1, (mlen - 1) * sizeof *x); + x[1] = z; + a = (a0 << 15) + x[mlen]; + b = m[mlen]; + } else { + a0 = (x[mlen] << (15 - mblr)) | (x[mlen - 1] >> mblr); + memmove(x + 2, x + 1, (mlen - 1) * sizeof *x); + x[1] = z; + a = (a0 << 15) | (((x[mlen] << (15 - mblr)) + | (x[mlen - 1] >> mblr)) & 0x7FFF); + b = (m[mlen] << (15 - mblr)) | (m[mlen - 1] >> mblr); + } + q = divrem16(a, b, NULL); + + /* + * We computed an estimate for q, but the real one may be q, + * q-1 or q-2; moreover, the division may have returned a value + * 8000 or even 8001 if the two high words were identical, and + * we want to avoid values beyond 7FFF. We thus adjust q so + * that the "true" multiplier will be q+1, q or q-1, and q is + * in the 0000..7FFF range. + */ + q = MUX(EQ(b, a0), 0x7FFF, q - 1 + ((q - 1) >> 31)); + + /* + * We subtract q*m from x (x has an extra high word of value 'hi'). + * Since q may be off by 1 (in either direction), we may have to + * add or subtract m afterwards. + * + * The 'tb' flag will be true (1) at the end of the loop if the + * result is greater than or equal to the modulus (not counting + * 'hi' or the carry). + */ + cc = 0; + tb = 1; + for (u = 1; u <= mlen; u ++) { + uint32_t mw, zl, xw, nxw; + + mw = m[u]; + zl = MUL15(mw, q) + cc; + cc = zl >> 15; + zl &= 0x7FFF; + xw = x[u]; + nxw = xw - zl; + cc += nxw >> 31; + nxw &= 0x7FFF; + x[u] = nxw; + tb = MUX(EQ(nxw, mw), tb, GT(nxw, mw)); + } + + /* + * If we underestimated q, then either cc < hi (one extra bit + * beyond the top array word), or cc == hi and tb is true (no + * extra bit, but the result is not lower than the modulus). + * + * If we overestimated q, then cc > hi. + */ + over = GT(cc, hi); + under = ~over & (tb | LT(cc, hi)); + br_i15_add(x, m, over); + br_i15_sub(x, m, under); +} + +/* see inner.h */ +void +br_i15_montymul(uint16_t *d, const uint16_t *x, const uint16_t *y, + const uint16_t *m, uint16_t m0i) +{ + size_t len, len4, u, v; + uint32_t dh; + + len = (m[0] + 15) >> 4; + len4 = len & ~(size_t)3; + br_i15_zero(d, m[0]); + dh = 0; + for (u = 0; u < len; u ++) { + uint32_t f, xu, r, zh; + + xu = x[u + 1]; + f = MUL15(d[1] + MUL15(x[u + 1], y[1]), m0i) & 0x7FFF; + + r = 0; + for (v = 0; v < len4; v += 4) { + uint32_t z; + + z = d[v + 1] + MUL15(xu, y[v + 1]) + + MUL15(f, m[v + 1]) + r; + r = z >> 15; + d[v + 0] = z & 0x7FFF; + z = d[v + 2] + MUL15(xu, y[v + 2]) + + MUL15(f, m[v + 2]) + r; + r = z >> 15; + d[v + 1] = z & 0x7FFF; + z = d[v + 3] + MUL15(xu, y[v + 3]) + + MUL15(f, m[v + 3]) + r; + r = z >> 15; + d[v + 2] = z & 0x7FFF; + z = d[v + 4] + MUL15(xu, y[v + 4]) + + MUL15(f, m[v + 4]) + r; + r = z >> 15; + d[v + 3] = z & 0x7FFF; + } + for (; v < len; v ++) { + uint32_t z; + + z = d[v + 1] + MUL15(xu, y[v + 1]) + + MUL15(f, m[v + 1]) + r; + r = z >> 15; + d[v + 0] = z & 0x7FFF; + } + + zh = dh + r; + d[len] = zh & 0x7FFF; + dh = zh >> 31; + } + + /* + * Restore the bit length (it was overwritten in the loop above). + */ + d[0] = m[0]; + + /* + * d[] may be greater than m[], but it is still lower than twice + * the modulus. + */ + br_i15_sub(d, m, NEQ(dh, 0) | NOT(br_i15_sub(d, m, 0))); +} + +/* see inner.h */ +void +br_i15_to_monty(uint16_t *x, const uint16_t *m) +{ + unsigned k; + + for (k = (m[0] + 15) >> 4; k > 0; k --) { + br_i15_muladd_small(x, 0, m); + } +} + +/* see inner.h */ +void +br_i15_modpow(uint16_t *x, + const unsigned char *e, size_t elen, + const uint16_t *m, uint16_t m0i, uint16_t *t1, uint16_t *t2) +{ + size_t mlen; + unsigned k; + + mlen = ((m[0] + 31) >> 4) * sizeof m[0]; + memcpy(t1, x, mlen); + br_i15_to_monty(t1, m); + br_i15_zero(x, m[0]); + x[1] = 1; + for (k = 0; k < ((unsigned)elen << 3); k ++) { + uint32_t ctl; + + ctl = (e[elen - 1 - (k >> 3)] >> (k & 7)) & 1; + br_i15_montymul(t2, x, t1, m, m0i); + CCOPY(ctl, x, t2, mlen); + br_i15_montymul(t2, t1, t1, m, m0i); + memcpy(t1, t2, mlen); + } +} + +/* see inner.h */ +void +br_i15_encode(void *dst, size_t len, const uint16_t *x) +{ + unsigned char *buf; + size_t u, xlen; + uint32_t acc; + int acc_len; + + xlen = (x[0] + 15) >> 4; + if (xlen == 0) { + memset(dst, 0, len); + return; + } + u = 1; + acc = 0; + acc_len = 0; + buf = dst; + while (len -- > 0) { + if (acc_len < 8) { + if (u <= xlen) { + acc += (uint32_t)x[u ++] << acc_len; + } + acc_len += 15; + } + buf[len] = (unsigned char)acc; + acc >>= 8; + acc_len -= 8; + } +} + +/* see inner.h */ +uint32_t +br_i15_decode_mod(uint16_t *x, const void *src, size_t len, const uint16_t *m) +{ + /* + * Two-pass algorithm: in the first pass, we determine whether the + * value fits; in the second pass, we do the actual write. + * + * During the first pass, 'r' contains the comparison result so + * far: + * 0x00000000 value is equal to the modulus + * 0x00000001 value is greater than the modulus + * 0xFFFFFFFF value is lower than the modulus + * + * Since we iterate starting with the least significant bytes (at + * the end of src[]), each new comparison overrides the previous + * except when the comparison yields 0 (equal). + * + * During the second pass, 'r' is either 0xFFFFFFFF (value fits) + * or 0x00000000 (value does not fit). + * + * We must iterate over all bytes of the source, _and_ possibly + * some extra virutal bytes (with value 0) so as to cover the + * complete modulus as well. We also add 4 such extra bytes beyond + * the modulus length because it then guarantees that no accumulated + * partial word remains to be processed. + */ + const unsigned char *buf; + size_t mlen, tlen; + int pass; + uint32_t r; + + buf = src; + mlen = (m[0] + 15) >> 4; + tlen = (mlen << 1); + if (tlen < len) { + tlen = len; + } + tlen += 4; + r = 0; + for (pass = 0; pass < 2; pass ++) { + size_t u, v; + uint32_t acc; + int acc_len; + + v = 1; + acc = 0; + acc_len = 0; + for (u = 0; u < tlen; u ++) { + uint32_t b; + + if (u < len) { + b = buf[len - 1 - u]; + } else { + b = 0; + } + acc |= (b << acc_len); + acc_len += 8; + if (acc_len >= 15) { + uint32_t xw; + + xw = acc & (uint32_t)0x7FFF; + acc_len -= 15; + acc = b >> (8 - acc_len); + if (v <= mlen) { + if (pass) { + x[v] = r & xw; + } else { + uint32_t cc; + + cc = (uint32_t)CMP(xw, m[v]); + r = MUX(EQ(cc, 0), r, cc); + } + } else { + if (!pass) { + r = MUX(EQ(xw, 0), r, 1); + } + } + v ++; + } + } + + /* + * When we reach this point at the end of the first pass: + * r is either 0, 1 or -1; we want to set r to 0 if it + * is equal to 0 or 1, and leave it to -1 otherwise. + * + * When we reach this point at the end of the second pass: + * r is either 0 or -1; we want to leave that value + * untouched. This is a subcase of the previous. + */ + r >>= 1; + r |= (r << 1); + } + + x[0] = m[0]; + return r & (uint32_t)1; +}