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=0000000000000000000000000000000000000000;hp=a33469ae7db8fc043b44c3505ee301fc6e7e817c;hb=2f454aad577ae53798935cc32438a2d3f02ba31f;hpb=bd3036844bd20b2b8d7bce7fee5ad010ce401915 diff --git a/src/int/i15_core.c b/src/int/i15_core.c deleted file mode 100644 index a33469a..0000000 --- a/src/int/i15_core.c +++ /dev/null @@ -1,480 +0,0 @@ -/* - * 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])) & 0x7FFF, 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 >> 15; - } - - /* - * 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; -}