+++ /dev/null
-/*
- * Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
- *
- * 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;
-}
projects / BearSSL / blobdiff