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Diffstat (limited to 'third_party/bearssl/src/i15_muladd.c')
| -rw-r--r-- | third_party/bearssl/src/i15_muladd.c | 173 |
1 files changed, 173 insertions, 0 deletions
diff --git a/third_party/bearssl/src/i15_muladd.c b/third_party/bearssl/src/i15_muladd.c new file mode 100644 index 0000000..c4b7216 --- /dev/null +++ b/third_party/bearssl/src/i15_muladd.c @@ -0,0 +1,173 @@ +/* + * Copyright (c) 2017 Thomas Pornin <[email protected]> + * + * 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" + +/* + * 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); +} |