88 lines
3.1 KiB
C
88 lines
3.1 KiB
C
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/* Copyright (c) 2018, Google Inc.
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*
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* Permission to use, copy, modify, and/or distribute this software for any
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* purpose with or without fee is hereby granted, provided that the above
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* copyright notice and this permission notice appear in all copies.
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*
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* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
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* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
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* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
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* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
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#include <openssl/bn.h>
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#include <assert.h>
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#include "internal.h"
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// The following functions use a Barrett reduction variant to avoid leaking the
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// numerator. See http://ridiculousfish.com/blog/posts/labor-of-division-episode-i.html
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//
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// We use 32-bit numerator and 16-bit divisor for simplicity. This allows
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// computing |m| and |q| without architecture-specific code.
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// mod_u16 returns |n| mod |d|. |p| and |m| are the "magic numbers" for |d| (see
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// reference). For proof of correctness in Coq, see
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// https://github.com/davidben/fiat-crypto/blob/barrett/src/Arithmetic/BarrettReduction/RidiculousFish.v
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// Note the Coq version of |mod_u16| additionally includes the computation of
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// |p| and |m| from |bn_mod_u16_consttime| below.
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static uint16_t mod_u16(uint32_t n, uint16_t d, uint32_t p, uint32_t m) {
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// Compute floor(n/d) per steps 3 through 5.
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uint32_t q = ((uint64_t)m * n) >> 32;
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// Note there is a typo in the reference. We right-shift by one, not two.
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uint32_t t = ((n - q) >> 1) + q;
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t = t >> (p - 1);
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// Multiply and subtract to get the remainder.
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n -= d * t;
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assert(n < d);
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return n;
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}
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// shift_and_add_mod_u16 returns |r| * 2^32 + |a| mod |d|. |p| and |m| are the
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// "magic numbers" for |d| (see reference).
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static uint16_t shift_and_add_mod_u16(uint16_t r, uint32_t a, uint16_t d,
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uint32_t p, uint32_t m) {
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// Incorporate |a| in two 16-bit chunks.
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uint32_t t = r;
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t <<= 16;
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t |= a >> 16;
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t = mod_u16(t, d, p, m);
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t <<= 16;
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t |= a & 0xffff;
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t = mod_u16(t, d, p, m);
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return t;
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}
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uint16_t bn_mod_u16_consttime(const BIGNUM *bn, uint16_t d) {
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if (d <= 1) {
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return 0;
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}
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// Compute the "magic numbers" for |d|. See steps 1 and 2.
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// This computes p = ceil(log_2(d)).
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uint32_t p = BN_num_bits_word(d - 1);
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// This operation is not constant-time, but |p| and |d| are public values.
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// Note that |p| is at most 16, so the computation fits in |uint64_t|.
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assert(p <= 16);
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uint32_t m = ((UINT64_C(1) << (32 + p)) + d - 1) / d;
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uint16_t ret = 0;
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for (int i = bn->width - 1; i >= 0; i--) {
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#if BN_BITS2 == 32
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ret = shift_and_add_mod_u16(ret, bn->d[i], d, p, m);
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#elif BN_BITS2 == 64
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ret = shift_and_add_mod_u16(ret, bn->d[i] >> 32, d, p, m);
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ret = shift_and_add_mod_u16(ret, bn->d[i] & 0xffffffff, d, p, m);
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#else
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#error "Unknown BN_ULONG size"
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#endif
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}
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return ret;
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}
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