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