1/* Copyright (c) 2018, Google Inc.
2 *
3 * Permission to use, copy, modify, and/or distribute this software for any
4 * purpose with or without fee is hereby granted, provided that the above
5 * copyright notice and this permission notice appear in all copies.
6 *
7 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
8 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
9 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
10 * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
11 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
12 * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
13 * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
14
15#include <openssl/bn.h>
16
17#include <assert.h>
18
19#include "internal.h"
20
21
22// The following functions use a Barrett reduction variant to avoid leaking the
23// numerator. See http://ridiculousfish.com/blog/posts/labor-of-division-episode-i.html
24//
25// We use 32-bit numerator and 16-bit divisor for simplicity. This allows
26// computing |m| and |q| without architecture-specific code.
27
28// mod_u16 returns |n| mod |d|. |p| and |m| are the "magic numbers" for |d| (see
29// reference). For proof of correctness in Coq, see
30// https://github.com/davidben/fiat-crypto/blob/barrett/src/Arithmetic/BarrettReduction/RidiculousFish.v
31// Note the Coq version of |mod_u16| additionally includes the computation of
32// |p| and |m| from |bn_mod_u16_consttime| below.
33static uint16_t mod_u16(uint32_t n, uint16_t d, uint32_t p, uint32_t m) {
34 // Compute floor(n/d) per steps 3 through 5.
35 uint32_t q = ((uint64_t)m * n) >> 32;
36 // Note there is a typo in the reference. We right-shift by one, not two.
37 uint32_t t = ((n - q) >> 1) + q;
38 t = t >> (p - 1);
39
40 // Multiply and subtract to get the remainder.
41 n -= d * t;
42 assert(n < d);
43 return n;
44}
45
46// shift_and_add_mod_u16 returns |r| * 2^32 + |a| mod |d|. |p| and |m| are the
47// "magic numbers" for |d| (see reference).
48static uint16_t shift_and_add_mod_u16(uint16_t r, uint32_t a, uint16_t d,
49 uint32_t p, uint32_t m) {
50 // Incorporate |a| in two 16-bit chunks.
51 uint32_t t = r;
52 t <<= 16;
53 t |= a >> 16;
54 t = mod_u16(t, d, p, m);
55
56 t <<= 16;
57 t |= a & 0xffff;
58 t = mod_u16(t, d, p, m);
59 return t;
60}
61
62uint16_t bn_mod_u16_consttime(const BIGNUM *bn, uint16_t d) {
63 if (d <= 1) {
64 return 0;
65 }
66
67 // Compute the "magic numbers" for |d|. See steps 1 and 2.
68 // This computes p = ceil(log_2(d)).
69 uint32_t p = BN_num_bits_word(d - 1);
70 // This operation is not constant-time, but |p| and |d| are public values.
71 // Note that |p| is at most 16, so the computation fits in |uint64_t|.
72 assert(p <= 16);
73 uint32_t m = ((UINT64_C(1) << (32 + p)) + d - 1) / d;
74
75 uint16_t ret = 0;
76 for (int i = bn->width - 1; i >= 0; i--) {
77#if BN_BITS2 == 32
78 ret = shift_and_add_mod_u16(ret, bn->d[i], d, p, m);
79#elif BN_BITS2 == 64
80 ret = shift_and_add_mod_u16(ret, bn->d[i] >> 32, d, p, m);
81 ret = shift_and_add_mod_u16(ret, bn->d[i] & 0xffffffff, d, p, m);
82#else
83#error "Unknown BN_ULONG size"
84#endif
85 }
86 return ret;
87}
88