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/ec.h>
16
17 #include <assert.h>
18
19 #include "internal.h"
20 #include "../bn/internal.h"
21 #include "../../internal.h"
22
23
ec_GFp_mont_mul(const EC_GROUP * group,EC_RAW_POINT * r,const EC_RAW_POINT * p,const EC_SCALAR * scalar)24 void ec_GFp_mont_mul(const EC_GROUP *group, EC_RAW_POINT *r,
25 const EC_RAW_POINT *p, const EC_SCALAR *scalar) {
26 // This is a generic implementation for uncommon curves that not do not
27 // warrant a tuned one. It uses unsigned digits so that the doubling case in
28 // |ec_GFp_mont_add| is always unreachable, erring on safety and simplicity.
29
30 // Compute a table of the first 32 multiples of |p| (including infinity).
31 EC_RAW_POINT precomp[32];
32 ec_GFp_simple_point_set_to_infinity(group, &precomp[0]);
33 ec_GFp_simple_point_copy(&precomp[1], p);
34 for (size_t j = 2; j < OPENSSL_ARRAY_SIZE(precomp); j++) {
35 if (j & 1) {
36 ec_GFp_mont_add(group, &precomp[j], &precomp[1], &precomp[j - 1]);
37 } else {
38 ec_GFp_mont_dbl(group, &precomp[j], &precomp[j / 2]);
39 }
40 }
41
42 // Divide bits in |scalar| into windows.
43 unsigned bits = BN_num_bits(&group->order);
44 int r_is_at_infinity = 1;
45 for (unsigned i = bits - 1; i < bits; i--) {
46 if (!r_is_at_infinity) {
47 ec_GFp_mont_dbl(group, r, r);
48 }
49 if (i % 5 == 0) {
50 // Compute the next window value.
51 const size_t width = group->order.width;
52 uint8_t window = bn_is_bit_set_words(scalar->words, width, i + 4) << 4;
53 window |= bn_is_bit_set_words(scalar->words, width, i + 3) << 3;
54 window |= bn_is_bit_set_words(scalar->words, width, i + 2) << 2;
55 window |= bn_is_bit_set_words(scalar->words, width, i + 1) << 1;
56 window |= bn_is_bit_set_words(scalar->words, width, i);
57
58 // Select the entry in constant-time.
59 EC_RAW_POINT tmp;
60 OPENSSL_memset(&tmp, 0, sizeof(EC_RAW_POINT));
61 for (size_t j = 0; j < OPENSSL_ARRAY_SIZE(precomp); j++) {
62 BN_ULONG mask = constant_time_eq_w(j, window);
63 ec_felem_select(group, &tmp.X, mask, &precomp[j].X, &tmp.X);
64 ec_felem_select(group, &tmp.Y, mask, &precomp[j].Y, &tmp.Y);
65 ec_felem_select(group, &tmp.Z, mask, &precomp[j].Z, &tmp.Z);
66 }
67
68 if (r_is_at_infinity) {
69 ec_GFp_simple_point_copy(r, &tmp);
70 r_is_at_infinity = 0;
71 } else {
72 ec_GFp_mont_add(group, r, r, &tmp);
73 }
74 }
75 }
76 if (r_is_at_infinity) {
77 ec_GFp_simple_point_set_to_infinity(group, r);
78 }
79 }
80
ec_GFp_mont_mul_base(const EC_GROUP * group,EC_RAW_POINT * r,const EC_SCALAR * scalar)81 void ec_GFp_mont_mul_base(const EC_GROUP *group, EC_RAW_POINT *r,
82 const EC_SCALAR *scalar) {
83 ec_GFp_mont_mul(group, r, &group->generator->raw, scalar);
84 }
85