1 /*
2 * Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
3 *
4 * Permission is hereby granted, free of charge, to any person obtaining
5 * a copy of this software and associated documentation files (the
6 * "Software"), to deal in the Software without restriction, including
7 * without limitation the rights to use, copy, modify, merge, publish,
8 * distribute, sublicense, and/or sell copies of the Software, and to
9 * permit persons to whom the Software is furnished to do so, subject to
10 * the following conditions:
11 *
12 * The above copyright notice and this permission notice shall be
13 * included in all copies or substantial portions of the Software.
14 *
15 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
16 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
17 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
18 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
19 * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
20 * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
21 * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
22 * SOFTWARE.
23 */
24
25 #include "inner.h"
26
27 /* see inner.h */
28 uint32_t
br_i31_modpow_opt(uint32_t * x,const unsigned char * e,size_t elen,const uint32_t * m,uint32_t m0i,uint32_t * tmp,size_t twlen)29 br_i31_modpow_opt(uint32_t *x,
30 const unsigned char *e, size_t elen,
31 const uint32_t *m, uint32_t m0i, uint32_t *tmp, size_t twlen)
32 {
33 size_t mlen, mwlen;
34 uint32_t *t1, *t2, *base;
35 size_t u, v;
36 uint32_t acc;
37 int acc_len, win_len;
38
39 /*
40 * Get modulus size.
41 */
42 mwlen = (m[0] + 63) >> 5;
43 mlen = mwlen * sizeof m[0];
44 mwlen += (mwlen & 1);
45 t1 = tmp;
46 t2 = tmp + mwlen;
47
48 /*
49 * Compute possible window size, with a maximum of 5 bits.
50 * When the window has size 1 bit, we use a specific code
51 * that requires only two temporaries. Otherwise, for a
52 * window of k bits, we need 2^k+1 temporaries.
53 */
54 if (twlen < (mwlen << 1)) {
55 return 0;
56 }
57 for (win_len = 5; win_len > 1; win_len --) {
58 if ((((uint32_t)1 << win_len) + 1) * mwlen <= twlen) {
59 break;
60 }
61 }
62
63 /*
64 * Everything is done in Montgomery representation.
65 */
66 br_i31_to_monty(x, m);
67
68 /*
69 * Compute window contents. If the window has size one bit only,
70 * then t2 is set to x; otherwise, t2[0] is left untouched, and
71 * t2[k] is set to x^k (for k >= 1).
72 */
73 if (win_len == 1) {
74 memcpy(t2, x, mlen);
75 } else {
76 memcpy(t2 + mwlen, x, mlen);
77 base = t2 + mwlen;
78 for (u = 2; u < ((unsigned)1 << win_len); u ++) {
79 br_i31_montymul(base + mwlen, base, x, m, m0i);
80 base += mwlen;
81 }
82 }
83
84 /*
85 * We need to set x to 1, in Montgomery representation. This can
86 * be done efficiently by setting the high word to 1, then doing
87 * one word-sized shift.
88 */
89 br_i31_zero(x, m[0]);
90 x[(m[0] + 31) >> 5] = 1;
91 br_i31_muladd_small(x, 0, m);
92
93 /*
94 * We process bits from most to least significant. At each
95 * loop iteration, we have acc_len bits in acc.
96 */
97 acc = 0;
98 acc_len = 0;
99 while (acc_len > 0 || elen > 0) {
100 int i, k;
101 uint32_t bits;
102
103 /*
104 * Get the next bits.
105 */
106 k = win_len;
107 if (acc_len < win_len) {
108 if (elen > 0) {
109 acc = (acc << 8) | *e ++;
110 elen --;
111 acc_len += 8;
112 } else {
113 k = acc_len;
114 }
115 }
116 bits = (acc >> (acc_len - k)) & (((uint32_t)1 << k) - 1);
117 acc_len -= k;
118
119 /*
120 * We could get exactly k bits. Compute k squarings.
121 */
122 for (i = 0; i < k; i ++) {
123 br_i31_montymul(t1, x, x, m, m0i);
124 memcpy(x, t1, mlen);
125 }
126
127 /*
128 * Window lookup: we want to set t2 to the window
129 * lookup value, assuming the bits are non-zero. If
130 * the window length is 1 bit only, then t2 is
131 * already set; otherwise, we do a constant-time lookup.
132 */
133 if (win_len > 1) {
134 br_i31_zero(t2, m[0]);
135 base = t2 + mwlen;
136 for (u = 1; u < ((uint32_t)1 << k); u ++) {
137 uint32_t mask;
138
139 mask = -EQ(u, bits);
140 for (v = 1; v < mwlen; v ++) {
141 t2[v] |= mask & base[v];
142 }
143 base += mwlen;
144 }
145 }
146
147 /*
148 * Multiply with the looked-up value. We keep the
149 * product only if the exponent bits are not all-zero.
150 */
151 br_i31_montymul(t1, x, t2, m, m0i);
152 CCOPY(NEQ(bits, 0), x, t1, mlen);
153 }
154
155 /*
156 * Convert back from Montgomery representation, and exit.
157 */
158 br_i31_from_monty(x, m, m0i);
159 return 1;
160 }
161