1 /*
2 * Copyright 1995-2022 The OpenSSL Project Authors. All Rights Reserved.
3 *
4 * Licensed under the Apache License 2.0 (the "License"). You may not use
5 * this file except in compliance with the License. You can obtain a copy
6 * in the file LICENSE in the source distribution or at
7 * https://www.openssl.org/source/license.html
8 */
9
10 #include <stdio.h>
11 #include "internal/cryptlib.h"
12 #include "bn_local.h"
13
14 #define TABLE_SIZE 32
15
BN_mod_exp2_mont(BIGNUM * rr,const BIGNUM * a1,const BIGNUM * p1,const BIGNUM * a2,const BIGNUM * p2,const BIGNUM * m,BN_CTX * ctx,BN_MONT_CTX * in_mont)16 int BN_mod_exp2_mont(BIGNUM *rr, const BIGNUM *a1, const BIGNUM *p1,
17 const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m,
18 BN_CTX *ctx, BN_MONT_CTX *in_mont)
19 {
20 int i, j, bits, b, bits1, bits2, ret =
21 0, wpos1, wpos2, window1, window2, wvalue1, wvalue2;
22 int r_is_one = 1;
23 BIGNUM *d, *r;
24 const BIGNUM *a_mod_m;
25 /* Tables of variables obtained from 'ctx' */
26 BIGNUM *val1[TABLE_SIZE], *val2[TABLE_SIZE];
27 BN_MONT_CTX *mont = NULL;
28
29 bn_check_top(a1);
30 bn_check_top(p1);
31 bn_check_top(a2);
32 bn_check_top(p2);
33 bn_check_top(m);
34
35 if (!BN_is_odd(m)) {
36 ERR_raise(ERR_LIB_BN, BN_R_CALLED_WITH_EVEN_MODULUS);
37 return 0;
38 }
39 bits1 = BN_num_bits(p1);
40 bits2 = BN_num_bits(p2);
41 if ((bits1 == 0) && (bits2 == 0)) {
42 ret = BN_one(rr);
43 return ret;
44 }
45
46 bits = (bits1 > bits2) ? bits1 : bits2;
47
48 BN_CTX_start(ctx);
49 d = BN_CTX_get(ctx);
50 r = BN_CTX_get(ctx);
51 val1[0] = BN_CTX_get(ctx);
52 val2[0] = BN_CTX_get(ctx);
53 if (val2[0] == NULL)
54 goto err;
55
56 if (in_mont != NULL)
57 mont = in_mont;
58 else {
59 if ((mont = BN_MONT_CTX_new()) == NULL)
60 goto err;
61 if (!BN_MONT_CTX_set(mont, m, ctx))
62 goto err;
63 }
64
65 window1 = BN_window_bits_for_exponent_size(bits1);
66 window2 = BN_window_bits_for_exponent_size(bits2);
67
68 /*
69 * Build table for a1: val1[i] := a1^(2*i + 1) mod m for i = 0 .. 2^(window1-1)
70 */
71 if (a1->neg || BN_ucmp(a1, m) >= 0) {
72 if (!BN_mod(val1[0], a1, m, ctx))
73 goto err;
74 a_mod_m = val1[0];
75 } else
76 a_mod_m = a1;
77 if (BN_is_zero(a_mod_m)) {
78 BN_zero(rr);
79 ret = 1;
80 goto err;
81 }
82
83 if (!BN_to_montgomery(val1[0], a_mod_m, mont, ctx))
84 goto err;
85 if (window1 > 1) {
86 if (!BN_mod_mul_montgomery(d, val1[0], val1[0], mont, ctx))
87 goto err;
88
89 j = 1 << (window1 - 1);
90 for (i = 1; i < j; i++) {
91 if (((val1[i] = BN_CTX_get(ctx)) == NULL) ||
92 !BN_mod_mul_montgomery(val1[i], val1[i - 1], d, mont, ctx))
93 goto err;
94 }
95 }
96
97 /*
98 * Build table for a2: val2[i] := a2^(2*i + 1) mod m for i = 0 .. 2^(window2-1)
99 */
100 if (a2->neg || BN_ucmp(a2, m) >= 0) {
101 if (!BN_mod(val2[0], a2, m, ctx))
102 goto err;
103 a_mod_m = val2[0];
104 } else
105 a_mod_m = a2;
106 if (BN_is_zero(a_mod_m)) {
107 BN_zero(rr);
108 ret = 1;
109 goto err;
110 }
111 if (!BN_to_montgomery(val2[0], a_mod_m, mont, ctx))
112 goto err;
113 if (window2 > 1) {
114 if (!BN_mod_mul_montgomery(d, val2[0], val2[0], mont, ctx))
115 goto err;
116
117 j = 1 << (window2 - 1);
118 for (i = 1; i < j; i++) {
119 if (((val2[i] = BN_CTX_get(ctx)) == NULL) ||
120 !BN_mod_mul_montgomery(val2[i], val2[i - 1], d, mont, ctx))
121 goto err;
122 }
123 }
124
125 /* Now compute the power product, using independent windows. */
126 r_is_one = 1;
127 wvalue1 = 0; /* The 'value' of the first window */
128 wvalue2 = 0; /* The 'value' of the second window */
129 wpos1 = 0; /* If wvalue1 > 0, the bottom bit of the
130 * first window */
131 wpos2 = 0; /* If wvalue2 > 0, the bottom bit of the
132 * second window */
133
134 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
135 goto err;
136 for (b = bits - 1; b >= 0; b--) {
137 if (!r_is_one) {
138 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
139 goto err;
140 }
141
142 if (!wvalue1)
143 if (BN_is_bit_set(p1, b)) {
144 /*
145 * consider bits b-window1+1 .. b for this window
146 */
147 i = b - window1 + 1;
148 while (!BN_is_bit_set(p1, i)) /* works for i<0 */
149 i++;
150 wpos1 = i;
151 wvalue1 = 1;
152 for (i = b - 1; i >= wpos1; i--) {
153 wvalue1 <<= 1;
154 if (BN_is_bit_set(p1, i))
155 wvalue1++;
156 }
157 }
158
159 if (!wvalue2)
160 if (BN_is_bit_set(p2, b)) {
161 /*
162 * consider bits b-window2+1 .. b for this window
163 */
164 i = b - window2 + 1;
165 while (!BN_is_bit_set(p2, i))
166 i++;
167 wpos2 = i;
168 wvalue2 = 1;
169 for (i = b - 1; i >= wpos2; i--) {
170 wvalue2 <<= 1;
171 if (BN_is_bit_set(p2, i))
172 wvalue2++;
173 }
174 }
175
176 if (wvalue1 && b == wpos1) {
177 /* wvalue1 is odd and < 2^window1 */
178 if (!BN_mod_mul_montgomery(r, r, val1[wvalue1 >> 1], mont, ctx))
179 goto err;
180 wvalue1 = 0;
181 r_is_one = 0;
182 }
183
184 if (wvalue2 && b == wpos2) {
185 /* wvalue2 is odd and < 2^window2 */
186 if (!BN_mod_mul_montgomery(r, r, val2[wvalue2 >> 1], mont, ctx))
187 goto err;
188 wvalue2 = 0;
189 r_is_one = 0;
190 }
191 }
192 if (!BN_from_montgomery(rr, r, mont, ctx))
193 goto err;
194 ret = 1;
195 err:
196 if (in_mont == NULL)
197 BN_MONT_CTX_free(mont);
198 BN_CTX_end(ctx);
199 bn_check_top(rr);
200 return ret;
201 }
202
