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 = 0, wpos1, wpos2, window1, window2, wvalue1, wvalue2;
21 int r_is_one = 1;
22 BIGNUM *d, *r;
23 const BIGNUM *a_mod_m;
24 /* Tables of variables obtained from 'ctx' */
25 BIGNUM *val1[TABLE_SIZE], *val2[TABLE_SIZE];
26 BN_MONT_CTX *mont = NULL;
27
28 bn_check_top(a1);
29 bn_check_top(p1);
30 bn_check_top(a2);
31 bn_check_top(p2);
32 bn_check_top(m);
33
34 if (!BN_is_odd(m)) {
35 ERR_raise(ERR_LIB_BN, BN_R_CALLED_WITH_EVEN_MODULUS);
36 return 0;
37 }
38 bits1 = BN_num_bits(p1);
39 bits2 = BN_num_bits(p2);
40 if ((bits1 == 0) && (bits2 == 0)) {
41 ret = BN_one(rr);
42 return ret;
43 }
44
45 bits = (bits1 > bits2) ? bits1 : bits2;
46
47 BN_CTX_start(ctx);
48 d = BN_CTX_get(ctx);
49 r = BN_CTX_get(ctx);
50 val1[0] = BN_CTX_get(ctx);
51 val2[0] = BN_CTX_get(ctx);
52 if (val2[0] == NULL)
53 goto err;
54
55 if (in_mont != NULL)
56 mont = in_mont;
57 else {
58 if ((mont = BN_MONT_CTX_new()) == NULL)
59 goto err;
60 if (!BN_MONT_CTX_set(mont, m, ctx))
61 goto err;
62 }
63
64 window1 = BN_window_bits_for_exponent_size(bits1);
65 window2 = BN_window_bits_for_exponent_size(bits2);
66
67 /*
68 * Build table for a1: val1[i] := a1^(2*i + 1) mod m for i = 0 .. 2^(window1-1)
69 */
70 if (a1->neg || BN_ucmp(a1, m) >= 0) {
71 if (!BN_mod(val1[0], a1, m, ctx))
72 goto err;
73 a_mod_m = val1[0];
74 } else
75 a_mod_m = a1;
76 if (BN_is_zero(a_mod_m)) {
77 BN_zero(rr);
78 ret = 1;
79 goto err;
80 }
81
82 if (!BN_to_montgomery(val1[0], a_mod_m, mont, ctx))
83 goto err;
84 if (window1 > 1) {
85 if (!BN_mod_mul_montgomery(d, val1[0], val1[0], mont, ctx))
86 goto err;
87
88 j = 1 << (window1 - 1);
89 for (i = 1; i < j; i++) {
90 if (((val1[i] = BN_CTX_get(ctx)) == NULL) || !BN_mod_mul_montgomery(val1[i], val1[i - 1], d, mont, ctx))
91 goto err;
92 }
93 }
94
95 /*
96 * Build table for a2: val2[i] := a2^(2*i + 1) mod m for i = 0 .. 2^(window2-1)
97 */
98 if (a2->neg || BN_ucmp(a2, m) >= 0) {
99 if (!BN_mod(val2[0], a2, m, ctx))
100 goto err;
101 a_mod_m = val2[0];
102 } else
103 a_mod_m = a2;
104 if (BN_is_zero(a_mod_m)) {
105 BN_zero(rr);
106 ret = 1;
107 goto err;
108 }
109 if (!BN_to_montgomery(val2[0], a_mod_m, mont, ctx))
110 goto err;
111 if (window2 > 1) {
112 if (!BN_mod_mul_montgomery(d, val2[0], val2[0], mont, ctx))
113 goto err;
114
115 j = 1 << (window2 - 1);
116 for (i = 1; i < j; i++) {
117 if (((val2[i] = BN_CTX_get(ctx)) == NULL) || !BN_mod_mul_montgomery(val2[i], val2[i - 1], d, mont, ctx))
118 goto err;
119 }
120 }
121
122 /* Now compute the power product, using independent windows. */
123 r_is_one = 1;
124 wvalue1 = 0; /* The 'value' of the first window */
125 wvalue2 = 0; /* The 'value' of the second window */
126 wpos1 = 0; /* If wvalue1 > 0, the bottom bit of the
127 * first window */
128 wpos2 = 0; /* If wvalue2 > 0, the bottom bit of the
129 * second window */
130
131 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
132 goto err;
133 for (b = bits - 1; b >= 0; b--) {
134 if (!r_is_one) {
135 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
136 goto err;
137 }
138
139 if (!wvalue1)
140 if (BN_is_bit_set(p1, b)) {
141 /*
142 * consider bits b-window1+1 .. b for this window
143 */
144 i = b - window1 + 1;
145 while (!BN_is_bit_set(p1, i)) /* works for i<0 */
146 i++;
147 wpos1 = i;
148 wvalue1 = 1;
149 for (i = b - 1; i >= wpos1; i--) {
150 wvalue1 <<= 1;
151 if (BN_is_bit_set(p1, i))
152 wvalue1++;
153 }
154 }
155
156 if (!wvalue2)
157 if (BN_is_bit_set(p2, b)) {
158 /*
159 * consider bits b-window2+1 .. b for this window
160 */
161 i = b - window2 + 1;
162 while (!BN_is_bit_set(p2, i))
163 i++;
164 wpos2 = i;
165 wvalue2 = 1;
166 for (i = b - 1; i >= wpos2; i--) {
167 wvalue2 <<= 1;
168 if (BN_is_bit_set(p2, i))
169 wvalue2++;
170 }
171 }
172
173 if (wvalue1 && b == wpos1) {
174 /* wvalue1 is odd and < 2^window1 */
175 if (!BN_mod_mul_montgomery(r, r, val1[wvalue1 >> 1], mont, ctx))
176 goto err;
177 wvalue1 = 0;
178 r_is_one = 0;
179 }
180
181 if (wvalue2 && b == wpos2) {
182 /* wvalue2 is odd and < 2^window2 */
183 if (!BN_mod_mul_montgomery(r, r, val2[wvalue2 >> 1], mont, ctx))
184 goto err;
185 wvalue2 = 0;
186 r_is_one = 0;
187 }
188 }
189 if (!BN_from_montgomery(rr, r, mont, ctx))
190 goto err;
191 ret = 1;
192 err:
193 if (in_mont == NULL)
194 BN_MONT_CTX_free(mont);
195 BN_CTX_end(ctx);
196 bn_check_top(rr);
197 return ret;
198 }
199