1 /* crypto/bn/bn_exp2.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
3 * All rights reserved.
4 *
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
8 *
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
15 *
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
22 *
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
25 * are met:
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
40 *
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
51 * SUCH DAMAGE.
52 *
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
57 */
58 /* ====================================================================
59 * Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved.
60 *
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
63 * are met:
64 *
65 * 1. Redistributions of source code must retain the above copyright
66 * notice, this list of conditions and the following disclaimer.
67 *
68 * 2. Redistributions in binary form must reproduce the above copyright
69 * notice, this list of conditions and the following disclaimer in
70 * the documentation and/or other materials provided with the
71 * distribution.
72 *
73 * 3. All advertising materials mentioning features or use of this
74 * software must display the following acknowledgment:
75 * "This product includes software developed by the OpenSSL Project
76 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
77 *
78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
79 * endorse or promote products derived from this software without
80 * prior written permission. For written permission, please contact
81 * openssl-core@openssl.org.
82 *
83 * 5. Products derived from this software may not be called "OpenSSL"
84 * nor may "OpenSSL" appear in their names without prior written
85 * permission of the OpenSSL Project.
86 *
87 * 6. Redistributions of any form whatsoever must retain the following
88 * acknowledgment:
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
91 *
92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
95 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
103 * OF THE POSSIBILITY OF SUCH DAMAGE.
104 * ====================================================================
105 *
106 * This product includes cryptographic software written by Eric Young
107 * (eay@cryptsoft.com). This product includes software written by Tim
108 * Hudson (tjh@cryptsoft.com).
109 *
110 */
111
112 #include <stdio.h>
113 #include "cryptlib.h"
114 #include "bn_lcl.h"
115
116 #define TABLE_SIZE 32
117
118 int BN_mod_exp2_mont(BIGNUM *rr, const BIGNUM *a1, const BIGNUM *p1,
119 const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m,
120 BN_CTX *ctx, BN_MONT_CTX *in_mont)
121 {
122 int i,j,bits,b,bits1,bits2,ret=0,wpos1,wpos2,window1,window2,wvalue1,wvalue2;
123 int r_is_one=1;
124 BIGNUM *d,*r;
125 const BIGNUM *a_mod_m;
126 /* Tables of variables obtained from 'ctx' */
127 BIGNUM *val1[TABLE_SIZE], *val2[TABLE_SIZE];
128 BN_MONT_CTX *mont=NULL;
129
130 bn_check_top(a1);
131 bn_check_top(p1);
132 bn_check_top(a2);
133 bn_check_top(p2);
134 bn_check_top(m);
135
136 if (!(m->d[0] & 1))
137 {
138 BNerr(BN_F_BN_MOD_EXP2_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
139 return(0);
140 }
141 bits1=BN_num_bits(p1);
142 bits2=BN_num_bits(p2);
143 if ((bits1 == 0) && (bits2 == 0))
144 {
145 ret = BN_one(rr);
146 return ret;
147 }
148
149 bits=(bits1 > bits2)?bits1:bits2;
150
151 BN_CTX_start(ctx);
152 d = BN_CTX_get(ctx);
153 r = BN_CTX_get(ctx);
154 val1[0] = BN_CTX_get(ctx);
155 val2[0] = BN_CTX_get(ctx);
156 if(!d || !r || !val1[0] || !val2[0]) goto err;
157
158 if (in_mont != NULL)
159 mont=in_mont;
160 else
161 {
162 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
163 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
164 }
165
166 window1 = BN_window_bits_for_exponent_size(bits1);
167 window2 = BN_window_bits_for_exponent_size(bits2);
168
169 /*
170 * Build table for a1: val1[i] := a1^(2*i + 1) mod m for i = 0 .. 2^(window1-1)
171 */
172 if (a1->neg || BN_ucmp(a1,m) >= 0)
173 {
174 if (!BN_mod(val1[0],a1,m,ctx))
175 goto err;
176 a_mod_m = val1[0];
177 }
178 else
179 a_mod_m = a1;
180 if (BN_is_zero(a_mod_m))
181 {
182 BN_zero(rr);
183 ret = 1;
184 goto err;
185 }
186
187 if (!BN_to_montgomery(val1[0],a_mod_m,mont,ctx)) goto err;
188 if (window1 > 1)
189 {
190 if (!BN_mod_mul_montgomery(d,val1[0],val1[0],mont,ctx)) goto err;
191
192 j=1<<(window1-1);
193 for (i=1; i<j; i++)
194 {
195 if(((val1[i] = BN_CTX_get(ctx)) == NULL) ||
196 !BN_mod_mul_montgomery(val1[i],val1[i-1],
197 d,mont,ctx))
198 goto err;
199 }
200 }
201
202
203 /*
204 * Build table for a2: val2[i] := a2^(2*i + 1) mod m for i = 0 .. 2^(window2-1)
205 */
206 if (a2->neg || BN_ucmp(a2,m) >= 0)
207 {
208 if (!BN_mod(val2[0],a2,m,ctx))
209 goto err;
210 a_mod_m = val2[0];
211 }
212 else
213 a_mod_m = a2;
214 if (BN_is_zero(a_mod_m))
215 {
216 BN_zero(rr);
217 ret = 1;
218 goto err;
219 }
220 if (!BN_to_montgomery(val2[0],a_mod_m,mont,ctx)) goto err;
221 if (window2 > 1)
222 {
223 if (!BN_mod_mul_montgomery(d,val2[0],val2[0],mont,ctx)) goto err;
224
225 j=1<<(window2-1);
226 for (i=1; i<j; i++)
227 {
228 if(((val2[i] = BN_CTX_get(ctx)) == NULL) ||
229 !BN_mod_mul_montgomery(val2[i],val2[i-1],
230 d,mont,ctx))
231 goto err;
232 }
233 }
234
235
236 /* Now compute the power product, using independent windows. */
237 r_is_one=1;
238 wvalue1=0; /* The 'value' of the first window */
239 wvalue2=0; /* The 'value' of the second window */
240 wpos1=0; /* If wvalue1 > 0, the bottom bit of the first window */
241 wpos2=0; /* If wvalue2 > 0, the bottom bit of the second window */
242
243 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
244 for (b=bits-1; b>=0; b--)
245 {
246 if (!r_is_one)
247 {
248 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
249 goto err;
250 }
251
252 if (!wvalue1)
253 if (BN_is_bit_set(p1, b))
254 {
255 /* consider bits b-window1+1 .. b for this window */
256 i = b-window1+1;
257 while (!BN_is_bit_set(p1, i)) /* works for i<0 */
258 i++;
259 wpos1 = i;
260 wvalue1 = 1;
261 for (i = b-1; i >= wpos1; i--)
262 {
263 wvalue1 <<= 1;
264 if (BN_is_bit_set(p1, i))
265 wvalue1++;
266 }
267 }
268
269 if (!wvalue2)
270 if (BN_is_bit_set(p2, b))
271 {
272 /* consider bits b-window2+1 .. b for this window */
273 i = b-window2+1;
274 while (!BN_is_bit_set(p2, i))
275 i++;
276 wpos2 = i;
277 wvalue2 = 1;
278 for (i = b-1; i >= wpos2; i--)
279 {
280 wvalue2 <<= 1;
281 if (BN_is_bit_set(p2, i))
282 wvalue2++;
283 }
284 }
285
286 if (wvalue1 && b == wpos1)
287 {
288 /* wvalue1 is odd and < 2^window1 */
289 if (!BN_mod_mul_montgomery(r,r,val1[wvalue1>>1],mont,ctx))
290 goto err;
291 wvalue1 = 0;
292 r_is_one = 0;
293 }
294
295 if (wvalue2 && b == wpos2)
296 {
297 /* wvalue2 is odd and < 2^window2 */
298 if (!BN_mod_mul_montgomery(r,r,val2[wvalue2>>1],mont,ctx))
299 goto err;
300 wvalue2 = 0;
301 r_is_one = 0;
302 }
303 }
304 if (!BN_from_montgomery(rr,r,mont,ctx))
305 goto err;
306 ret=1;
307 err:
308 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
309 BN_CTX_end(ctx);
310 bn_check_top(rr);
311 return(ret);
312 }