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bn_exp2.c
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1 /* crypto/bn/bn_exp2.c */
2 /* Copyright (C) 1995-1998 Eric Young ([email protected])
3  * All rights reserved.
4  *
5  * This package is an SSL implementation written
6  * by Eric Young ([email protected]).
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 ([email protected]).
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 ([email protected])"
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 ([email protected])"
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  * [email protected].
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  * ([email protected]). This product includes software written by Tim
108  * Hudson ([email protected]).
109  *
110  */
111 
112 #include <stdio.h>
113 #if defined( INC_ALL )
114  #include "bn_lcl.h"
115 #else
116  #include "bn/bn_lcl.h"
117 #endif /* Compiler-specific includes */
118 
119 #define TABLE_SIZE 32
120 
121 int BN_mod_exp2_mont(BIGNUM *rr, const BIGNUM *a1, const BIGNUM *p1,
122  const BIGNUM *a2, const BIGNUM *p2, const BIGNUM *m,
123  BN_CTX *ctx, BN_MONT_CTX *in_mont)
124  {
125  int i,j,bits,b,bits1,bits2,ret=0,wpos1,wpos2,window1,window2,wvalue1,wvalue2;
126  int r_is_one=1;
127  BIGNUM *d,*r;
128  const BIGNUM *a_mod_m;
129  /* Tables of variables obtained from 'ctx' */
130  BIGNUM *val1[TABLE_SIZE], *val2[TABLE_SIZE];
131  BN_MONT_CTX *mont=NULL;
132 
133  bn_check_top(a1);
134  bn_check_top(p1);
135  bn_check_top(a2);
136  bn_check_top(p2);
137  bn_check_top(m);
138 
139  if (!(m->d[0] & 1))
140  {
141  BNerr(BN_F_BN_MOD_EXP2_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
142  return(0);
143  }
144  bits1=BN_num_bits(p1);
145  bits2=BN_num_bits(p2);
146  if ((bits1 == 0) && (bits2 == 0))
147  {
148  ret = BN_one(rr);
149  return ret;
150  }
151 
152  bits=(bits1 > bits2)?bits1:bits2;
153 
154  BN_CTX_start(ctx);
155  d = BN_CTX_get(ctx);
156  r = BN_CTX_get(ctx);
157  val1[0] = BN_CTX_get(ctx);
158  val2[0] = BN_CTX_get(ctx);
159  if(!d || !r || !val1[0] || !val2[0]) goto err;
160 
161  if (in_mont != NULL)
162  mont=in_mont;
163  else
164  {
165  if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
166  if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
167  }
168 
169  window1 = BN_window_bits_for_exponent_size(bits1);
170  window2 = BN_window_bits_for_exponent_size(bits2);
171 
172  /*
173  * Build table for a1: val1[i] := a1^(2*i + 1) mod m for i = 0 .. 2^(window1-1)
174  */
175  if (a1->neg || BN_ucmp(a1,m) >= 0)
176  {
177  if (!BN_mod(val1[0],a1,m,ctx))
178  goto err;
179  a_mod_m = val1[0];
180  }
181  else
182  a_mod_m = a1;
183  if (BN_is_zero(a_mod_m))
184  {
185  BN_zero(rr);
186  ret = 1;
187  goto err;
188  }
189 
190  if (!BN_to_montgomery(val1[0],a_mod_m,mont,ctx)) goto err;
191  if (window1 > 1)
192  {
193  if (!BN_mod_mul_montgomery(d,val1[0],val1[0],mont,ctx)) goto err;
194 
195  j=1<<(window1-1);
196  for (i=1; i<j; i++)
197  {
198  if(((val1[i] = BN_CTX_get(ctx)) == NULL) ||
199  !BN_mod_mul_montgomery(val1[i],val1[i-1],
200  d,mont,ctx))
201  goto err;
202  }
203  }
204 
205 
206  /*
207  * Build table for a2: val2[i] := a2^(2*i + 1) mod m for i = 0 .. 2^(window2-1)
208  */
209  if (a2->neg || BN_ucmp(a2,m) >= 0)
210  {
211  if (!BN_mod(val2[0],a2,m,ctx))
212  goto err;
213  a_mod_m = val2[0];
214  }
215  else
216  a_mod_m = a2;
217  if (BN_is_zero(a_mod_m))
218  {
219  BN_zero(rr);
220  ret = 1;
221  goto err;
222  }
223  if (!BN_to_montgomery(val2[0],a_mod_m,mont,ctx)) goto err;
224  if (window2 > 1)
225  {
226  if (!BN_mod_mul_montgomery(d,val2[0],val2[0],mont,ctx)) goto err;
227 
228  j=1<<(window2-1);
229  for (i=1; i<j; i++)
230  {
231  if(((val2[i] = BN_CTX_get(ctx)) == NULL) ||
232  !BN_mod_mul_montgomery(val2[i],val2[i-1],
233  d,mont,ctx))
234  goto err;
235  }
236  }
237 
238 
239  /* Now compute the power product, using independent windows. */
240  r_is_one=1;
241  wvalue1=0; /* The 'value' of the first window */
242  wvalue2=0; /* The 'value' of the second window */
243  wpos1=0; /* If wvalue1 > 0, the bottom bit of the first window */
244  wpos2=0; /* If wvalue2 > 0, the bottom bit of the second window */
245 
246  if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
247  for (b=bits-1; b>=0; b--)
248  {
249  if (!r_is_one)
250  {
251  if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
252  goto err;
253  }
254 
255  if (!wvalue1)
256  if (BN_is_bit_set(p1, b))
257  {
258  /* consider bits b-window1+1 .. b for this window */
259  i = b-window1+1;
260  while (!BN_is_bit_set(p1, i)) /* works for i<0 */
261  i++;
262  wpos1 = i;
263  wvalue1 = 1;
264  for (i = b-1; i >= wpos1; i--)
265  {
266  wvalue1 <<= 1;
267  if (BN_is_bit_set(p1, i))
268  wvalue1++;
269  }
270  }
271 
272  if (!wvalue2)
273  if (BN_is_bit_set(p2, b))
274  {
275  /* consider bits b-window2+1 .. b for this window */
276  i = b-window2+1;
277  while (!BN_is_bit_set(p2, i))
278  i++;
279  wpos2 = i;
280  wvalue2 = 1;
281  for (i = b-1; i >= wpos2; i--)
282  {
283  wvalue2 <<= 1;
284  if (BN_is_bit_set(p2, i))
285  wvalue2++;
286  }
287  }
288 
289  if (wvalue1 && b == wpos1)
290  {
291  /* wvalue1 is odd and < 2^window1 */
292  if (!BN_mod_mul_montgomery(r,r,val1[wvalue1>>1],mont,ctx))
293  goto err;
294  wvalue1 = 0;
295  r_is_one = 0;
296  }
297 
298  if (wvalue2 && b == wpos2)
299  {
300  /* wvalue2 is odd and < 2^window2 */
301  if (!BN_mod_mul_montgomery(r,r,val2[wvalue2>>1],mont,ctx))
302  goto err;
303  wvalue2 = 0;
304  r_is_one = 0;
305  }
306  }
307  BN_from_montgomery(rr,r,mont,ctx);
308  ret=1;
309 err:
310  if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
311  BN_CTX_end(ctx);
312  bn_check_top(rr);
313  return(ret);
314  }
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