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-rw-r--r--src/lib/libcrypto/bn/bn_exp.c553
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diff --git a/src/lib/libcrypto/bn/bn_exp.c b/src/lib/libcrypto/bn/bn_exp.c
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1/* crypto/bn/bn_exp.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#include <stdio.h>
60#include "cryptlib.h"
61#include "bn_lcl.h"
62
63/* slow but works */
64int BN_mod_mul(ret, a, b, m, ctx)
65BIGNUM *ret;
66BIGNUM *a;
67BIGNUM *b;
68BIGNUM *m;
69BN_CTX *ctx;
70 {
71 BIGNUM *t;
72 int r=0;
73
74 t=ctx->bn[ctx->tos++];
75 if (a == b)
76 { if (!BN_sqr(t,a,ctx)) goto err; }
77 else
78 { if (!BN_mul(t,a,b)) goto err; }
79 if (!BN_mod(ret,t,m,ctx)) goto err;
80 r=1;
81err:
82 ctx->tos--;
83 return(r);
84 }
85
86#if 0
87/* this one works - simple but works */
88int BN_mod_exp(r,a,p,m,ctx)
89BIGNUM *r,*a,*p,*m;
90BN_CTX *ctx;
91 {
92 int i,bits,ret=0;
93 BIGNUM *v,*tmp;
94
95 v=ctx->bn[ctx->tos++];
96 tmp=ctx->bn[ctx->tos++];
97
98 if (BN_copy(v,a) == NULL) goto err;
99 bits=BN_num_bits(p);
100
101 if (BN_is_odd(p))
102 { if (BN_copy(r,a) == NULL) goto err; }
103 else { if (BN_one(r)) goto err; }
104
105 for (i=1; i<bits; i++)
106 {
107 if (!BN_sqr(tmp,v,ctx)) goto err;
108 if (!BN_mod(v,tmp,m,ctx)) goto err;
109 if (BN_is_bit_set(p,i))
110 {
111 if (!BN_mul(tmp,r,v)) goto err;
112 if (!BN_mod(r,tmp,m,ctx)) goto err;
113 }
114 }
115 ret=1;
116err:
117 ctx->tos-=2;
118 return(ret);
119 }
120
121#endif
122
123/* this one works - simple but works */
124int BN_exp(r,a,p,ctx)
125BIGNUM *r,*a,*p;
126BN_CTX *ctx;
127 {
128 int i,bits,ret=0;
129 BIGNUM *v,*tmp;
130
131 v=ctx->bn[ctx->tos++];
132 tmp=ctx->bn[ctx->tos++];
133
134 if (BN_copy(v,a) == NULL) goto err;
135 bits=BN_num_bits(p);
136
137 if (BN_is_odd(p))
138 { if (BN_copy(r,a) == NULL) goto err; }
139 else { if (BN_one(r)) goto err; }
140
141 for (i=1; i<bits; i++)
142 {
143 if (!BN_sqr(tmp,v,ctx)) goto err;
144 if (BN_is_bit_set(p,i))
145 {
146 if (!BN_mul(tmp,r,v)) goto err;
147 }
148 }
149 ret=1;
150err:
151 ctx->tos-=2;
152 return(ret);
153 }
154
155int BN_mod_exp(r,a,p,m,ctx)
156BIGNUM *r;
157BIGNUM *a;
158BIGNUM *p;
159BIGNUM *m;
160BN_CTX *ctx;
161 {
162 int ret;
163
164#ifdef MONT_MUL_MOD
165 /* I have finally been able to take out this pre-condition of
166 * the top bit being set. It was caused by an error in BN_div
167 * with negatives. There was also another problem when for a^b%m
168 * a >= m. eay 07-May-97 */
169/* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
170
171 if (BN_is_odd(m))
172 { ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL); }
173 else
174#endif
175#ifdef RECP_MUL_MOD
176 { ret=BN_mod_exp_recp(r,a,p,m,ctx); }
177#else
178 { ret=BN_mod_exp_simple(r,a,p,m,ctx); }
179#endif
180
181 return(ret);
182 }
183
184/* #ifdef RECP_MUL_MOD */
185int BN_mod_exp_recp(r,a,p,m,ctx)
186BIGNUM *r;
187BIGNUM *a;
188BIGNUM *p;
189BIGNUM *m;
190BN_CTX *ctx;
191 {
192 int nb,i,j,bits,ret=0,wstart,wend,window,wvalue;
193 int start=1;
194 BIGNUM *d,*aa;
195 BIGNUM *val[16];
196
197 d=ctx->bn[ctx->tos++];
198 aa=ctx->bn[ctx->tos++];
199 bits=BN_num_bits(p);
200
201 if (bits == 0)
202 {
203 BN_one(r);
204 return(1);
205 }
206 nb=BN_reciprocal(d,m,ctx);
207 if (nb == -1) goto err;
208
209 val[0]=BN_new();
210 if (!BN_mod(val[0],a,m,ctx)) goto err; /* 1 */
211 if (!BN_mod_mul_reciprocal(aa,val[0],val[0],m,d,nb,ctx))
212 goto err; /* 2 */
213
214 if (bits <= 17) /* This is probably 3 or 0x10001, so just do singles */
215 window=1;
216 else if (bits >= 256)
217 window=5; /* max size of window */
218 else if (bits >= 128)
219 window=4;
220 else
221 window=3;
222
223 j=1<<(window-1);
224 for (i=1; i<j; i++)
225 {
226 val[i]=BN_new();
227 if (!BN_mod_mul_reciprocal(val[i],val[i-1],aa,m,d,nb,ctx))
228 goto err;
229 }
230 for (; i<16; i++)
231 val[i]=NULL;
232
233 start=1; /* This is used to avoid multiplication etc
234 * when there is only the value '1' in the
235 * buffer. */
236 wvalue=0; /* The 'value' of the window */
237 wstart=bits-1; /* The top bit of the window */
238 wend=0; /* The bottom bit of the window */
239
240 if (!BN_one(r)) goto err;
241
242 for (;;)
243 {
244 if (BN_is_bit_set(p,wstart) == 0)
245 {
246 if (!start)
247 if (!BN_mod_mul_reciprocal(r,r,r,m,d,nb,ctx))
248 goto err;
249 if (wstart == 0) break;
250 wstart--;
251 continue;
252 }
253 /* We now have wstart on a 'set' bit, we now need to work out
254 * how bit a window to do. To do this we need to scan
255 * forward until the last set bit before the end of the
256 * window */
257 j=wstart;
258 wvalue=1;
259 wend=0;
260 for (i=1; i<window; i++)
261 {
262 if (wstart-i < 0) break;
263 if (BN_is_bit_set(p,wstart-i))
264 {
265 wvalue<<=(i-wend);
266 wvalue|=1;
267 wend=i;
268 }
269 }
270
271 /* wend is the size of the current window */
272 j=wend+1;
273 /* add the 'bytes above' */
274 if (!start)
275 for (i=0; i<j; i++)
276 {
277 if (!BN_mod_mul_reciprocal(r,r,r,m,d,nb,ctx))
278 goto err;
279 }
280
281 /* wvalue will be an odd number < 2^window */
282 if (!BN_mod_mul_reciprocal(r,r,val[wvalue>>1],m,d,nb,ctx))
283 goto err;
284
285 /* move the 'window' down further */
286 wstart-=wend+1;
287 wvalue=0;
288 start=0;
289 if (wstart < 0) break;
290 }
291 ret=1;
292err:
293 ctx->tos-=2;
294 for (i=0; i<16; i++)
295 if (val[i] != NULL) BN_clear_free(val[i]);
296 return(ret);
297 }
298/* #endif */
299
300/* #ifdef MONT_MUL_MOD */
301int BN_mod_exp_mont(r,a,p,m,ctx,in_mont)
302BIGNUM *r;
303BIGNUM *a;
304BIGNUM *p;
305BIGNUM *m;
306BN_CTX *ctx;
307BN_MONT_CTX *in_mont;
308 {
309#define TABLE_SIZE 16
310 int i,j,bits,ret=0,wstart,wend,window,wvalue;
311 int start=1;
312 BIGNUM *d,*aa;
313 BIGNUM *val[TABLE_SIZE];
314 BN_MONT_CTX *mont=NULL;
315
316 if (!(m->d[0] & 1))
317 {
318 BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
319 return(0);
320 }
321 d=ctx->bn[ctx->tos++];
322 bits=BN_num_bits(p);
323 if (bits == 0)
324 {
325 BN_one(r);
326 return(1);
327 }
328
329 /* If this is not done, things will break in the montgomery
330 * part */
331
332#if 1
333 if (in_mont != NULL)
334 mont=in_mont;
335 else
336#endif
337 {
338 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
339 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
340 }
341
342 val[0]=BN_new();
343 if (BN_ucmp(a,m) >= 0)
344 {
345 BN_mod(val[0],a,m,ctx);
346 aa=val[0];
347 }
348 else
349 aa=a;
350 if (!BN_to_montgomery(val[0],aa,mont,ctx)) goto err; /* 1 */
351 if (!BN_mod_mul_montgomery(d,val[0],val[0],mont,ctx)) goto err; /* 2 */
352
353 if (bits <= 20) /* This is probably 3 or 0x10001, so just do singles */
354 window=1;
355 else if (bits > 250)
356 window=5; /* max size of window */
357 else if (bits >= 120)
358 window=4;
359 else
360 window=3;
361
362 j=1<<(window-1);
363 for (i=1; i<j; i++)
364 {
365 val[i]=BN_new();
366 if (!BN_mod_mul_montgomery(val[i],val[i-1],d,mont,ctx))
367 goto err;
368 }
369 for (; i<TABLE_SIZE; i++)
370 val[i]=NULL;
371
372 start=1; /* This is used to avoid multiplication etc
373 * when there is only the value '1' in the
374 * buffer. */
375 wvalue=0; /* The 'value' of the window */
376 wstart=bits-1; /* The top bit of the window */
377 wend=0; /* The bottom bit of the window */
378
379 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
380 for (;;)
381 {
382 if (BN_is_bit_set(p,wstart) == 0)
383 {
384 if (!start)
385 {
386 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
387 goto err;
388 }
389 if (wstart == 0) break;
390 wstart--;
391 continue;
392 }
393 /* We now have wstart on a 'set' bit, we now need to work out
394 * how bit a window to do. To do this we need to scan
395 * forward until the last set bit before the end of the
396 * window */
397 j=wstart;
398 wvalue=1;
399 wend=0;
400 for (i=1; i<window; i++)
401 {
402 if (wstart-i < 0) break;
403 if (BN_is_bit_set(p,wstart-i))
404 {
405 wvalue<<=(i-wend);
406 wvalue|=1;
407 wend=i;
408 }
409 }
410
411 /* wend is the size of the current window */
412 j=wend+1;
413 /* add the 'bytes above' */
414 if (!start)
415 for (i=0; i<j; i++)
416 {
417 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
418 goto err;
419 }
420
421 /* wvalue will be an odd number < 2^window */
422 if (!BN_mod_mul_montgomery(r,r,val[wvalue>>1],mont,ctx))
423 goto err;
424
425 /* move the 'window' down further */
426 wstart-=wend+1;
427 wvalue=0;
428 start=0;
429 if (wstart < 0) break;
430 }
431 BN_from_montgomery(r,r,mont,ctx);
432 ret=1;
433err:
434 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
435 ctx->tos--;
436 for (i=0; i<TABLE_SIZE; i++)
437 if (val[i] != NULL) BN_clear_free(val[i]);
438 return(ret);
439 }
440/* #endif */
441
442/* The old fallback, simple version :-) */
443int BN_mod_exp_simple(r,a,p,m,ctx)
444BIGNUM *r;
445BIGNUM *a;
446BIGNUM *p;
447BIGNUM *m;
448BN_CTX *ctx;
449 {
450 int i,j,bits,ret=0,wstart,wend,window,wvalue;
451 int start=1;
452 BIGNUM *d;
453 BIGNUM *val[16];
454
455 d=ctx->bn[ctx->tos++];
456 bits=BN_num_bits(p);
457
458 if (bits == 0)
459 {
460 BN_one(r);
461 return(1);
462 }
463
464 val[0]=BN_new();
465 if (!BN_mod(val[0],a,m,ctx)) goto err; /* 1 */
466 if (!BN_mod_mul(d,val[0],val[0],m,ctx))
467 goto err; /* 2 */
468
469 if (bits <= 17) /* This is probably 3 or 0x10001, so just do singles */
470 window=1;
471 else if (bits >= 256)
472 window=5; /* max size of window */
473 else if (bits >= 128)
474 window=4;
475 else
476 window=3;
477
478 j=1<<(window-1);
479 for (i=1; i<j; i++)
480 {
481 val[i]=BN_new();
482 if (!BN_mod_mul(val[i],val[i-1],d,m,ctx))
483 goto err;
484 }
485 for (; i<16; i++)
486 val[i]=NULL;
487
488 start=1; /* This is used to avoid multiplication etc
489 * when there is only the value '1' in the
490 * buffer. */
491 wvalue=0; /* The 'value' of the window */
492 wstart=bits-1; /* The top bit of the window */
493 wend=0; /* The bottom bit of the window */
494
495 if (!BN_one(r)) goto err;
496
497 for (;;)
498 {
499 if (BN_is_bit_set(p,wstart) == 0)
500 {
501 if (!start)
502 if (!BN_mod_mul(r,r,r,m,ctx))
503 goto err;
504 if (wstart == 0) break;
505 wstart--;
506 continue;
507 }
508 /* We now have wstart on a 'set' bit, we now need to work out
509 * how bit a window to do. To do this we need to scan
510 * forward until the last set bit before the end of the
511 * window */
512 j=wstart;
513 wvalue=1;
514 wend=0;
515 for (i=1; i<window; i++)
516 {
517 if (wstart-i < 0) break;
518 if (BN_is_bit_set(p,wstart-i))
519 {
520 wvalue<<=(i-wend);
521 wvalue|=1;
522 wend=i;
523 }
524 }
525
526 /* wend is the size of the current window */
527 j=wend+1;
528 /* add the 'bytes above' */
529 if (!start)
530 for (i=0; i<j; i++)
531 {
532 if (!BN_mod_mul(r,r,r,m,ctx))
533 goto err;
534 }
535
536 /* wvalue will be an odd number < 2^window */
537 if (!BN_mod_mul(r,r,val[wvalue>>1],m,ctx))
538 goto err;
539
540 /* move the 'window' down further */
541 wstart-=wend+1;
542 wvalue=0;
543 start=0;
544 if (wstart < 0) break;
545 }
546 ret=1;
547err:
548 ctx->tos--;
549 for (i=0; i<16; i++)
550 if (val[i] != NULL) BN_clear_free(val[i]);
551 return(ret);
552 }
553
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