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-rw-r--r--src/lib/libcrypto/bn/bn_exp.c549
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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#define TABLE_SIZE 16
64
65/* slow but works */
66int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx)
67 {
68 BIGNUM *t;
69 int r=0;
70
71 bn_check_top(a);
72 bn_check_top(b);
73 bn_check_top(m);
74
75 t= &(ctx->bn[ctx->tos++]);
76 if (a == b)
77 { if (!BN_sqr(t,a,ctx)) goto err; }
78 else
79 { if (!BN_mul(t,a,b,ctx)) goto err; }
80 if (!BN_mod(ret,t,m,ctx)) goto err;
81 r=1;
82err:
83 ctx->tos--;
84 return(r);
85 }
86
87#if 0
88/* this one works - simple but works */
89int BN_mod_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BIGNUM *m, BN_CTX *ctx)
90 {
91 int i,bits,ret=0;
92 BIGNUM *v,*tmp;
93
94 v= &(ctx->bn[ctx->tos++]);
95 tmp= &(ctx->bn[ctx->tos++]);
96
97 if (BN_copy(v,a) == NULL) goto err;
98 bits=BN_num_bits(p);
99
100 if (BN_is_odd(p))
101 { if (BN_copy(r,a) == NULL) goto err; }
102 else { if (!BN_one(r)) goto err; }
103
104 for (i=1; i<bits; i++)
105 {
106 if (!BN_sqr(tmp,v,ctx)) goto err;
107 if (!BN_mod(v,tmp,m,ctx)) goto err;
108 if (BN_is_bit_set(p,i))
109 {
110 if (!BN_mul(tmp,r,v,ctx)) goto err;
111 if (!BN_mod(r,tmp,m,ctx)) goto err;
112 }
113 }
114 ret=1;
115err:
116 ctx->tos-=2;
117 return(ret);
118 }
119
120#endif
121
122/* this one works - simple but works */
123int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx)
124 {
125 int i,bits,ret=0,tos;
126 BIGNUM *v,*rr;
127
128 tos=ctx->tos;
129 v= &(ctx->bn[ctx->tos++]);
130 if ((r == a) || (r == p))
131 rr= &(ctx->bn[ctx->tos++]);
132 else
133 rr=r;
134
135 if (BN_copy(v,a) == NULL) goto err;
136 bits=BN_num_bits(p);
137
138 if (BN_is_odd(p))
139 { if (BN_copy(rr,a) == NULL) goto err; }
140 else { if (!BN_one(rr)) goto err; }
141
142 for (i=1; i<bits; i++)
143 {
144 if (!BN_sqr(v,v,ctx)) goto err;
145 if (BN_is_bit_set(p,i))
146 {
147 if (!BN_mul(rr,rr,v,ctx)) goto err;
148 }
149 }
150 ret=1;
151err:
152 ctx->tos=tos;
153 if (r != rr) BN_copy(r,rr);
154 return(ret);
155 }
156
157int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
158 BN_CTX *ctx)
159 {
160 int ret;
161
162 bn_check_top(a);
163 bn_check_top(p);
164 bn_check_top(m);
165
166#ifdef MONT_MUL_MOD
167 /* I have finally been able to take out this pre-condition of
168 * the top bit being set. It was caused by an error in BN_div
169 * with negatives. There was also another problem when for a^b%m
170 * a >= m. eay 07-May-97 */
171/* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
172
173 if (BN_is_odd(m))
174 { ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL); }
175 else
176#endif
177#ifdef RECP_MUL_MOD
178 { ret=BN_mod_exp_recp(r,a,p,m,ctx); }
179#else
180 { ret=BN_mod_exp_simple(r,a,p,m,ctx); }
181#endif
182
183 return(ret);
184 }
185
186/* #ifdef RECP_MUL_MOD */
187int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
188 const BIGNUM *m, BN_CTX *ctx)
189 {
190 int i,j,bits,ret=0,wstart,wend,window,wvalue;
191 int start=1,ts=0;
192 BIGNUM *aa;
193 BIGNUM val[TABLE_SIZE];
194 BN_RECP_CTX recp;
195
196 aa= &(ctx->bn[ctx->tos++]);
197 bits=BN_num_bits(p);
198
199 if (bits == 0)
200 {
201 BN_one(r);
202 return(1);
203 }
204 BN_RECP_CTX_init(&recp);
205 if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;
206
207 BN_init(&(val[0]));
208 ts=1;
209
210 if (!BN_mod(&(val[0]),a,m,ctx)) goto err; /* 1 */
211 if (!BN_mod_mul_reciprocal(aa,&(val[0]),&(val[0]),&recp,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 BN_init(&val[i]);
227 if (!BN_mod_mul_reciprocal(&(val[i]),&(val[i-1]),aa,&recp,ctx))
228 goto err;
229 }
230 ts=i;
231
232 start=1; /* This is used to avoid multiplication etc
233 * when there is only the value '1' in the
234 * buffer. */
235 wvalue=0; /* The 'value' of the window */
236 wstart=bits-1; /* The top bit of the window */
237 wend=0; /* The bottom bit of the window */
238
239 if (!BN_one(r)) goto err;
240
241 for (;;)
242 {
243 if (BN_is_bit_set(p,wstart) == 0)
244 {
245 if (!start)
246 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
247 goto err;
248 if (wstart == 0) break;
249 wstart--;
250 continue;
251 }
252 /* We now have wstart on a 'set' bit, we now need to work out
253 * how bit a window to do. To do this we need to scan
254 * forward until the last set bit before the end of the
255 * window */
256 j=wstart;
257 wvalue=1;
258 wend=0;
259 for (i=1; i<window; i++)
260 {
261 if (wstart-i < 0) break;
262 if (BN_is_bit_set(p,wstart-i))
263 {
264 wvalue<<=(i-wend);
265 wvalue|=1;
266 wend=i;
267 }
268 }
269
270 /* wend is the size of the current window */
271 j=wend+1;
272 /* add the 'bytes above' */
273 if (!start)
274 for (i=0; i<j; i++)
275 {
276 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
277 goto err;
278 }
279
280 /* wvalue will be an odd number < 2^window */
281 if (!BN_mod_mul_reciprocal(r,r,&(val[wvalue>>1]),&recp,ctx))
282 goto err;
283
284 /* move the 'window' down further */
285 wstart-=wend+1;
286 wvalue=0;
287 start=0;
288 if (wstart < 0) break;
289 }
290 ret=1;
291err:
292 ctx->tos--;
293 for (i=0; i<ts; i++)
294 BN_clear_free(&(val[i]));
295 BN_RECP_CTX_free(&recp);
296 return(ret);
297 }
298/* #endif */
299
300/* #ifdef MONT_MUL_MOD */
301int BN_mod_exp_mont(BIGNUM *rr, BIGNUM *a, const BIGNUM *p,
302 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
303 {
304 int i,j,bits,ret=0,wstart,wend,window,wvalue;
305 int start=1,ts=0;
306 BIGNUM *d,*r;
307 BIGNUM *aa;
308 BIGNUM val[TABLE_SIZE];
309 BN_MONT_CTX *mont=NULL;
310
311 bn_check_top(a);
312 bn_check_top(p);
313 bn_check_top(m);
314
315 if (!(m->d[0] & 1))
316 {
317 BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
318 return(0);
319 }
320 d= &(ctx->bn[ctx->tos++]);
321 r= &(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 BN_init(&val[0]);
343 ts=1;
344 if (BN_ucmp(a,m) >= 0)
345 {
346 BN_mod(&(val[0]),a,m,ctx);
347 aa= &(val[0]);
348 }
349 else
350 aa=a;
351 if (!BN_to_montgomery(&(val[0]),aa,mont,ctx)) goto err; /* 1 */
352 if (!BN_mod_mul_montgomery(d,&(val[0]),&(val[0]),mont,ctx)) goto err; /* 2 */
353
354 if (bits <= 20) /* This is probably 3 or 0x10001, so just do singles */
355 window=1;
356 else if (bits >= 256)
357 window=5; /* max size of window */
358 else if (bits >= 128)
359 window=4;
360 else
361 window=3;
362
363 j=1<<(window-1);
364 for (i=1; i<j; i++)
365 {
366 BN_init(&(val[i]));
367 if (!BN_mod_mul_montgomery(&(val[i]),&(val[i-1]),d,mont,ctx))
368 goto err;
369 }
370 ts=i;
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(rr,r,mont,ctx);
432 ret=1;
433err:
434 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
435 ctx->tos-=2;
436 for (i=0; i<ts; i++)
437 BN_clear_free(&(val[i]));
438 return(ret);
439 }
440/* #endif */
441
442/* The old fallback, simple version :-) */
443int BN_mod_exp_simple(BIGNUM *r, BIGNUM *a, BIGNUM *p, BIGNUM *m,
444 BN_CTX *ctx)
445 {
446 int i,j,bits,ret=0,wstart,wend,window,wvalue,ts=0;
447 int start=1;
448 BIGNUM *d;
449 BIGNUM val[TABLE_SIZE];
450
451 d= &(ctx->bn[ctx->tos++]);
452 bits=BN_num_bits(p);
453
454 if (bits == 0)
455 {
456 BN_one(r);
457 return(1);
458 }
459
460 BN_init(&(val[0]));
461 ts=1;
462 if (!BN_mod(&(val[0]),a,m,ctx)) goto err; /* 1 */
463 if (!BN_mod_mul(d,&(val[0]),&(val[0]),m,ctx))
464 goto err; /* 2 */
465
466 if (bits <= 17) /* This is probably 3 or 0x10001, so just do singles */
467 window=1;
468 else if (bits >= 256)
469 window=5; /* max size of window */
470 else if (bits >= 128)
471 window=4;
472 else
473 window=3;
474
475 j=1<<(window-1);
476 for (i=1; i<j; i++)
477 {
478 BN_init(&(val[i]));
479 if (!BN_mod_mul(&(val[i]),&(val[i-1]),d,m,ctx))
480 goto err;
481 }
482 ts=i;
483
484 start=1; /* This is used to avoid multiplication etc
485 * when there is only the value '1' in the
486 * buffer. */
487 wvalue=0; /* The 'value' of the window */
488 wstart=bits-1; /* The top bit of the window */
489 wend=0; /* The bottom bit of the window */
490
491 if (!BN_one(r)) goto err;
492
493 for (;;)
494 {
495 if (BN_is_bit_set(p,wstart) == 0)
496 {
497 if (!start)
498 if (!BN_mod_mul(r,r,r,m,ctx))
499 goto err;
500 if (wstart == 0) break;
501 wstart--;
502 continue;
503 }
504 /* We now have wstart on a 'set' bit, we now need to work out
505 * how bit a window to do. To do this we need to scan
506 * forward until the last set bit before the end of the
507 * window */
508 j=wstart;
509 wvalue=1;
510 wend=0;
511 for (i=1; i<window; i++)
512 {
513 if (wstart-i < 0) break;
514 if (BN_is_bit_set(p,wstart-i))
515 {
516 wvalue<<=(i-wend);
517 wvalue|=1;
518 wend=i;
519 }
520 }
521
522 /* wend is the size of the current window */
523 j=wend+1;
524 /* add the 'bytes above' */
525 if (!start)
526 for (i=0; i<j; i++)
527 {
528 if (!BN_mod_mul(r,r,r,m,ctx))
529 goto err;
530 }
531
532 /* wvalue will be an odd number < 2^window */
533 if (!BN_mod_mul(r,r,&(val[wvalue>>1]),m,ctx))
534 goto err;
535
536 /* move the 'window' down further */
537 wstart-=wend+1;
538 wvalue=0;
539 start=0;
540 if (wstart < 0) break;
541 }
542 ret=1;
543err:
544 ctx->tos--;
545 for (i=0; i<ts; i++)
546 BN_clear_free(&(val[i]));
547 return(ret);
548 }
549
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