1 /* crypto/bn/bn_exp.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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.
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).
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.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
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)"
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
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.]
64 int BN_mod_mul(ret, a, b, m, ctx)
74 t=ctx->bn[ctx->tos++];
76 { if (!BN_sqr(t,a,ctx)) goto err; }
78 { if (!BN_mul(t,a,b)) goto err; }
79 if (!BN_mod(ret,t,m,ctx)) goto err;
87 /* this one works - simple but works */
88 int BN_mod_exp(r,a,p,m,ctx)
95 v=ctx->bn[ctx->tos++];
96 tmp=ctx->bn[ctx->tos++];
98 if (BN_copy(v,a) == NULL) goto err;
102 { if (BN_copy(r,a) == NULL) goto err; }
103 else { if (BN_one(r)) goto err; }
105 for (i=1; i<bits; i++)
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))
111 if (!BN_mul(tmp,r,v)) goto err;
112 if (!BN_mod(r,tmp,m,ctx)) goto err;
123 /* this one works - simple but works */
124 int BN_exp(r,a,p,ctx)
131 v=ctx->bn[ctx->tos++];
132 tmp=ctx->bn[ctx->tos++];
134 if (BN_copy(v,a) == NULL) goto err;
138 { if (BN_copy(r,a) == NULL) goto err; }
139 else { if (BN_one(r)) goto err; }
141 for (i=1; i<bits; i++)
143 if (!BN_sqr(tmp,v,ctx)) goto err;
144 if (BN_is_bit_set(p,i))
146 if (!BN_mul(tmp,r,v)) goto err;
155 int BN_mod_exp(r,a,p,m,ctx)
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)) */
172 { ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL); }
176 { ret=BN_mod_exp_recp(r,a,p,m,ctx); }
178 { ret=BN_mod_exp_simple(r,a,p,m,ctx); }
184 /* #ifdef RECP_MUL_MOD */
185 int BN_mod_exp_recp(r,a,p,m,ctx)
192 int nb,i,j,bits,ret=0,wstart,wend,window,wvalue;
197 d=ctx->bn[ctx->tos++];
198 aa=ctx->bn[ctx->tos++];
206 nb=BN_reciprocal(d,m,ctx);
207 if (nb == -1) goto err;
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))
214 if (bits <= 17) /* This is probably 3 or 0x10001, so just do singles */
216 else if (bits >= 256)
217 window=5; /* max size of window */
218 else if (bits >= 128)
227 if (!BN_mod_mul_reciprocal(val[i],val[i-1],aa,m,d,nb,ctx))
233 start=1; /* This is used to avoid multiplication etc
234 * when there is only the value '1' in the
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 */
240 if (!BN_one(r)) goto err;
244 if (BN_is_bit_set(p,wstart) == 0)
247 if (!BN_mod_mul_reciprocal(r,r,r,m,d,nb,ctx))
249 if (wstart == 0) break;
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
260 for (i=1; i<window; i++)
262 if (wstart-i < 0) break;
263 if (BN_is_bit_set(p,wstart-i))
271 /* wend is the size of the current window */
273 /* add the 'bytes above' */
277 if (!BN_mod_mul_reciprocal(r,r,r,m,d,nb,ctx))
281 /* wvalue will be an odd number < 2^window */
282 if (!BN_mod_mul_reciprocal(r,r,val[wvalue>>1],m,d,nb,ctx))
285 /* move the 'window' down further */
289 if (wstart < 0) break;
295 if (val[i] != NULL) BN_clear_free(val[i]);
300 /* #ifdef MONT_MUL_MOD */
301 int BN_mod_exp_mont(r,a,p,m,ctx,in_mont)
307 BN_MONT_CTX *in_mont;
309 #define TABLE_SIZE 16
310 int i,j,bits,ret=0,wstart,wend,window,wvalue;
313 BIGNUM *val[TABLE_SIZE];
314 BN_MONT_CTX *mont=NULL;
318 BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
321 d=ctx->bn[ctx->tos++];
329 /* If this is not done, things will break in the montgomery
338 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
339 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
343 if (BN_ucmp(a,m) >= 0)
345 BN_mod(val[0],a,m,ctx);
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 */
353 if (bits <= 20) /* This is probably 3 or 0x10001, so just do singles */
356 window=5; /* max size of window */
357 else if (bits >= 120)
366 if (!BN_mod_mul_montgomery(val[i],val[i-1],d,mont,ctx))
369 for (; i<TABLE_SIZE; i++)
372 start=1; /* This is used to avoid multiplication etc
373 * when there is only the value '1' in the
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 */
379 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
382 if (BN_is_bit_set(p,wstart) == 0)
386 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
389 if (wstart == 0) break;
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
400 for (i=1; i<window; i++)
402 if (wstart-i < 0) break;
403 if (BN_is_bit_set(p,wstart-i))
411 /* wend is the size of the current window */
413 /* add the 'bytes above' */
417 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
421 /* wvalue will be an odd number < 2^window */
422 if (!BN_mod_mul_montgomery(r,r,val[wvalue>>1],mont,ctx))
425 /* move the 'window' down further */
429 if (wstart < 0) break;
431 BN_from_montgomery(r,r,mont,ctx);
434 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
436 for (i=0; i<TABLE_SIZE; i++)
437 if (val[i] != NULL) BN_clear_free(val[i]);
442 /* The old fallback, simple version :-) */
443 int BN_mod_exp_simple(r,a,p,m,ctx)
450 int i,j,bits,ret=0,wstart,wend,window,wvalue;
455 d=ctx->bn[ctx->tos++];
465 if (!BN_mod(val[0],a,m,ctx)) goto err; /* 1 */
466 if (!BN_mod_mul(d,val[0],val[0],m,ctx))
469 if (bits <= 17) /* This is probably 3 or 0x10001, so just do singles */
471 else if (bits >= 256)
472 window=5; /* max size of window */
473 else if (bits >= 128)
482 if (!BN_mod_mul(val[i],val[i-1],d,m,ctx))
488 start=1; /* This is used to avoid multiplication etc
489 * when there is only the value '1' in the
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 */
495 if (!BN_one(r)) goto err;
499 if (BN_is_bit_set(p,wstart) == 0)
502 if (!BN_mod_mul(r,r,r,m,ctx))
504 if (wstart == 0) break;
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
515 for (i=1; i<window; i++)
517 if (wstart-i < 0) break;
518 if (BN_is_bit_set(p,wstart-i))
526 /* wend is the size of the current window */
528 /* add the 'bytes above' */
532 if (!BN_mod_mul(r,r,r,m,ctx))
536 /* wvalue will be an odd number < 2^window */
537 if (!BN_mod_mul(r,r,val[wvalue>>1],m,ctx))
540 /* move the 'window' down further */
544 if (wstart < 0) break;
550 if (val[i] != NULL) BN_clear_free(val[i]);