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.]
66 int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx)
75 t= &(ctx->bn[ctx->tos++]);
77 { if (!BN_sqr(t,a,ctx)) goto err; }
79 { if (!BN_mul(t,a,b,ctx)) goto err; }
80 if (!BN_mod(ret,t,m,ctx)) goto err;
88 /* this one works - simple but works */
89 int BN_mod_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BIGNUM *m, BN_CTX *ctx)
94 v= &(ctx->bn[ctx->tos++]);
95 tmp= &(ctx->bn[ctx->tos++]);
97 if (BN_copy(v,a) == NULL) goto err;
101 { if (BN_copy(r,a) == NULL) goto err; }
102 else { if (!BN_one(r)) goto err; }
104 for (i=1; i<bits; i++)
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))
110 if (!BN_mul(tmp,r,v,ctx)) goto err;
111 if (!BN_mod(r,tmp,m,ctx)) goto err;
122 /* this one works - simple but works */
123 int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx)
125 int i,bits,ret=0,tos;
129 v= &(ctx->bn[ctx->tos++]);
130 if ((r == a) || (r == p))
131 rr= &(ctx->bn[ctx->tos++]);
135 if (BN_copy(v,a) == NULL) goto err;
139 { if (BN_copy(rr,a) == NULL) goto err; }
140 else { if (!BN_one(rr)) goto err; }
142 for (i=1; i<bits; i++)
144 if (!BN_sqr(v,v,ctx)) goto err;
145 if (BN_is_bit_set(p,i))
147 if (!BN_mul(rr,rr,v,ctx)) goto err;
153 if (r != rr) BN_copy(r,rr);
157 int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
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)) */
174 { ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL); }
178 { ret=BN_mod_exp_recp(r,a,p,m,ctx); }
180 { ret=BN_mod_exp_simple(r,a,p,m,ctx); }
186 /* #ifdef RECP_MUL_MOD */
187 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
188 const BIGNUM *m, BN_CTX *ctx)
190 int i,j,bits,ret=0,wstart,wend,window,wvalue;
193 BIGNUM val[TABLE_SIZE];
196 aa= &(ctx->bn[ctx->tos++]);
204 BN_RECP_CTX_init(&recp);
205 if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) 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]),&recp,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,&recp,ctx))
232 start=1; /* This is used to avoid multiplication etc
233 * when there is only the value '1' in the
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 */
239 if (!BN_one(r)) goto err;
243 if (BN_is_bit_set(p,wstart) == 0)
246 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
248 if (wstart == 0) break;
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
259 for (i=1; i<window; i++)
261 if (wstart-i < 0) break;
262 if (BN_is_bit_set(p,wstart-i))
270 /* wend is the size of the current window */
272 /* add the 'bytes above' */
276 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
280 /* wvalue will be an odd number < 2^window */
281 if (!BN_mod_mul_reciprocal(r,r,&(val[wvalue>>1]),&recp,ctx))
284 /* move the 'window' down further */
288 if (wstart < 0) break;
294 BN_clear_free(&(val[i]));
295 BN_RECP_CTX_free(&recp);
300 /* #ifdef MONT_MUL_MOD */
301 int BN_mod_exp_mont(BIGNUM *rr, BIGNUM *a, const BIGNUM *p,
302 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
304 int i,j,bits,ret=0,wstart,wend,window,wvalue;
308 BIGNUM val[TABLE_SIZE];
309 BN_MONT_CTX *mont=NULL;
317 BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
320 d= &(ctx->bn[ctx->tos++]);
321 r= &(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;
344 if (BN_ucmp(a,m) >= 0)
346 BN_mod(&(val[0]),a,m,ctx);
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 */
354 if (bits <= 20) /* This is probably 3 or 0x10001, so just do singles */
356 else if (bits >= 256)
357 window=5; /* max size of window */
358 else if (bits >= 128)
367 if (!BN_mod_mul_montgomery(&(val[i]),&(val[i-1]),d,mont,ctx))
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(rr,r,mont,ctx);
434 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
437 BN_clear_free(&(val[i]));
442 /* The old fallback, simple version :-) */
443 int BN_mod_exp_simple(BIGNUM *r, BIGNUM *a, BIGNUM *p, BIGNUM *m,
446 int i,j,bits,ret=0,wstart,wend,window,wvalue,ts=0;
449 BIGNUM val[TABLE_SIZE];
451 d= &(ctx->bn[ctx->tos++]);
462 if (!BN_mod(&(val[0]),a,m,ctx)) goto err; /* 1 */
463 if (!BN_mod_mul(d,&(val[0]),&(val[0]),m,ctx))
466 if (bits <= 17) /* This is probably 3 or 0x10001, so just do singles */
468 else if (bits >= 256)
469 window=5; /* max size of window */
470 else if (bits >= 128)
479 if (!BN_mod_mul(&(val[i]),&(val[i-1]),d,m,ctx))
484 start=1; /* This is used to avoid multiplication etc
485 * when there is only the value '1' in the
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 */
491 if (!BN_one(r)) goto err;
495 if (BN_is_bit_set(p,wstart) == 0)
498 if (!BN_mod_mul(r,r,r,m,ctx))
500 if (wstart == 0) break;
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
511 for (i=1; i<window; i++)
513 if (wstart-i < 0) break;
514 if (BN_is_bit_set(p,wstart-i))
522 /* wend is the size of the current window */
524 /* add the 'bytes above' */
528 if (!BN_mod_mul(r,r,r,m,ctx))
532 /* wvalue will be an odd number < 2^window */
533 if (!BN_mod_mul(r,r,&(val[wvalue>>1]),m,ctx))
536 /* move the 'window' down further */
540 if (wstart < 0) break;
546 BN_clear_free(&(val[i]));