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)
76 if ((t = BN_CTX_get(ctx)) == NULL) goto err;
78 { if (!BN_sqr(t,a,ctx)) goto err; }
80 { if (!BN_mul(t,a,b,ctx)) goto err; }
81 if (!BN_mod(ret,t,m,ctx)) goto err;
89 /* this one works - simple but works */
90 int BN_mod_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BIGNUM *m, BN_CTX *ctx)
97 tmp = BN_CTX_get(ctx);
98 if (v == NULL || tmp == NULL) goto err;
100 if (BN_copy(v,a) == NULL) goto err;
104 { if (BN_copy(r,a) == NULL) goto err; }
105 else { if (!BN_one(r)) goto err; }
107 for (i=1; i<bits; i++)
109 if (!BN_sqr(tmp,v,ctx)) goto err;
110 if (!BN_mod(v,tmp,m,ctx)) goto err;
111 if (BN_is_bit_set(p,i))
113 if (!BN_mul(tmp,r,v,ctx)) goto err;
114 if (!BN_mod(r,tmp,m,ctx)) goto err;
125 /* this one works - simple but works */
126 int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx)
132 if ((r == a) || (r == p))
133 rr = BN_CTX_get(ctx);
136 if ((v = BN_CTX_get(ctx)) == NULL) goto err;
138 if (BN_copy(v,a) == NULL) goto err;
142 { if (BN_copy(rr,a) == NULL) goto err; }
143 else { if (!BN_one(rr)) goto err; }
145 for (i=1; i<bits; i++)
147 if (!BN_sqr(v,v,ctx)) goto err;
148 if (BN_is_bit_set(p,i))
150 if (!BN_mul(rr,rr,v,ctx)) goto err;
155 if (r != rr) BN_copy(r,rr);
160 int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
170 /* I have finally been able to take out this pre-condition of
171 * the top bit being set. It was caused by an error in BN_div
172 * with negatives. There was also another problem when for a^b%m
173 * a >= m. eay 07-May-97 */
174 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
177 { ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL); }
181 { ret=BN_mod_exp_recp(r,a,p,m,ctx); }
183 { ret=BN_mod_exp_simple(r,a,p,m,ctx); }
189 /* #ifdef RECP_MUL_MOD */
190 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
191 const BIGNUM *m, BN_CTX *ctx)
193 int i,j,bits,ret=0,wstart,wend,window,wvalue;
196 BIGNUM val[TABLE_SIZE];
208 if ((aa = BN_CTX_get(ctx)) == NULL) goto err;
210 BN_RECP_CTX_init(&recp);
211 if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;
216 if (!BN_mod(&(val[0]),a,m,ctx)) goto err; /* 1 */
217 if (!BN_mod_mul_reciprocal(aa,&(val[0]),&(val[0]),&recp,ctx))
220 if (bits <= 17) /* This is probably 3 or 0x10001, so just do singles */
222 else if (bits >= 256)
223 window=5; /* max size of window */
224 else if (bits >= 128)
233 if (!BN_mod_mul_reciprocal(&(val[i]),&(val[i-1]),aa,&recp,ctx))
238 start=1; /* This is used to avoid multiplication etc
239 * when there is only the value '1' in the
241 wvalue=0; /* The 'value' of the window */
242 wstart=bits-1; /* The top bit of the window */
243 wend=0; /* The bottom bit of the window */
245 if (!BN_one(r)) goto err;
249 if (BN_is_bit_set(p,wstart) == 0)
252 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
254 if (wstart == 0) break;
258 /* We now have wstart on a 'set' bit, we now need to work out
259 * how bit a window to do. To do this we need to scan
260 * forward until the last set bit before the end of the
265 for (i=1; i<window; i++)
267 if (wstart-i < 0) break;
268 if (BN_is_bit_set(p,wstart-i))
276 /* wend is the size of the current window */
278 /* add the 'bytes above' */
282 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
286 /* wvalue will be an odd number < 2^window */
287 if (!BN_mod_mul_reciprocal(r,r,&(val[wvalue>>1]),&recp,ctx))
290 /* move the 'window' down further */
294 if (wstart < 0) break;
300 BN_clear_free(&(val[i]));
301 BN_RECP_CTX_free(&recp);
306 /* #ifdef MONT_MUL_MOD */
307 int BN_mod_exp_mont(BIGNUM *rr, BIGNUM *a, const BIGNUM *p,
308 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
310 int i,j,bits,ret=0,wstart,wend,window,wvalue;
314 BIGNUM val[TABLE_SIZE];
315 BN_MONT_CTX *mont=NULL;
323 BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
335 if (d == NULL || r == NULL) goto err;
337 /* If this is not done, things will break in the montgomery
346 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
347 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
352 if (BN_ucmp(a,m) >= 0)
354 BN_mod(&(val[0]),a,m,ctx);
359 if (!BN_to_montgomery(&(val[0]),aa,mont,ctx)) goto err; /* 1 */
360 if (!BN_mod_mul_montgomery(d,&(val[0]),&(val[0]),mont,ctx)) goto err; /* 2 */
362 if (bits <= 20) /* This is probably 3 or 0x10001, so just do singles */
364 else if (bits >= 256)
365 window=5; /* max size of window */
366 else if (bits >= 128)
375 if (!BN_mod_mul_montgomery(&(val[i]),&(val[i-1]),d,mont,ctx))
380 start=1; /* This is used to avoid multiplication etc
381 * when there is only the value '1' in the
383 wvalue=0; /* The 'value' of the window */
384 wstart=bits-1; /* The top bit of the window */
385 wend=0; /* The bottom bit of the window */
387 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
390 if (BN_is_bit_set(p,wstart) == 0)
394 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
397 if (wstart == 0) break;
401 /* We now have wstart on a 'set' bit, we now need to work out
402 * how bit a window to do. To do this we need to scan
403 * forward until the last set bit before the end of the
408 for (i=1; i<window; i++)
410 if (wstart-i < 0) break;
411 if (BN_is_bit_set(p,wstart-i))
419 /* wend is the size of the current window */
421 /* add the 'bytes above' */
425 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
429 /* wvalue will be an odd number < 2^window */
430 if (!BN_mod_mul_montgomery(r,r,&(val[wvalue>>1]),mont,ctx))
433 /* move the 'window' down further */
437 if (wstart < 0) break;
439 BN_from_montgomery(rr,r,mont,ctx);
442 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
445 BN_clear_free(&(val[i]));
450 /* The old fallback, simple version :-) */
451 int BN_mod_exp_simple(BIGNUM *r, BIGNUM *a, BIGNUM *p, BIGNUM *m,
454 int i,j,bits,ret=0,wstart,wend,window,wvalue,ts=0;
457 BIGNUM val[TABLE_SIZE];
468 if ((d = BN_CTX_get(ctx)) == NULL) goto err;
472 if (!BN_mod(&(val[0]),a,m,ctx)) goto err; /* 1 */
473 if (!BN_mod_mul(d,&(val[0]),&(val[0]),m,ctx))
476 if (bits <= 17) /* This is probably 3 or 0x10001, so just do singles */
478 else if (bits >= 256)
479 window=5; /* max size of window */
480 else if (bits >= 128)
489 if (!BN_mod_mul(&(val[i]),&(val[i-1]),d,m,ctx))
494 start=1; /* This is used to avoid multiplication etc
495 * when there is only the value '1' in the
497 wvalue=0; /* The 'value' of the window */
498 wstart=bits-1; /* The top bit of the window */
499 wend=0; /* The bottom bit of the window */
501 if (!BN_one(r)) goto err;
505 if (BN_is_bit_set(p,wstart) == 0)
508 if (!BN_mod_mul(r,r,r,m,ctx))
510 if (wstart == 0) break;
514 /* We now have wstart on a 'set' bit, we now need to work out
515 * how bit a window to do. To do this we need to scan
516 * forward until the last set bit before the end of the
521 for (i=1; i<window; i++)
523 if (wstart-i < 0) break;
524 if (BN_is_bit_set(p,wstart-i))
532 /* wend is the size of the current window */
534 /* add the 'bytes above' */
538 if (!BN_mod_mul(r,r,r,m,ctx))
542 /* wvalue will be an odd number < 2^window */
543 if (!BN_mod_mul(r,r,&(val[wvalue>>1]),m,ctx))
546 /* move the 'window' down further */
550 if (wstart < 0) break;
556 BN_clear_free(&(val[i]));