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.]
58 /* ====================================================================
59 * Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved.
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
65 * 1. Redistributions of source code must retain the above copyright
66 * notice, this list of conditions and the following disclaimer.
68 * 2. Redistributions in binary form must reproduce the above copyright
69 * notice, this list of conditions and the following disclaimer in
70 * the documentation and/or other materials provided with the
73 * 3. All advertising materials mentioning features or use of this
74 * software must display the following acknowledgment:
75 * "This product includes software developed by the OpenSSL Project
76 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
79 * endorse or promote products derived from this software without
80 * prior written permission. For written permission, please contact
81 * openssl-core@openssl.org.
83 * 5. Products derived from this software may not be called "OpenSSL"
84 * nor may "OpenSSL" appear in their names without prior written
85 * permission of the OpenSSL Project.
87 * 6. Redistributions of any form whatsoever must retain the following
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
95 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
103 * OF THE POSSIBILITY OF SUCH DAMAGE.
104 * ====================================================================
106 * This product includes cryptographic software written by Eric Young
107 * (eay@cryptsoft.com). This product includes software written by Tim
108 * Hudson (tjh@cryptsoft.com).
113 #include "cryptlib.h"
116 #define TABLE_SIZE 32
118 /* this one works - simple but works */
119 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
125 if ((r == a) || (r == p))
126 rr = BN_CTX_get(ctx);
129 if ((v = BN_CTX_get(ctx)) == NULL) goto err;
131 if (BN_copy(v,a) == NULL) goto err;
135 { if (BN_copy(rr,a) == NULL) goto err; }
136 else { if (!BN_one(rr)) goto err; }
138 for (i=1; i<bits; i++)
140 if (!BN_sqr(v,v,ctx)) goto err;
141 if (BN_is_bit_set(p,i))
143 if (!BN_mul(rr,rr,v,ctx)) goto err;
148 if (r != rr) BN_copy(r,rr);
154 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
163 /* For even modulus m = 2^k*m_odd, it might make sense to compute
164 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
165 * exponentiation for the odd part), using appropriate exponent
166 * reductions, and combine the results using the CRT.
168 * For now, we use Montgomery only if the modulus is odd; otherwise,
169 * exponentiation using the reciprocal-based quick remaindering
172 * (Timing obtained with expspeed.c [computations a^p mod m
173 * where a, p, m are of the same length: 256, 512, 1024, 2048,
174 * 4096, 8192 bits], compared to the running time of the
175 * standard algorithm:
177 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
178 * 55 .. 77 % [UltraSparc processor, but
179 * debug-solaris-sparcv8-gcc conf.]
181 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
182 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
184 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
185 * at 2048 and more bits, but at 512 and 1024 bits, it was
186 * slower even than the standard algorithm!
188 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
189 * should be obtained when the new Montgomery reduction code
190 * has been integrated into OpenSSL.)
197 /* I have finally been able to take out this pre-condition of
198 * the top bit being set. It was caused by an error in BN_div
199 * with negatives. There was also another problem when for a^b%m
200 * a >= m. eay 07-May-97 */
201 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
205 if (a->top == 1 && !a->neg)
207 BN_ULONG A = a->d[0];
208 ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);
211 ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL);
216 { ret=BN_mod_exp_recp(r,a,p,m,ctx); }
218 { ret=BN_mod_exp_simple(r,a,p,m,ctx); }
225 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
226 const BIGNUM *m, BN_CTX *ctx)
228 int i,j,bits,ret=0,wstart,wend,window,wvalue;
231 BIGNUM val[TABLE_SIZE];
243 if ((aa = BN_CTX_get(ctx)) == NULL) goto err;
245 BN_RECP_CTX_init(&recp);
246 if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;
251 if (!BN_nnmod(&(val[0]),a,m,ctx)) goto err; /* 1 */
253 window = BN_window_bits_for_exponent_size(bits);
256 if (!BN_mod_mul_reciprocal(aa,&(val[0]),&(val[0]),&recp,ctx))
262 if (!BN_mod_mul_reciprocal(&(val[i]),&(val[i-1]),aa,&recp,ctx))
268 start=1; /* This is used to avoid multiplication etc
269 * when there is only the value '1' in the
271 wvalue=0; /* The 'value' of the window */
272 wstart=bits-1; /* The top bit of the window */
273 wend=0; /* The bottom bit of the window */
275 if (!BN_one(r)) goto err;
279 if (BN_is_bit_set(p,wstart) == 0)
282 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
284 if (wstart == 0) break;
288 /* We now have wstart on a 'set' bit, we now need to work out
289 * how bit a window to do. To do this we need to scan
290 * forward until the last set bit before the end of the
295 for (i=1; i<window; i++)
297 if (wstart-i < 0) break;
298 if (BN_is_bit_set(p,wstart-i))
306 /* wend is the size of the current window */
308 /* add the 'bytes above' */
312 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
316 /* wvalue will be an odd number < 2^window */
317 if (!BN_mod_mul_reciprocal(r,r,&(val[wvalue>>1]),&recp,ctx))
320 /* move the 'window' down further */
324 if (wstart < 0) break;
330 BN_clear_free(&(val[i]));
331 BN_RECP_CTX_free(&recp);
336 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
337 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
339 int i,j,bits,ret=0,wstart,wend,window,wvalue;
343 BIGNUM val[TABLE_SIZE];
344 BN_MONT_CTX *mont=NULL;
352 BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
364 if (d == NULL || r == NULL) goto err;
366 /* If this is not done, things will break in the montgomery
373 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
374 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
379 if (a->neg || BN_ucmp(a,m) >= 0)
381 if (!BN_nnmod(&(val[0]),a,m,ctx))
387 if (!BN_to_montgomery(&(val[0]),aa,mont,ctx)) goto err; /* 1 */
389 window = BN_window_bits_for_exponent_size(bits);
392 if (!BN_mod_mul_montgomery(d,&(val[0]),&(val[0]),mont,ctx)) goto err; /* 2 */
397 if (!BN_mod_mul_montgomery(&(val[i]),&(val[i-1]),d,mont,ctx))
403 start=1; /* This is used to avoid multiplication etc
404 * when there is only the value '1' in the
406 wvalue=0; /* The 'value' of the window */
407 wstart=bits-1; /* The top bit of the window */
408 wend=0; /* The bottom bit of the window */
410 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
413 if (BN_is_bit_set(p,wstart) == 0)
417 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
420 if (wstart == 0) break;
424 /* We now have wstart on a 'set' bit, we now need to work out
425 * how bit a window to do. To do this we need to scan
426 * forward until the last set bit before the end of the
431 for (i=1; i<window; i++)
433 if (wstart-i < 0) break;
434 if (BN_is_bit_set(p,wstart-i))
442 /* wend is the size of the current window */
444 /* add the 'bytes above' */
448 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
452 /* wvalue will be an odd number < 2^window */
453 if (!BN_mod_mul_montgomery(r,r,&(val[wvalue>>1]),mont,ctx))
456 /* move the 'window' down further */
460 if (wstart < 0) break;
462 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
465 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
468 BN_clear_free(&(val[i]));
472 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
473 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
475 BN_MONT_CTX *mont = NULL;
481 #define BN_MOD_MUL_WORD(r, w, m) \
482 (BN_mul_word(r, (w)) && \
483 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
484 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
485 /* BN_MOD_MUL_WORD is only used with 'w' large,
486 * so the BN_ucmp test is probably more overhead
487 * than always using BN_mod (which uses BN_copy if
488 * a similar test returns true). */
489 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
490 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
497 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
500 bits = BN_num_bits(p);
510 if (d == NULL || r == NULL || t == NULL) goto err;
516 if ((mont = BN_MONT_CTX_new()) == NULL) goto err;
517 if (!BN_MONT_CTX_set(mont, m, ctx)) goto err;
520 r_is_one = 1; /* except for Montgomery factor */
524 /* The result is accumulated in the product r*w. */
525 w = a; /* bit 'bits-1' of 'p' is always set */
526 for (b = bits-2; b >= 0; b--)
528 /* First, square r*w. */
530 if ((next_w/w) != w) /* overflow */
534 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
539 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
546 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err;
549 /* Second, multiply r*w by 'a' if exponent bit is set. */
550 if (BN_is_bit_set(p, b))
553 if ((next_w/a) != w) /* overflow */
557 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
562 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
570 /* Finally, set r:=r*w. */
575 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
580 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
584 if (r_is_one) /* can happen only if a == 1*/
586 if (!BN_one(rr)) goto err;
590 if (!BN_from_montgomery(rr, r, mont, ctx)) goto err;
594 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
600 /* The old fallback, simple version :-) */
601 int BN_mod_exp_simple(BIGNUM *r,
602 const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
605 int i,j,bits,ret=0,wstart,wend,window,wvalue,ts=0;
608 BIGNUM val[TABLE_SIZE];
619 if ((d = BN_CTX_get(ctx)) == NULL) goto err;
623 if (!BN_nnmod(&(val[0]),a,m,ctx)) goto err; /* 1 */
625 window = BN_window_bits_for_exponent_size(bits);
628 if (!BN_mod_mul(d,&(val[0]),&(val[0]),m,ctx))
634 if (!BN_mod_mul(&(val[i]),&(val[i-1]),d,m,ctx))
640 start=1; /* This is used to avoid multiplication etc
641 * when there is only the value '1' in the
643 wvalue=0; /* The 'value' of the window */
644 wstart=bits-1; /* The top bit of the window */
645 wend=0; /* The bottom bit of the window */
647 if (!BN_one(r)) goto err;
651 if (BN_is_bit_set(p,wstart) == 0)
654 if (!BN_mod_mul(r,r,r,m,ctx))
656 if (wstart == 0) break;
660 /* We now have wstart on a 'set' bit, we now need to work out
661 * how bit a window to do. To do this we need to scan
662 * forward until the last set bit before the end of the
667 for (i=1; i<window; i++)
669 if (wstart-i < 0) break;
670 if (BN_is_bit_set(p,wstart-i))
678 /* wend is the size of the current window */
680 /* add the 'bytes above' */
684 if (!BN_mod_mul(r,r,r,m,ctx))
688 /* wvalue will be an odd number < 2^window */
689 if (!BN_mod_mul(r,r,&(val[wvalue>>1]),m,ctx))
692 /* move the 'window' down further */
696 if (wstart < 0) break;
702 BN_clear_free(&(val[i]));