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) 1998-2005 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 /* maximum precomputation table size for *variable* sliding windows */
117 #define TABLE_SIZE 32
119 /* this one works - simple but works */
120 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
125 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
127 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
128 BNerr(BN_F_BN_EXP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
133 if ((r == a) || (r == p))
134 rr = BN_CTX_get(ctx);
138 if (rr == NULL || v == NULL) goto err;
140 if (BN_copy(v,a) == NULL) goto err;
144 { if (BN_copy(rr,a) == NULL) goto err; }
145 else { if (!BN_one(rr)) goto err; }
147 for (i=1; i<bits; i++)
149 if (!BN_sqr(v,v,ctx)) goto err;
150 if (BN_is_bit_set(p,i))
152 if (!BN_mul(rr,rr,v,ctx)) goto err;
157 if (r != rr) BN_copy(r,rr);
164 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
174 * For even modulus m = 2^k*m_odd, it might make sense to compute
175 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
176 * exponentiation for the odd part), using appropriate exponent
177 * reductions, and combine the results using the CRT.
179 * For now, we use Montgomery only if the modulus is odd; otherwise,
180 * exponentiation using the reciprocal-based quick remaindering
183 * (Timing obtained with expspeed.c [computations a^p mod m
184 * where a, p, m are of the same length: 256, 512, 1024, 2048,
185 * 4096, 8192 bits], compared to the running time of the
186 * standard algorithm:
188 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
189 * 55 .. 77 % [UltraSparc processor, but
190 * debug-solaris-sparcv8-gcc conf.]
192 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
193 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
195 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
196 * at 2048 and more bits, but at 512 and 1024 bits, it was
197 * slower even than the standard algorithm!
199 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
200 * should be obtained when the new Montgomery reduction code
201 * has been integrated into OpenSSL.)
205 #define MONT_EXP_WORD
209 /* I have finally been able to take out this pre-condition of
210 * the top bit being set. It was caused by an error in BN_div
211 * with negatives. There was also another problem when for a^b%m
212 * a >= m. eay 07-May-97 */
213 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
217 # ifdef MONT_EXP_WORD
218 if (a->top == 1 && !a->neg && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0))
220 BN_ULONG A = a->d[0];
221 ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);
225 ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL);
230 { ret=BN_mod_exp_recp(r,a,p,m,ctx); }
232 { ret=BN_mod_exp_simple(r,a,p,m,ctx); }
240 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
241 const BIGNUM *m, BN_CTX *ctx)
243 int i,j,bits,ret=0,wstart,wend,window,wvalue;
246 /* Table of variables obtained from 'ctx' */
247 BIGNUM *val[TABLE_SIZE];
250 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
252 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
253 BNerr(BN_F_BN_MOD_EXP_RECP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
266 aa = BN_CTX_get(ctx);
267 val[0] = BN_CTX_get(ctx);
268 if(!aa || !val[0]) goto err;
270 BN_RECP_CTX_init(&recp);
273 /* ignore sign of 'm' */
274 if (!BN_copy(aa, m)) goto err;
276 if (BN_RECP_CTX_set(&recp,aa,ctx) <= 0) goto err;
280 if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;
283 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
284 if (BN_is_zero(val[0]))
291 window = BN_window_bits_for_exponent_size(bits);
294 if (!BN_mod_mul_reciprocal(aa,val[0],val[0],&recp,ctx))
299 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
300 !BN_mod_mul_reciprocal(val[i],val[i-1],
306 start=1; /* This is used to avoid multiplication etc
307 * when there is only the value '1' in the
309 wvalue=0; /* The 'value' of the window */
310 wstart=bits-1; /* The top bit of the window */
311 wend=0; /* The bottom bit of the window */
313 if (!BN_one(r)) goto err;
317 if (BN_is_bit_set(p,wstart) == 0)
320 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
322 if (wstart == 0) break;
326 /* We now have wstart on a 'set' bit, we now need to work out
327 * how bit a window to do. To do this we need to scan
328 * forward until the last set bit before the end of the
333 for (i=1; i<window; i++)
335 if (wstart-i < 0) break;
336 if (BN_is_bit_set(p,wstart-i))
344 /* wend is the size of the current window */
346 /* add the 'bytes above' */
350 if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
354 /* wvalue will be an odd number < 2^window */
355 if (!BN_mod_mul_reciprocal(r,r,val[wvalue>>1],&recp,ctx))
358 /* move the 'window' down further */
362 if (wstart < 0) break;
367 BN_RECP_CTX_free(&recp);
373 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
374 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
376 int i,j,bits,ret=0,wstart,wend,window,wvalue;
380 /* Table of variables obtained from 'ctx' */
381 BIGNUM *val[TABLE_SIZE];
382 BN_MONT_CTX *mont=NULL;
384 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
386 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
395 BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
408 val[0] = BN_CTX_get(ctx);
409 if (!d || !r || !val[0]) goto err;
411 /* If this is not done, things will break in the montgomery
418 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
419 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
422 if (a->neg || BN_ucmp(a,m) >= 0)
424 if (!BN_nnmod(val[0],a,m,ctx))
436 if (!BN_to_montgomery(val[0],aa,mont,ctx)) goto err; /* 1 */
438 window = BN_window_bits_for_exponent_size(bits);
441 if (!BN_mod_mul_montgomery(d,val[0],val[0],mont,ctx)) goto err; /* 2 */
445 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
446 !BN_mod_mul_montgomery(val[i],val[i-1],
452 start=1; /* This is used to avoid multiplication etc
453 * when there is only the value '1' in the
455 wvalue=0; /* The 'value' of the window */
456 wstart=bits-1; /* The top bit of the window */
457 wend=0; /* The bottom bit of the window */
459 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
462 if (BN_is_bit_set(p,wstart) == 0)
466 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
469 if (wstart == 0) break;
473 /* We now have wstart on a 'set' bit, we now need to work out
474 * how bit a window to do. To do this we need to scan
475 * forward until the last set bit before the end of the
480 for (i=1; i<window; i++)
482 if (wstart-i < 0) break;
483 if (BN_is_bit_set(p,wstart-i))
491 /* wend is the size of the current window */
493 /* add the 'bytes above' */
497 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
501 /* wvalue will be an odd number < 2^window */
502 if (!BN_mod_mul_montgomery(r,r,val[wvalue>>1],mont,ctx))
505 /* move the 'window' down further */
509 if (wstart < 0) break;
511 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
514 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
521 /* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout
522 * so that accessing any of these table values shows the same access pattern as far
523 * as cache lines are concerned. The following functions are used to transfer a BIGNUM
524 * from/to that table. */
526 static int MOD_EXP_CTIME_COPY_TO_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
530 if (bn_wexpand(b, top) == NULL)
537 for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
539 buf[j] = ((unsigned char*)b->d)[i];
546 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
550 if (bn_wexpand(b, top) == NULL)
553 for (i=0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
555 ((unsigned char*)b->d)[i] = buf[j];
563 /* Given a pointer value, compute the next address that is a cache line multiple. */
564 #define MOD_EXP_CTIME_ALIGN(x_) \
565 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((BN_ULONG)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
567 /* This variant of BN_mod_exp_mont() uses fixed windows and the special
568 * precomputation memory layout to limit data-dependency to a minimum
569 * to protect secret exponents (cf. the hyper-threading timing attacks
570 * pointed out by Colin Percival,
571 * http://www.daemonology.net/hyperthreading-considered-harmful/)
573 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
574 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
576 int i,bits,ret=0,idx,window,wvalue;
580 BN_MONT_CTX *mont=NULL;
583 unsigned char *powerbufFree=NULL;
585 unsigned char *powerbuf=NULL;
586 BIGNUM *computeTemp=NULL, *am=NULL;
596 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,BN_R_CALLED_WITH_EVEN_MODULUS);
606 /* Initialize BIGNUM context and allocate intermediate result */
609 if (r == NULL) goto err;
611 /* Allocate a montgomery context if it was not supplied by the caller.
612 * If this is not done, things will break in the montgomery part.
618 if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
619 if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
622 /* Get the window size to use with size of p. */
623 window = BN_window_bits_for_ctime_exponent_size(bits);
625 /* Allocate a buffer large enough to hold all of the pre-computed
628 numPowers = 1 << window;
629 powerbufLen = sizeof(m->d[0])*top*numPowers;
630 if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL)
633 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
634 memset(powerbuf, 0, powerbufLen);
636 /* Initialize the intermediate result. Do this early to save double conversion,
637 * once each for a^0 and intermediate result.
639 if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
640 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(r, top, powerbuf, 0, numPowers)) goto err;
642 /* Initialize computeTemp as a^1 with montgomery precalcs */
643 computeTemp = BN_CTX_get(ctx);
644 am = BN_CTX_get(ctx);
645 if (computeTemp==NULL || am==NULL) goto err;
647 if (a->neg || BN_ucmp(a,m) >= 0)
649 if (!BN_mod(am,a,m,ctx))
655 if (!BN_to_montgomery(am,aa,mont,ctx)) goto err;
656 if (!BN_copy(computeTemp, am)) goto err;
657 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(am, top, powerbuf, 1, numPowers)) goto err;
659 /* If the window size is greater than 1, then calculate
660 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
661 * (even powers could instead be computed as (a^(i/2))^2
662 * to use the slight performance advantage of sqr over mul).
666 for (i=2; i<numPowers; i++)
668 /* Calculate a^i = a^(i-1) * a */
669 if (!BN_mod_mul_montgomery(computeTemp,am,computeTemp,mont,ctx))
671 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(computeTemp, top, powerbuf, i, numPowers)) goto err;
675 /* Adjust the number of bits up to a multiple of the window size.
676 * If the exponent length is not a multiple of the window size, then
677 * this pads the most significant bits with zeros to normalize the
678 * scanning loop to there's no special cases.
680 * * NOTE: Making the window size a power of two less than the native
681 * * word size ensures that the padded bits won't go past the last
682 * * word in the internal BIGNUM structure. Going past the end will
683 * * still produce the correct result, but causes a different branch
684 * * to be taken in the BN_is_bit_set function.
686 bits = ((bits+window-1)/window)*window;
687 idx=bits-1; /* The top bit of the window */
689 /* Scan the exponent one window at a time starting from the most
694 wvalue=0; /* The 'value' of the window */
696 /* Scan the window, squaring the result as we go */
697 for (i=0; i<window; i++,idx--)
699 if (!BN_mod_mul_montgomery(r,r,r,mont,ctx)) goto err;
700 wvalue = (wvalue<<1)+BN_is_bit_set(p,idx);
703 /* Fetch the appropriate pre-computed value from the pre-buf */
704 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(computeTemp, top, powerbuf, wvalue, numPowers)) goto err;
706 /* Multiply the result into the intermediate result */
707 if (!BN_mod_mul_montgomery(r,r,computeTemp,mont,ctx)) goto err;
710 /* Convert the final result from montgomery to standard format */
711 if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
714 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
717 OPENSSL_cleanse(powerbuf,powerbufLen);
718 OPENSSL_free(powerbufFree);
720 if (am!=NULL) BN_clear(am);
721 if (computeTemp!=NULL) BN_clear(computeTemp);
726 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
727 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
729 BN_MONT_CTX *mont = NULL;
735 #define BN_MOD_MUL_WORD(r, w, m) \
736 (BN_mul_word(r, (w)) && \
737 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
738 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
739 /* BN_MOD_MUL_WORD is only used with 'w' large,
740 * so the BN_ucmp test is probably more overhead
741 * than always using BN_mod (which uses BN_copy if
742 * a similar test returns true). */
743 /* We can use BN_mod and do not need BN_nnmod because our
744 * accumulator is never negative (the result of BN_mod does
745 * not depend on the sign of the modulus).
747 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
748 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
750 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
752 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
753 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
762 BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
766 a %= m->d[0]; /* make sure that 'a' is reduced */
768 bits = BN_num_bits(p);
771 /* x**0 mod 1 is still zero. */
792 if (d == NULL || r == NULL || t == NULL) goto err;
798 if ((mont = BN_MONT_CTX_new()) == NULL) goto err;
799 if (!BN_MONT_CTX_set(mont, m, ctx)) goto err;
802 r_is_one = 1; /* except for Montgomery factor */
806 /* The result is accumulated in the product r*w. */
807 w = a; /* bit 'bits-1' of 'p' is always set */
808 for (b = bits-2; b >= 0; b--)
810 /* First, square r*w. */
812 if ((next_w/w) != w) /* overflow */
816 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
821 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
828 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err;
831 /* Second, multiply r*w by 'a' if exponent bit is set. */
832 if (BN_is_bit_set(p, b))
835 if ((next_w/a) != w) /* overflow */
839 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
844 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
852 /* Finally, set r:=r*w. */
857 if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
862 if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
866 if (r_is_one) /* can happen only if a == 1*/
868 if (!BN_one(rr)) goto err;
872 if (!BN_from_montgomery(rr, r, mont, ctx)) goto err;
876 if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
883 /* The old fallback, simple version :-) */
884 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
885 const BIGNUM *m, BN_CTX *ctx)
887 int i,j,bits,ret=0,wstart,wend,window,wvalue;
890 /* Table of variables obtained from 'ctx' */
891 BIGNUM *val[TABLE_SIZE];
893 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
895 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
896 BNerr(BN_F_BN_MOD_EXP_SIMPLE,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
910 val[0] = BN_CTX_get(ctx);
911 if(!d || !val[0]) goto err;
913 if (!BN_nnmod(val[0],a,m,ctx)) goto err; /* 1 */
914 if (BN_is_zero(val[0]))
921 window = BN_window_bits_for_exponent_size(bits);
924 if (!BN_mod_mul(d,val[0],val[0],m,ctx))
929 if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
930 !BN_mod_mul(val[i],val[i-1],d,m,ctx))
935 start=1; /* This is used to avoid multiplication etc
936 * when there is only the value '1' in the
938 wvalue=0; /* The 'value' of the window */
939 wstart=bits-1; /* The top bit of the window */
940 wend=0; /* The bottom bit of the window */
942 if (!BN_one(r)) goto err;
946 if (BN_is_bit_set(p,wstart) == 0)
949 if (!BN_mod_mul(r,r,r,m,ctx))
951 if (wstart == 0) break;
955 /* We now have wstart on a 'set' bit, we now need to work out
956 * how bit a window to do. To do this we need to scan
957 * forward until the last set bit before the end of the
962 for (i=1; i<window; i++)
964 if (wstart-i < 0) break;
965 if (BN_is_bit_set(p,wstart-i))
973 /* wend is the size of the current window */
975 /* add the 'bytes above' */
979 if (!BN_mod_mul(r,r,r,m,ctx))
983 /* wvalue will be an odd number < 2^window */
984 if (!BN_mod_mul(r,r,val[wvalue>>1],m,ctx))
987 /* move the 'window' down further */
991 if (wstart < 0) break;