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).
112 #include "cryptlib.h"
113 #include "constant_time_locl.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)
122 int i, bits, ret = 0;
125 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
126 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
127 BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
132 if ((r == a) || (r == p))
133 rr = BN_CTX_get(ctx);
137 if (rr == NULL || v == NULL)
140 if (BN_copy(v, a) == NULL)
142 bits = BN_num_bits(p);
145 if (BN_copy(rr, a) == NULL)
152 for (i = 1; i < bits; i++) {
153 if (!BN_sqr(v, v, ctx))
155 if (BN_is_bit_set(p, i)) {
156 if (!BN_mul(rr, rr, v, ctx))
169 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
179 * For even modulus m = 2^k*m_odd, it might make sense to compute
180 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
181 * exponentiation for the odd part), using appropriate exponent
182 * reductions, and combine the results using the CRT.
184 * For now, we use Montgomery only if the modulus is odd; otherwise,
185 * exponentiation using the reciprocal-based quick remaindering
188 * (Timing obtained with expspeed.c [computations a^p mod m
189 * where a, p, m are of the same length: 256, 512, 1024, 2048,
190 * 4096, 8192 bits], compared to the running time of the
191 * standard algorithm:
193 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
194 * 55 .. 77 % [UltraSparc processor, but
195 * debug-solaris-sparcv8-gcc conf.]
197 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
198 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
200 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
201 * at 2048 and more bits, but at 512 and 1024 bits, it was
202 * slower even than the standard algorithm!
204 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
205 * should be obtained when the new Montgomery reduction code
206 * has been integrated into OpenSSL.)
210 #define MONT_EXP_WORD
215 * I have finally been able to take out this pre-condition of the top bit
216 * being set. It was caused by an error in BN_div with negatives. There
217 * was also another problem when for a^b%m a >= m. eay 07-May-97
219 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
222 # ifdef MONT_EXP_WORD
223 if (a->top == 1 && !a->neg
224 && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) {
225 BN_ULONG A = a->d[0];
226 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
229 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
234 ret = BN_mod_exp_recp(r, a, p, m, ctx);
238 ret = BN_mod_exp_simple(r, a, p, m, ctx);
246 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
247 const BIGNUM *m, BN_CTX *ctx)
249 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
252 /* Table of variables obtained from 'ctx' */
253 BIGNUM *val[TABLE_SIZE];
256 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
257 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
258 BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
262 bits = BN_num_bits(p);
270 aa = BN_CTX_get(ctx);
271 val[0] = BN_CTX_get(ctx);
275 BN_RECP_CTX_init(&recp);
277 /* ignore sign of 'm' */
281 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
284 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
288 if (!BN_nnmod(val[0], a, m, ctx))
290 if (BN_is_zero(val[0])) {
296 window = BN_window_bits_for_exponent_size(bits);
298 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
300 j = 1 << (window - 1);
301 for (i = 1; i < j; i++) {
302 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
303 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
308 start = 1; /* This is used to avoid multiplication etc
309 * when there is only the value '1' in the
311 wvalue = 0; /* The 'value' of the window */
312 wstart = bits - 1; /* The top bit of the window */
313 wend = 0; /* The bottom bit of the window */
319 if (BN_is_bit_set(p, wstart) == 0) {
321 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
329 * We now have wstart on a 'set' bit, we now need to work out how bit
330 * a window to do. To do this we need to scan forward until the last
331 * set bit before the end of the window
336 for (i = 1; i < window; i++) {
339 if (BN_is_bit_set(p, wstart - i)) {
340 wvalue <<= (i - wend);
346 /* wend is the size of the current window */
348 /* add the 'bytes above' */
350 for (i = 0; i < j; i++) {
351 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
355 /* wvalue will be an odd number < 2^window */
356 if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
359 /* move the 'window' down further */
369 BN_RECP_CTX_free(&recp);
374 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
375 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
377 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
381 /* Table of variables obtained from 'ctx' */
382 BIGNUM *val[TABLE_SIZE];
383 BN_MONT_CTX *mont = NULL;
385 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
386 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
394 BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
397 bits = BN_num_bits(p);
406 val[0] = BN_CTX_get(ctx);
407 if (!d || !r || !val[0])
411 * If this is not done, things will break in the montgomery part
417 if ((mont = BN_MONT_CTX_new()) == NULL)
419 if (!BN_MONT_CTX_set(mont, m, ctx))
423 if (a->neg || BN_ucmp(a, m) >= 0) {
424 if (!BN_nnmod(val[0], a, m, ctx))
429 if (BN_is_zero(aa)) {
434 if (!BN_to_montgomery(val[0], aa, mont, ctx))
437 window = BN_window_bits_for_exponent_size(bits);
439 if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx))
441 j = 1 << (window - 1);
442 for (i = 1; i < j; i++) {
443 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
444 !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx))
449 start = 1; /* This is used to avoid multiplication etc
450 * when there is only the value '1' in the
452 wvalue = 0; /* The 'value' of the window */
453 wstart = bits - 1; /* The top bit of the window */
454 wend = 0; /* The bottom bit of the window */
456 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
459 if (BN_is_bit_set(p, wstart) == 0) {
461 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
470 * We now have wstart on a 'set' bit, we now need to work out how bit
471 * a window to do. To do this we need to scan forward until the last
472 * set bit before the end of the window
477 for (i = 1; i < window; i++) {
480 if (BN_is_bit_set(p, wstart - i)) {
481 wvalue <<= (i - wend);
487 /* wend is the size of the current window */
489 /* add the 'bytes above' */
491 for (i = 0; i < j; i++) {
492 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
496 /* wvalue will be an odd number < 2^window */
497 if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
500 /* move the 'window' down further */
507 if (!BN_from_montgomery(rr, r, mont, ctx))
511 if ((in_mont == NULL) && (mont != NULL))
512 BN_MONT_CTX_free(mont);
519 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
520 * layout so that accessing any of these table values shows the same access
521 * pattern as far as cache lines are concerned. The following functions are
522 * used to transfer a BIGNUM from/to that table.
525 static int MOD_EXP_CTIME_COPY_TO_PREBUF(BIGNUM *b, int top,
526 unsigned char *buf, int idx,
530 int width = 1 << window;
531 BN_ULONG *table = (BN_ULONG *)buf;
533 if (bn_wexpand(b, top) == NULL)
535 while (b->top < top) {
539 for (i = 0, j = idx; i < top; i++, j += width) {
547 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
548 unsigned char *buf, int idx,
552 int width = 1 << window;
553 volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
555 if (bn_wexpand(b, top) == NULL)
559 for (i = 0; i < top; i++, table += width) {
562 for (j = 0; j < width; j++) {
564 ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
570 int xstride = 1 << (window - 2);
571 BN_ULONG y0, y1, y2, y3;
573 i = idx >> (window - 2); /* equivalent of idx / xstride */
574 idx &= xstride - 1; /* equivalent of idx % xstride */
576 y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1);
577 y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1);
578 y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1);
579 y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1);
581 for (i = 0; i < top; i++, table += width) {
584 for (j = 0; j < xstride; j++) {
585 acc |= ( (table[j + 0 * xstride] & y0) |
586 (table[j + 1 * xstride] & y1) |
587 (table[j + 2 * xstride] & y2) |
588 (table[j + 3 * xstride] & y3) )
589 & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
602 * Given a pointer value, compute the next address that is a cache line
605 #define MOD_EXP_CTIME_ALIGN(x_) \
606 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((BN_ULONG)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
609 * This variant of BN_mod_exp_mont() uses fixed windows and the special
610 * precomputation memory layout to limit data-dependency to a minimum to
611 * protect secret exponents (cf. the hyper-threading timing attacks pointed
612 * out by Colin Percival,
613 * http://www.daemong-consideredperthreading-considered-harmful/)
615 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
616 const BIGNUM *m, BN_CTX *ctx,
617 BN_MONT_CTX *in_mont)
619 int i, bits, ret = 0, idx, window, wvalue;
623 BN_MONT_CTX *mont = NULL;
626 unsigned char *powerbufFree = NULL;
628 unsigned char *powerbuf = NULL;
629 BIGNUM *computeTemp = NULL, *am = NULL;
637 if (!(m->d[0] & 1)) {
638 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
641 bits = BN_num_bits(p);
647 /* Initialize BIGNUM context and allocate intermediate result */
654 * Allocate a montgomery context if it was not supplied by the caller. If
655 * this is not done, things will break in the montgomery part.
660 if ((mont = BN_MONT_CTX_new()) == NULL)
662 if (!BN_MONT_CTX_set(mont, m, ctx))
666 /* Get the window size to use with size of p. */
667 window = BN_window_bits_for_ctime_exponent_size(bits);
670 * Allocate a buffer large enough to hold all of the pre-computed powers
673 numPowers = 1 << window;
674 powerbufLen = sizeof(m->d[0]) * top * numPowers;
676 (unsigned char *)OPENSSL_malloc(powerbufLen +
677 MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
681 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
682 memset(powerbuf, 0, powerbufLen);
685 * Initialize the intermediate result. Do this early to save double
686 * conversion, once each for a^0 and intermediate result.
688 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
690 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(r, top, powerbuf, 0, window))
693 /* Initialize computeTemp as a^1 with montgomery precalcs */
694 computeTemp = BN_CTX_get(ctx);
695 am = BN_CTX_get(ctx);
696 if (computeTemp == NULL || am == NULL)
699 if (a->neg || BN_ucmp(a, m) >= 0) {
700 if (!BN_mod(am, a, m, ctx))
705 if (!BN_to_montgomery(am, aa, mont, ctx))
707 if (!BN_copy(computeTemp, am))
709 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(am, top, powerbuf, 1, window))
713 * If the window size is greater than 1, then calculate
714 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even powers
715 * could instead be computed as (a^(i/2))^2 to use the slight performance
716 * advantage of sqr over mul).
719 for (i = 2; i < numPowers; i++) {
720 /* Calculate a^i = a^(i-1) * a */
721 if (!BN_mod_mul_montgomery
722 (computeTemp, am, computeTemp, mont, ctx))
724 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(computeTemp, top, powerbuf, i,
731 * Adjust the number of bits up to a multiple of the window size. If the
732 * exponent length is not a multiple of the window size, then this pads
733 * the most significant bits with zeros to normalize the scanning loop to
734 * there's no special cases. * NOTE: Making the window size a power of
735 * two less than the native * word size ensures that the padded bits
736 * won't go past the last * word in the internal BIGNUM structure. Going
737 * past the end will * still produce the correct result, but causes a
738 * different branch * to be taken in the BN_is_bit_set function.
740 bits = ((bits + window - 1) / window) * window;
741 idx = bits - 1; /* The top bit of the window */
744 * Scan the exponent one window at a time starting from the most
748 wvalue = 0; /* The 'value' of the window */
750 /* Scan the window, squaring the result as we go */
751 for (i = 0; i < window; i++, idx--) {
752 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
754 wvalue = (wvalue << 1) + BN_is_bit_set(p, idx);
758 * Fetch the appropriate pre-computed value from the pre-buf
760 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF
761 (computeTemp, top, powerbuf, wvalue, window))
764 /* Multiply the result into the intermediate result */
765 if (!BN_mod_mul_montgomery(r, r, computeTemp, mont, ctx))
769 /* Convert the final result from montgomery to standard format */
770 if (!BN_from_montgomery(rr, r, mont, ctx))
774 if ((in_mont == NULL) && (mont != NULL))
775 BN_MONT_CTX_free(mont);
776 if (powerbuf != NULL) {
777 OPENSSL_cleanse(powerbuf, powerbufLen);
778 OPENSSL_free(powerbufFree);
782 if (computeTemp != NULL)
783 BN_clear(computeTemp);
788 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
789 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
791 BN_MONT_CTX *mont = NULL;
792 int b, bits, ret = 0;
797 #define BN_MOD_MUL_WORD(r, w, m) \
798 (BN_mul_word(r, (w)) && \
799 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
800 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
802 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
803 * probably more overhead than always using BN_mod (which uses BN_copy if
804 * a similar test returns true).
807 * We can use BN_mod and do not need BN_nnmod because our accumulator is
808 * never negative (the result of BN_mod does not depend on the sign of
811 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
812 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
814 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
815 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
816 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
824 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
828 a %= m->d[0]; /* make sure that 'a' is reduced */
830 bits = BN_num_bits(p);
832 /* x**0 mod 1 is still zero. */
850 if (d == NULL || r == NULL || t == NULL)
856 if ((mont = BN_MONT_CTX_new()) == NULL)
858 if (!BN_MONT_CTX_set(mont, m, ctx))
862 r_is_one = 1; /* except for Montgomery factor */
866 /* The result is accumulated in the product r*w. */
867 w = a; /* bit 'bits-1' of 'p' is always set */
868 for (b = bits - 2; b >= 0; b--) {
869 /* First, square r*w. */
871 if ((next_w / w) != w) { /* overflow */
873 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
877 if (!BN_MOD_MUL_WORD(r, w, m))
884 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
888 /* Second, multiply r*w by 'a' if exponent bit is set. */
889 if (BN_is_bit_set(p, b)) {
891 if ((next_w / a) != w) { /* overflow */
893 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
897 if (!BN_MOD_MUL_WORD(r, w, m))
906 /* Finally, set r:=r*w. */
909 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
913 if (!BN_MOD_MUL_WORD(r, w, m))
918 if (r_is_one) { /* can happen only if a == 1 */
922 if (!BN_from_montgomery(rr, r, mont, ctx))
927 if ((in_mont == NULL) && (mont != NULL))
928 BN_MONT_CTX_free(mont);
934 /* The old fallback, simple version :-) */
935 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
936 const BIGNUM *m, BN_CTX *ctx)
938 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
941 /* Table of variables obtained from 'ctx' */
942 BIGNUM *val[TABLE_SIZE];
944 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
945 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
946 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
950 bits = BN_num_bits(p);
959 val[0] = BN_CTX_get(ctx);
963 if (!BN_nnmod(val[0], a, m, ctx))
965 if (BN_is_zero(val[0])) {
971 window = BN_window_bits_for_exponent_size(bits);
973 if (!BN_mod_mul(d, val[0], val[0], m, ctx))
975 j = 1 << (window - 1);
976 for (i = 1; i < j; i++) {
977 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
978 !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
983 start = 1; /* This is used to avoid multiplication etc
984 * when there is only the value '1' in the
986 wvalue = 0; /* The 'value' of the window */
987 wstart = bits - 1; /* The top bit of the window */
988 wend = 0; /* The bottom bit of the window */
994 if (BN_is_bit_set(p, wstart) == 0) {
996 if (!BN_mod_mul(r, r, r, m, ctx))
1004 * We now have wstart on a 'set' bit, we now need to work out how bit
1005 * a window to do. To do this we need to scan forward until the last
1006 * set bit before the end of the window
1011 for (i = 1; i < window; i++) {
1014 if (BN_is_bit_set(p, wstart - i)) {
1015 wvalue <<= (i - wend);
1021 /* wend is the size of the current window */
1023 /* add the 'bytes above' */
1025 for (i = 0; i < j; i++) {
1026 if (!BN_mod_mul(r, r, r, m, ctx))
1030 /* wvalue will be an odd number < 2^window */
1031 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1034 /* move the 'window' down further */