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"
115 /* maximum precomputation table size for *variable* sliding windows */
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)
121 int i, bits, ret = 0;
124 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
125 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
126 BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
131 if ((r == a) || (r == p))
132 rr = BN_CTX_get(ctx);
136 if (rr == NULL || v == NULL)
139 if (BN_copy(v, a) == NULL)
141 bits = BN_num_bits(p);
144 if (BN_copy(rr, a) == NULL)
151 for (i = 1; i < bits; i++) {
152 if (!BN_sqr(v, v, ctx))
154 if (BN_is_bit_set(p, i)) {
155 if (!BN_mul(rr, rr, v, ctx))
168 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
178 * For even modulus m = 2^k*m_odd, it might make sense to compute
179 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
180 * exponentiation for the odd part), using appropriate exponent
181 * reductions, and combine the results using the CRT.
183 * For now, we use Montgomery only if the modulus is odd; otherwise,
184 * exponentiation using the reciprocal-based quick remaindering
187 * (Timing obtained with expspeed.c [computations a^p mod m
188 * where a, p, m are of the same length: 256, 512, 1024, 2048,
189 * 4096, 8192 bits], compared to the running time of the
190 * standard algorithm:
192 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
193 * 55 .. 77 % [UltraSparc processor, but
194 * debug-solaris-sparcv8-gcc conf.]
196 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
197 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
199 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
200 * at 2048 and more bits, but at 512 and 1024 bits, it was
201 * slower even than the standard algorithm!
203 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
204 * should be obtained when the new Montgomery reduction code
205 * has been integrated into OpenSSL.)
209 #define MONT_EXP_WORD
214 * I have finally been able to take out this pre-condition of the top bit
215 * being set. It was caused by an error in BN_div with negatives. There
216 * was also another problem when for a^b%m a >= m. eay 07-May-97
218 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
221 # ifdef MONT_EXP_WORD
222 if (a->top == 1 && !a->neg
223 && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) {
224 BN_ULONG A = a->d[0];
225 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
228 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
233 ret = BN_mod_exp_recp(r, a, p, m, ctx);
237 ret = BN_mod_exp_simple(r, a, p, m, ctx);
245 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
246 const BIGNUM *m, BN_CTX *ctx)
248 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
251 /* Table of variables obtained from 'ctx' */
252 BIGNUM *val[TABLE_SIZE];
255 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
256 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
257 BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
261 bits = BN_num_bits(p);
269 aa = BN_CTX_get(ctx);
270 val[0] = BN_CTX_get(ctx);
274 BN_RECP_CTX_init(&recp);
276 /* ignore sign of 'm' */
280 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
283 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
287 if (!BN_nnmod(val[0], a, m, ctx))
289 if (BN_is_zero(val[0])) {
295 window = BN_window_bits_for_exponent_size(bits);
297 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
299 j = 1 << (window - 1);
300 for (i = 1; i < j; i++) {
301 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
302 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
307 start = 1; /* This is used to avoid multiplication etc
308 * when there is only the value '1' in the
310 wvalue = 0; /* The 'value' of the window */
311 wstart = bits - 1; /* The top bit of the window */
312 wend = 0; /* The bottom bit of the window */
318 if (BN_is_bit_set(p, wstart) == 0) {
320 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
328 * We now have wstart on a 'set' bit, we now need to work out how bit
329 * a window to do. To do this we need to scan forward until the last
330 * set bit before the end of the window
335 for (i = 1; i < window; i++) {
338 if (BN_is_bit_set(p, wstart - i)) {
339 wvalue <<= (i - wend);
345 /* wend is the size of the current window */
347 /* add the 'bytes above' */
349 for (i = 0; i < j; i++) {
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 */
368 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) {
385 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
393 BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
396 bits = BN_num_bits(p);
405 val[0] = BN_CTX_get(ctx);
406 if (!d || !r || !val[0])
410 * If this is not done, things will break in the montgomery part
416 if ((mont = BN_MONT_CTX_new()) == NULL)
418 if (!BN_MONT_CTX_set(mont, m, ctx))
422 if (a->neg || BN_ucmp(a, m) >= 0) {
423 if (!BN_nnmod(val[0], a, m, ctx))
428 if (BN_is_zero(aa)) {
433 if (!BN_to_montgomery(val[0], aa, mont, ctx))
436 window = BN_window_bits_for_exponent_size(bits);
438 if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx))
440 j = 1 << (window - 1);
441 for (i = 1; i < j; i++) {
442 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
443 !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx))
448 start = 1; /* This is used to avoid multiplication etc
449 * when there is only the value '1' in the
451 wvalue = 0; /* The 'value' of the window */
452 wstart = bits - 1; /* The top bit of the window */
453 wend = 0; /* The bottom bit of the window */
455 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
458 if (BN_is_bit_set(p, wstart) == 0) {
460 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
469 * We now have wstart on a 'set' bit, we now need to work out how bit
470 * a window to do. To do this we need to scan forward until the last
471 * set bit before the end of the window
476 for (i = 1; i < window; i++) {
479 if (BN_is_bit_set(p, wstart - i)) {
480 wvalue <<= (i - wend);
486 /* wend is the size of the current window */
488 /* add the 'bytes above' */
490 for (i = 0; i < j; i++) {
491 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
495 /* wvalue will be an odd number < 2^window */
496 if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
499 /* move the 'window' down further */
506 if (!BN_from_montgomery(rr, r, mont, ctx))
510 if ((in_mont == NULL) && (mont != NULL))
511 BN_MONT_CTX_free(mont);
518 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
519 * layout so that accessing any of these table values shows the same access
520 * pattern as far as cache lines are concerned. The following functions are
521 * used to transfer a BIGNUM from/to that table.
524 static int MOD_EXP_CTIME_COPY_TO_PREBUF(BIGNUM *b, int top,
525 unsigned char *buf, int idx,
530 if (bn_wexpand(b, top) == NULL)
532 while (b->top < top) {
536 for (i = 0, j = idx; i < top * sizeof b->d[0]; i++, j += width) {
537 buf[j] = ((unsigned char *)b->d)[i];
544 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
545 unsigned char *buf, int idx,
550 if (bn_wexpand(b, top) == NULL)
553 for (i = 0, j = idx; i < top * sizeof b->d[0]; i++, j += width) {
554 ((unsigned char *)b->d)[i] = buf[j];
563 * Given a pointer value, compute the next address that is a cache line
566 #define MOD_EXP_CTIME_ALIGN(x_) \
567 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((BN_ULONG)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
570 * This variant of BN_mod_exp_mont() uses fixed windows and the special
571 * precomputation memory layout to limit data-dependency to a minimum to
572 * protect secret exponents (cf. the hyper-threading timing attacks pointed
573 * out by Colin Percival,
574 * http://www.daemong-consideredperthreading-considered-harmful/)
576 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
577 const BIGNUM *m, BN_CTX *ctx,
578 BN_MONT_CTX *in_mont)
580 int i, bits, ret = 0, idx, window, wvalue;
584 BN_MONT_CTX *mont = NULL;
587 unsigned char *powerbufFree = NULL;
589 unsigned char *powerbuf = NULL;
590 BIGNUM *computeTemp = NULL, *am = NULL;
598 if (!(m->d[0] & 1)) {
599 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
602 bits = BN_num_bits(p);
608 /* Initialize BIGNUM context and allocate intermediate result */
615 * Allocate a montgomery context if it was not supplied by the caller. If
616 * this is not done, things will break in the montgomery part.
621 if ((mont = BN_MONT_CTX_new()) == NULL)
623 if (!BN_MONT_CTX_set(mont, m, ctx))
627 /* Get the window size to use with size of p. */
628 window = BN_window_bits_for_ctime_exponent_size(bits);
631 * Allocate a buffer large enough to hold all of the pre-computed powers
634 numPowers = 1 << window;
635 powerbufLen = sizeof(m->d[0]) * top * numPowers;
637 (unsigned char *)OPENSSL_malloc(powerbufLen +
638 MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
642 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
643 memset(powerbuf, 0, powerbufLen);
646 * Initialize the intermediate result. Do this early to save double
647 * conversion, once each for a^0 and intermediate result.
649 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
651 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(r, top, powerbuf, 0, numPowers))
654 /* Initialize computeTemp as a^1 with montgomery precalcs */
655 computeTemp = BN_CTX_get(ctx);
656 am = BN_CTX_get(ctx);
657 if (computeTemp == NULL || am == NULL)
660 if (a->neg || BN_ucmp(a, m) >= 0) {
661 if (!BN_mod(am, a, m, ctx))
666 if (!BN_to_montgomery(am, aa, mont, ctx))
668 if (!BN_copy(computeTemp, am))
670 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(am, top, powerbuf, 1, numPowers))
674 * If the window size is greater than 1, then calculate
675 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even powers
676 * could instead be computed as (a^(i/2))^2 to use the slight performance
677 * advantage of sqr over mul).
680 for (i = 2; i < numPowers; i++) {
681 /* Calculate a^i = a^(i-1) * a */
682 if (!BN_mod_mul_montgomery
683 (computeTemp, am, computeTemp, mont, ctx))
685 if (!MOD_EXP_CTIME_COPY_TO_PREBUF
686 (computeTemp, top, powerbuf, i, numPowers))
692 * Adjust the number of bits up to a multiple of the window size. If the
693 * exponent length is not a multiple of the window size, then this pads
694 * the most significant bits with zeros to normalize the scanning loop to
695 * there's no special cases. * NOTE: Making the window size a power of
696 * two less than the native * word size ensures that the padded bits
697 * won't go past the last * word in the internal BIGNUM structure. Going
698 * past the end will * still produce the correct result, but causes a
699 * different branch * to be taken in the BN_is_bit_set function.
701 bits = ((bits + window - 1) / window) * window;
702 idx = bits - 1; /* The top bit of the window */
705 * Scan the exponent one window at a time starting from the most
709 wvalue = 0; /* The 'value' of the window */
711 /* Scan the window, squaring the result as we go */
712 for (i = 0; i < window; i++, idx--) {
713 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
715 wvalue = (wvalue << 1) + BN_is_bit_set(p, idx);
719 * Fetch the appropriate pre-computed value from the pre-buf
721 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF
722 (computeTemp, top, powerbuf, wvalue, numPowers))
725 /* Multiply the result into the intermediate result */
726 if (!BN_mod_mul_montgomery(r, r, computeTemp, mont, ctx))
730 /* Convert the final result from montgomery to standard format */
731 if (!BN_from_montgomery(rr, r, mont, ctx))
735 if ((in_mont == NULL) && (mont != NULL))
736 BN_MONT_CTX_free(mont);
737 if (powerbuf != NULL) {
738 OPENSSL_cleanse(powerbuf, powerbufLen);
739 OPENSSL_free(powerbufFree);
743 if (computeTemp != NULL)
744 BN_clear(computeTemp);
749 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
750 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
752 BN_MONT_CTX *mont = NULL;
753 int b, bits, ret = 0;
758 #define BN_MOD_MUL_WORD(r, w, m) \
759 (BN_mul_word(r, (w)) && \
760 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
761 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
763 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
764 * probably more overhead than always using BN_mod (which uses BN_copy if
765 * a similar test returns true).
768 * We can use BN_mod and do not need BN_nnmod because our accumulator is
769 * never negative (the result of BN_mod does not depend on the sign of
772 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
773 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
775 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
776 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
777 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
785 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
789 a %= m->d[0]; /* make sure that 'a' is reduced */
791 bits = BN_num_bits(p);
793 /* x**0 mod 1 is still zero. */
811 if (d == NULL || r == NULL || t == NULL)
817 if ((mont = BN_MONT_CTX_new()) == NULL)
819 if (!BN_MONT_CTX_set(mont, m, ctx))
823 r_is_one = 1; /* except for Montgomery factor */
827 /* The result is accumulated in the product r*w. */
828 w = a; /* bit 'bits-1' of 'p' is always set */
829 for (b = bits - 2; b >= 0; b--) {
830 /* First, square r*w. */
832 if ((next_w / w) != w) { /* overflow */
834 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
838 if (!BN_MOD_MUL_WORD(r, w, m))
845 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
849 /* Second, multiply r*w by 'a' if exponent bit is set. */
850 if (BN_is_bit_set(p, b)) {
852 if ((next_w / a) != w) { /* overflow */
854 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
858 if (!BN_MOD_MUL_WORD(r, w, m))
867 /* Finally, set r:=r*w. */
870 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
874 if (!BN_MOD_MUL_WORD(r, w, m))
879 if (r_is_one) { /* can happen only if a == 1 */
883 if (!BN_from_montgomery(rr, r, mont, ctx))
888 if ((in_mont == NULL) && (mont != NULL))
889 BN_MONT_CTX_free(mont);
895 /* The old fallback, simple version :-) */
896 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
897 const BIGNUM *m, BN_CTX *ctx)
899 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
902 /* Table of variables obtained from 'ctx' */
903 BIGNUM *val[TABLE_SIZE];
905 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
906 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
907 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
911 bits = BN_num_bits(p);
920 val[0] = BN_CTX_get(ctx);
924 if (!BN_nnmod(val[0], a, m, ctx))
926 if (BN_is_zero(val[0])) {
932 window = BN_window_bits_for_exponent_size(bits);
934 if (!BN_mod_mul(d, val[0], val[0], m, ctx))
936 j = 1 << (window - 1);
937 for (i = 1; i < j; i++) {
938 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
939 !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
944 start = 1; /* This is used to avoid multiplication etc
945 * when there is only the value '1' in the
947 wvalue = 0; /* The 'value' of the window */
948 wstart = bits - 1; /* The top bit of the window */
949 wend = 0; /* The bottom bit of the window */
955 if (BN_is_bit_set(p, wstart) == 0) {
957 if (!BN_mod_mul(r, r, r, m, ctx))
965 * We now have wstart on a 'set' bit, we now need to work out how bit
966 * a window to do. To do this we need to scan forward until the last
967 * set bit before the end of the window
972 for (i = 1; i < window; i++) {
975 if (BN_is_bit_set(p, wstart - i)) {
976 wvalue <<= (i - wend);
982 /* wend is the size of the current window */
984 /* add the 'bytes above' */
986 for (i = 0; i < j; i++) {
987 if (!BN_mod_mul(r, r, r, m, ctx))
991 /* wvalue will be an odd number < 2^window */
992 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
995 /* move the 'window' down further */