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"
119 # define alloca _alloca
121 #elif defined(__GNUC__)
123 # define alloca(s) __builtin_alloca((s))
127 /* maximum precomputation table size for *variable* sliding windows */
128 #define TABLE_SIZE 32
130 /* this one works - simple but works */
131 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
133 int i, bits, ret = 0;
136 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
137 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
138 BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
143 if ((r == a) || (r == p))
144 rr = BN_CTX_get(ctx);
148 if (rr == NULL || v == NULL)
151 if (BN_copy(v, a) == NULL)
153 bits = BN_num_bits(p);
156 if (BN_copy(rr, a) == NULL)
163 for (i = 1; i < bits; i++) {
164 if (!BN_sqr(v, v, ctx))
166 if (BN_is_bit_set(p, i)) {
167 if (!BN_mul(rr, rr, v, ctx))
180 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
190 * For even modulus m = 2^k*m_odd, it might make sense to compute
191 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
192 * exponentiation for the odd part), using appropriate exponent
193 * reductions, and combine the results using the CRT.
195 * For now, we use Montgomery only if the modulus is odd; otherwise,
196 * exponentiation using the reciprocal-based quick remaindering
199 * (Timing obtained with expspeed.c [computations a^p mod m
200 * where a, p, m are of the same length: 256, 512, 1024, 2048,
201 * 4096, 8192 bits], compared to the running time of the
202 * standard algorithm:
204 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
205 * 55 .. 77 % [UltraSparc processor, but
206 * debug-solaris-sparcv8-gcc conf.]
208 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
209 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
211 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
212 * at 2048 and more bits, but at 512 and 1024 bits, it was
213 * slower even than the standard algorithm!
215 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
216 * should be obtained when the new Montgomery reduction code
217 * has been integrated into OpenSSL.)
221 #define MONT_EXP_WORD
226 * I have finally been able to take out this pre-condition of the top bit
227 * being set. It was caused by an error in BN_div with negatives. There
228 * was also another problem when for a^b%m a >= m. eay 07-May-97
230 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
233 # ifdef MONT_EXP_WORD
234 if (a->top == 1 && !a->neg
235 && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) {
236 BN_ULONG A = a->d[0];
237 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
240 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
245 ret = BN_mod_exp_recp(r, a, p, m, ctx);
249 ret = BN_mod_exp_simple(r, a, p, m, ctx);
257 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
258 const BIGNUM *m, BN_CTX *ctx)
260 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
263 /* Table of variables obtained from 'ctx' */
264 BIGNUM *val[TABLE_SIZE];
267 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
268 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
269 BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
273 bits = BN_num_bits(p);
281 aa = BN_CTX_get(ctx);
282 val[0] = BN_CTX_get(ctx);
286 BN_RECP_CTX_init(&recp);
288 /* ignore sign of 'm' */
292 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
295 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
299 if (!BN_nnmod(val[0], a, m, ctx))
301 if (BN_is_zero(val[0])) {
307 window = BN_window_bits_for_exponent_size(bits);
309 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
311 j = 1 << (window - 1);
312 for (i = 1; i < j; i++) {
313 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
314 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
319 start = 1; /* This is used to avoid multiplication etc
320 * when there is only the value '1' in the
322 wvalue = 0; /* The 'value' of the window */
323 wstart = bits - 1; /* The top bit of the window */
324 wend = 0; /* The bottom bit of the window */
330 if (BN_is_bit_set(p, wstart) == 0) {
332 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
340 * We now have wstart on a 'set' bit, we now need to work out how bit
341 * a window to do. To do this we need to scan forward until the last
342 * set bit before the end of the window
347 for (i = 1; i < window; i++) {
350 if (BN_is_bit_set(p, wstart - i)) {
351 wvalue <<= (i - wend);
357 /* wend is the size of the current window */
359 /* add the 'bytes above' */
361 for (i = 0; i < j; i++) {
362 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
366 /* wvalue will be an odd number < 2^window */
367 if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
370 /* move the 'window' down further */
380 BN_RECP_CTX_free(&recp);
385 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
386 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
388 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
392 /* Table of variables obtained from 'ctx' */
393 BIGNUM *val[TABLE_SIZE];
394 BN_MONT_CTX *mont = NULL;
396 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
397 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
405 BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
408 bits = BN_num_bits(p);
417 val[0] = BN_CTX_get(ctx);
418 if (!d || !r || !val[0])
422 * If this is not done, things will break in the montgomery part
428 if ((mont = BN_MONT_CTX_new()) == NULL)
430 if (!BN_MONT_CTX_set(mont, m, ctx))
434 if (a->neg || BN_ucmp(a, m) >= 0) {
435 if (!BN_nnmod(val[0], a, m, ctx))
440 if (BN_is_zero(aa)) {
445 if (!BN_to_montgomery(val[0], aa, mont, ctx))
448 window = BN_window_bits_for_exponent_size(bits);
450 if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx))
452 j = 1 << (window - 1);
453 for (i = 1; i < j; i++) {
454 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
455 !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx))
460 start = 1; /* This is used to avoid multiplication etc
461 * when there is only the value '1' in the
463 wvalue = 0; /* The 'value' of the window */
464 wstart = bits - 1; /* The top bit of the window */
465 wend = 0; /* The bottom bit of the window */
467 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
470 if (BN_is_bit_set(p, wstart) == 0) {
472 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
481 * We now have wstart on a 'set' bit, we now need to work out how bit
482 * a window to do. To do this we need to scan forward until the last
483 * set bit before the end of the window
488 for (i = 1; i < window; i++) {
491 if (BN_is_bit_set(p, wstart - i)) {
492 wvalue <<= (i - wend);
498 /* wend is the size of the current window */
500 /* add the 'bytes above' */
502 for (i = 0; i < j; i++) {
503 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
507 /* wvalue will be an odd number < 2^window */
508 if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
511 /* move the 'window' down further */
518 if (!BN_from_montgomery(rr, r, mont, ctx))
522 if ((in_mont == NULL) && (mont != NULL))
523 BN_MONT_CTX_free(mont);
530 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
531 * layout so that accessing any of these table values shows the same access
532 * pattern as far as cache lines are concerned. The following functions are
533 * used to transfer a BIGNUM from/to that table.
536 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
537 unsigned char *buf, int idx,
543 top = b->top; /* this works because 'buf' is explicitly
545 for (i = 0, j = idx; i < top * sizeof b->d[0]; i++, j += width) {
546 buf[j] = ((unsigned char *)b->d)[i];
552 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
553 unsigned char *buf, int idx,
558 if (bn_wexpand(b, top) == NULL)
561 for (i = 0, j = idx; i < top * sizeof b->d[0]; i++, j += width) {
562 ((unsigned char *)b->d)[i] = buf[j];
571 * Given a pointer value, compute the next address that is a cache line
574 #define MOD_EXP_CTIME_ALIGN(x_) \
575 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
578 * This variant of BN_mod_exp_mont() uses fixed windows and the special
579 * precomputation memory layout to limit data-dependency to a minimum to
580 * protect secret exponents (cf. the hyper-threading timing attacks pointed
581 * out by Colin Percival,
582 * http://www.daemong-consideredperthreading-considered-harmful/)
584 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
585 const BIGNUM *m, BN_CTX *ctx,
586 BN_MONT_CTX *in_mont)
588 int i, bits, ret = 0, window, wvalue;
590 BN_MONT_CTX *mont = NULL;
593 unsigned char *powerbufFree = NULL;
595 unsigned char *powerbuf = NULL;
604 if (!(m->d[0] & 1)) {
605 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
608 bits = BN_num_bits(p);
617 * Allocate a montgomery context if it was not supplied by the caller. If
618 * this is not done, things will break in the montgomery part.
623 if ((mont = BN_MONT_CTX_new()) == NULL)
625 if (!BN_MONT_CTX_set(mont, m, ctx))
629 /* Get the window size to use with size of p. */
630 window = BN_window_bits_for_ctime_exponent_size(bits);
631 #if defined(OPENSSL_BN_ASM_MONT5)
632 if (window == 6 && bits <= 1024)
633 window = 5; /* ~5% improvement of 2048-bit RSA sign */
637 * Allocate a buffer large enough to hold all of the pre-computed powers
638 * of am, am itself and tmp.
640 numPowers = 1 << window;
641 powerbufLen = sizeof(m->d[0]) * (top * numPowers +
643 numPowers ? (2 * top) : numPowers));
645 if (powerbufLen < 3072)
647 alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
651 (unsigned char *)OPENSSL_malloc(powerbufLen +
652 MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
656 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
657 memset(powerbuf, 0, powerbufLen);
660 if (powerbufLen < 3072)
664 /* lay down tmp and am right after powers table */
665 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
667 tmp.top = am.top = 0;
668 tmp.dmax = am.dmax = top;
669 tmp.neg = am.neg = 0;
670 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
672 /* prepare a^0 in Montgomery domain */
674 if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx))
677 tmp.d[0] = (0 - m->d[0]) & BN_MASK2; /* 2^(top*BN_BITS2) - m */
678 for (i = 1; i < top; i++)
679 tmp.d[i] = (~m->d[i]) & BN_MASK2;
683 /* prepare a^1 in Montgomery domain */
684 if (a->neg || BN_ucmp(a, m) >= 0) {
685 if (!BN_mod(&am, a, m, ctx))
687 if (!BN_to_montgomery(&am, &am, mont, ctx))
689 } else if (!BN_to_montgomery(&am, a, mont, ctx))
692 #if defined(OPENSSL_BN_ASM_MONT5)
693 if (window == 5 && top > 1) {
695 * This optimization uses ideas from http://eprint.iacr.org/2011/239,
696 * specifically optimization of cache-timing attack countermeasures
697 * and pre-computation optimization.
701 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
702 * 512-bit RSA is hardly relevant, we omit it to spare size...
704 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
705 const void *table, const BN_ULONG *np,
706 const BN_ULONG *n0, int num, int power);
707 void bn_scatter5(const BN_ULONG *inp, size_t num,
708 void *table, size_t power);
709 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
711 BN_ULONG *np = mont->N.d, *n0 = mont->n0;
714 * BN_to_montgomery can contaminate words above .top [in
715 * BN_DEBUG[_DEBUG] build]...
717 for (i = am.top; i < top; i++)
719 for (i = tmp.top; i < top; i++)
722 bn_scatter5(tmp.d, top, powerbuf, 0);
723 bn_scatter5(am.d, am.top, powerbuf, 1);
724 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
725 bn_scatter5(tmp.d, top, powerbuf, 2);
728 for (i = 3; i < 32; i++) {
729 /* Calculate a^i = a^(i-1) * a */
730 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
731 bn_scatter5(tmp.d, top, powerbuf, i);
734 /* same as above, but uses squaring for 1/2 of operations */
735 for (i = 4; i < 32; i *= 2) {
736 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
737 bn_scatter5(tmp.d, top, powerbuf, i);
739 for (i = 3; i < 8; i += 2) {
741 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
742 bn_scatter5(tmp.d, top, powerbuf, i);
743 for (j = 2 * i; j < 32; j *= 2) {
744 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
745 bn_scatter5(tmp.d, top, powerbuf, j);
748 for (; i < 16; i += 2) {
749 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
750 bn_scatter5(tmp.d, top, powerbuf, i);
751 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
752 bn_scatter5(tmp.d, top, powerbuf, 2 * i);
754 for (; i < 32; i += 2) {
755 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
756 bn_scatter5(tmp.d, top, powerbuf, i);
760 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
761 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
762 bn_gather5(tmp.d, top, powerbuf, wvalue);
765 * Scan the exponent one window at a time starting from the most
769 for (wvalue = 0, i = 0; i < 5; i++, bits--)
770 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
772 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
773 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
774 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
775 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
776 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
777 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue);
781 bn_correct_top(&tmp);
785 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, numPowers))
787 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, numPowers))
791 * If the window size is greater than 1, then calculate
792 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
793 * powers could instead be computed as (a^(i/2))^2 to use the slight
794 * performance advantage of sqr over mul).
797 if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx))
799 if (!MOD_EXP_CTIME_COPY_TO_PREBUF
800 (&tmp, top, powerbuf, 2, numPowers))
802 for (i = 3; i < numPowers; i++) {
803 /* Calculate a^i = a^(i-1) * a */
804 if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx))
806 if (!MOD_EXP_CTIME_COPY_TO_PREBUF
807 (&tmp, top, powerbuf, i, numPowers))
813 for (wvalue = 0, i = bits % window; i >= 0; i--, bits--)
814 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
815 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF
816 (&tmp, top, powerbuf, wvalue, numPowers))
820 * Scan the exponent one window at a time starting from the most
824 wvalue = 0; /* The 'value' of the window */
826 /* Scan the window, squaring the result as we go */
827 for (i = 0; i < window; i++, bits--) {
828 if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx))
830 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
834 * Fetch the appropriate pre-computed value from the pre-buf
836 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF
837 (&am, top, powerbuf, wvalue, numPowers))
840 /* Multiply the result into the intermediate result */
841 if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx))
846 /* Convert the final result from montgomery to standard format */
847 if (!BN_from_montgomery(rr, &tmp, mont, ctx))
851 if ((in_mont == NULL) && (mont != NULL))
852 BN_MONT_CTX_free(mont);
853 if (powerbuf != NULL) {
854 OPENSSL_cleanse(powerbuf, powerbufLen);
856 OPENSSL_free(powerbufFree);
862 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
863 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
865 BN_MONT_CTX *mont = NULL;
866 int b, bits, ret = 0;
871 #define BN_MOD_MUL_WORD(r, w, m) \
872 (BN_mul_word(r, (w)) && \
873 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
874 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
876 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
877 * probably more overhead than always using BN_mod (which uses BN_copy if
878 * a similar test returns true).
881 * We can use BN_mod and do not need BN_nnmod because our accumulator is
882 * never negative (the result of BN_mod does not depend on the sign of
885 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
886 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
888 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
889 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
890 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
898 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
902 a %= m->d[0]; /* make sure that 'a' is reduced */
904 bits = BN_num_bits(p);
906 /* x**0 mod 1 is still zero. */
924 if (d == NULL || r == NULL || t == NULL)
930 if ((mont = BN_MONT_CTX_new()) == NULL)
932 if (!BN_MONT_CTX_set(mont, m, ctx))
936 r_is_one = 1; /* except for Montgomery factor */
940 /* The result is accumulated in the product r*w. */
941 w = a; /* bit 'bits-1' of 'p' is always set */
942 for (b = bits - 2; b >= 0; b--) {
943 /* First, square r*w. */
945 if ((next_w / w) != w) { /* overflow */
947 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
951 if (!BN_MOD_MUL_WORD(r, w, m))
958 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
962 /* Second, multiply r*w by 'a' if exponent bit is set. */
963 if (BN_is_bit_set(p, b)) {
965 if ((next_w / a) != w) { /* overflow */
967 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
971 if (!BN_MOD_MUL_WORD(r, w, m))
980 /* Finally, set r:=r*w. */
983 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
987 if (!BN_MOD_MUL_WORD(r, w, m))
992 if (r_is_one) { /* can happen only if a == 1 */
996 if (!BN_from_montgomery(rr, r, mont, ctx))
1001 if ((in_mont == NULL) && (mont != NULL))
1002 BN_MONT_CTX_free(mont);
1008 /* The old fallback, simple version :-) */
1009 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1010 const BIGNUM *m, BN_CTX *ctx)
1012 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
1015 /* Table of variables obtained from 'ctx' */
1016 BIGNUM *val[TABLE_SIZE];
1018 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
1019 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1020 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1024 bits = BN_num_bits(p);
1032 d = BN_CTX_get(ctx);
1033 val[0] = BN_CTX_get(ctx);
1037 if (!BN_nnmod(val[0], a, m, ctx))
1039 if (BN_is_zero(val[0])) {
1045 window = BN_window_bits_for_exponent_size(bits);
1047 if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1049 j = 1 << (window - 1);
1050 for (i = 1; i < j; i++) {
1051 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
1052 !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
1057 start = 1; /* This is used to avoid multiplication etc
1058 * when there is only the value '1' in the
1060 wvalue = 0; /* The 'value' of the window */
1061 wstart = bits - 1; /* The top bit of the window */
1062 wend = 0; /* The bottom bit of the window */
1068 if (BN_is_bit_set(p, wstart) == 0) {
1070 if (!BN_mod_mul(r, r, r, m, ctx))
1078 * We now have wstart on a 'set' bit, we now need to work out how bit
1079 * a window to do. To do this we need to scan forward until the last
1080 * set bit before the end of the window
1085 for (i = 1; i < window; i++) {
1088 if (BN_is_bit_set(p, wstart - i)) {
1089 wvalue <<= (i - wend);
1095 /* wend is the size of the current window */
1097 /* add the 'bytes above' */
1099 for (i = 0; i < j; i++) {
1100 if (!BN_mod_mul(r, r, r, m, ctx))
1104 /* wvalue will be an odd number < 2^window */
1105 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1108 /* move the 'window' down further */