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) 1998-2018 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"
120 # define alloca _alloca
122 #elif defined(__GNUC__)
124 # define alloca(s) __builtin_alloca((s))
130 #include "rsaz_exp.h"
133 #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
134 # include "sparc_arch.h"
135 extern unsigned int OPENSSL_sparcv9cap_P[];
136 # define SPARC_T4_MONT
139 /* maximum precomputation table size for *variable* sliding windows */
140 #define TABLE_SIZE 32
142 /* this one works - simple but works */
143 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
145 int i, bits, ret = 0;
148 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
149 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0) {
150 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
151 BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
156 if ((r == a) || (r == p))
157 rr = BN_CTX_get(ctx);
161 if (rr == NULL || v == NULL)
164 if (BN_copy(v, a) == NULL)
166 bits = BN_num_bits(p);
169 if (BN_copy(rr, a) == NULL)
176 for (i = 1; i < bits; i++) {
177 if (!BN_sqr(v, v, ctx))
179 if (BN_is_bit_set(p, i)) {
180 if (!BN_mul(rr, rr, v, ctx))
184 if (r != rr && BN_copy(r, rr) == NULL)
194 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
204 * For even modulus m = 2^k*m_odd, it might make sense to compute
205 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
206 * exponentiation for the odd part), using appropriate exponent
207 * reductions, and combine the results using the CRT.
209 * For now, we use Montgomery only if the modulus is odd; otherwise,
210 * exponentiation using the reciprocal-based quick remaindering
213 * (Timing obtained with expspeed.c [computations a^p mod m
214 * where a, p, m are of the same length: 256, 512, 1024, 2048,
215 * 4096, 8192 bits], compared to the running time of the
216 * standard algorithm:
218 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
219 * 55 .. 77 % [UltraSparc processor, but
220 * debug-solaris-sparcv8-gcc conf.]
222 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
223 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
225 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
226 * at 2048 and more bits, but at 512 and 1024 bits, it was
227 * slower even than the standard algorithm!
229 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
230 * should be obtained when the new Montgomery reduction code
231 * has been integrated into OpenSSL.)
235 #define MONT_EXP_WORD
240 * I have finally been able to take out this pre-condition of the top bit
241 * being set. It was caused by an error in BN_div with negatives. There
242 * was also another problem when for a^b%m a >= m. eay 07-May-97
244 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
247 # ifdef MONT_EXP_WORD
248 if (a->top == 1 && !a->neg
249 && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)
250 && (BN_get_flags(a, BN_FLG_CONSTTIME) == 0)
251 && (BN_get_flags(m, BN_FLG_CONSTTIME) == 0)) {
252 BN_ULONG A = a->d[0];
253 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
256 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
261 ret = BN_mod_exp_recp(r, a, p, m, ctx);
265 ret = BN_mod_exp_simple(r, a, p, m, ctx);
273 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
274 const BIGNUM *m, BN_CTX *ctx)
276 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
279 /* Table of variables obtained from 'ctx' */
280 BIGNUM *val[TABLE_SIZE];
283 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
284 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
285 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
286 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
287 BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
291 bits = BN_num_bits(p);
293 /* x**0 mod 1, or x**0 mod -1 is still zero. */
294 if (BN_abs_is_word(m, 1)) {
304 aa = BN_CTX_get(ctx);
305 val[0] = BN_CTX_get(ctx);
309 BN_RECP_CTX_init(&recp);
311 /* ignore sign of 'm' */
315 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
318 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
322 if (!BN_nnmod(val[0], a, m, ctx))
324 if (BN_is_zero(val[0])) {
330 window = BN_window_bits_for_exponent_size(bits);
332 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
334 j = 1 << (window - 1);
335 for (i = 1; i < j; i++) {
336 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
337 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
342 start = 1; /* This is used to avoid multiplication etc
343 * when there is only the value '1' in the
345 wvalue = 0; /* The 'value' of the window */
346 wstart = bits - 1; /* The top bit of the window */
347 wend = 0; /* The bottom bit of the window */
353 if (BN_is_bit_set(p, wstart) == 0) {
355 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
363 * We now have wstart on a 'set' bit, we now need to work out how bit
364 * a window to do. To do this we need to scan forward until the last
365 * set bit before the end of the window
370 for (i = 1; i < window; i++) {
373 if (BN_is_bit_set(p, wstart - i)) {
374 wvalue <<= (i - wend);
380 /* wend is the size of the current window */
382 /* add the 'bytes above' */
384 for (i = 0; i < j; i++) {
385 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
389 /* wvalue will be an odd number < 2^window */
390 if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
393 /* move the 'window' down further */
403 BN_RECP_CTX_free(&recp);
408 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
409 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
411 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
415 /* Table of variables obtained from 'ctx' */
416 BIGNUM *val[TABLE_SIZE];
417 BN_MONT_CTX *mont = NULL;
419 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
420 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
421 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
422 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
430 BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
433 bits = BN_num_bits(p);
435 /* x**0 mod 1, or x**0 mod -1 is still zero. */
436 if (BN_abs_is_word(m, 1)) {
448 val[0] = BN_CTX_get(ctx);
449 if (!d || !r || !val[0])
453 * If this is not done, things will break in the montgomery part
459 if ((mont = BN_MONT_CTX_new()) == NULL)
461 if (!BN_MONT_CTX_set(mont, m, ctx))
465 if (a->neg || BN_ucmp(a, m) >= 0) {
466 if (!BN_nnmod(val[0], a, m, ctx))
471 if (BN_is_zero(aa)) {
476 if (!bn_to_mont_fixed_top(val[0], aa, mont, ctx))
479 window = BN_window_bits_for_exponent_size(bits);
481 if (!bn_mul_mont_fixed_top(d, val[0], val[0], mont, ctx))
483 j = 1 << (window - 1);
484 for (i = 1; i < j; i++) {
485 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
486 !bn_mul_mont_fixed_top(val[i], val[i - 1], d, mont, ctx))
491 start = 1; /* This is used to avoid multiplication etc
492 * when there is only the value '1' in the
494 wvalue = 0; /* The 'value' of the window */
495 wstart = bits - 1; /* The top bit of the window */
496 wend = 0; /* The bottom bit of the window */
498 #if 1 /* by Shay Gueron's suggestion */
499 j = m->top; /* borrow j */
500 if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
501 if (bn_wexpand(r, j) == NULL)
503 /* 2^(top*BN_BITS2) - m */
504 r->d[0] = (0 - m->d[0]) & BN_MASK2;
505 for (i = 1; i < j; i++)
506 r->d[i] = (~m->d[i]) & BN_MASK2;
508 r->flags |= BN_FLG_FIXED_TOP;
511 if (!bn_to_mont_fixed_top(r, BN_value_one(), mont, ctx))
514 if (BN_is_bit_set(p, wstart) == 0) {
516 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx))
525 * We now have wstart on a 'set' bit, we now need to work out how bit
526 * a window to do. To do this we need to scan forward until the last
527 * set bit before the end of the window
532 for (i = 1; i < window; i++) {
535 if (BN_is_bit_set(p, wstart - i)) {
536 wvalue <<= (i - wend);
542 /* wend is the size of the current window */
544 /* add the 'bytes above' */
546 for (i = 0; i < j; i++) {
547 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx))
551 /* wvalue will be an odd number < 2^window */
552 if (!bn_mul_mont_fixed_top(r, r, val[wvalue >> 1], mont, ctx))
555 /* move the 'window' down further */
563 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
564 * removes padding [if any] and makes return value suitable for public
567 #if defined(SPARC_T4_MONT)
568 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
569 j = mont->N.top; /* borrow j */
570 val[0]->d[0] = 1; /* borrow val[0] */
571 for (i = 1; i < j; i++)
574 if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
578 if (!BN_from_montgomery(rr, r, mont, ctx))
582 if ((in_mont == NULL) && (mont != NULL))
583 BN_MONT_CTX_free(mont);
589 #if defined(SPARC_T4_MONT)
590 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
595 wordpos = bitpos / BN_BITS2;
597 if (wordpos >= 0 && wordpos < a->top) {
598 ret = a->d[wordpos] & BN_MASK2;
601 if (++wordpos < a->top)
602 ret |= a->d[wordpos] << (BN_BITS2 - bitpos);
606 return ret & BN_MASK2;
611 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
612 * layout so that accessing any of these table values shows the same access
613 * pattern as far as cache lines are concerned. The following functions are
614 * used to transfer a BIGNUM from/to that table.
617 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
618 unsigned char *buf, int idx,
622 int width = 1 << window;
623 BN_ULONG *table = (BN_ULONG *)buf;
626 top = b->top; /* this works because 'buf' is explicitly
628 for (i = 0, j = idx; i < top; i++, j += width) {
635 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
636 unsigned char *buf, int idx,
640 int width = 1 << window;
641 volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
643 if (bn_wexpand(b, top) == NULL)
647 for (i = 0; i < top; i++, table += width) {
650 for (j = 0; j < width; j++) {
652 ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
658 int xstride = 1 << (window - 2);
659 BN_ULONG y0, y1, y2, y3;
661 i = idx >> (window - 2); /* equivalent of idx / xstride */
662 idx &= xstride - 1; /* equivalent of idx % xstride */
664 y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1);
665 y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1);
666 y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1);
667 y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1);
669 for (i = 0; i < top; i++, table += width) {
672 for (j = 0; j < xstride; j++) {
673 acc |= ( (table[j + 0 * xstride] & y0) |
674 (table[j + 1 * xstride] & y1) |
675 (table[j + 2 * xstride] & y2) |
676 (table[j + 3 * xstride] & y3) )
677 & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
685 b->flags |= BN_FLG_FIXED_TOP;
690 * Given a pointer value, compute the next address that is a cache line
693 #define MOD_EXP_CTIME_ALIGN(x_) \
694 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
697 * This variant of BN_mod_exp_mont() uses fixed windows and the special
698 * precomputation memory layout to limit data-dependency to a minimum to
699 * protect secret exponents (cf. the hyper-threading timing attacks pointed
700 * out by Colin Percival,
701 * http://www.daemonology.net/hyperthreading-considered-harmful/)
703 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
704 const BIGNUM *m, BN_CTX *ctx,
705 BN_MONT_CTX *in_mont)
707 int i, bits, ret = 0, window, wvalue;
709 BN_MONT_CTX *mont = NULL;
712 unsigned char *powerbufFree = NULL;
714 unsigned char *powerbuf = NULL;
716 #if defined(SPARC_T4_MONT)
725 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
732 * Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak
733 * whether the top bits are zero.
735 bits = p->top * BN_BITS2;
737 /* x**0 mod 1, or x**0 mod -1 is still zero. */
738 if (BN_abs_is_word(m, 1)) {
750 * Allocate a montgomery context if it was not supplied by the caller. If
751 * this is not done, things will break in the montgomery part.
756 if ((mont = BN_MONT_CTX_new()) == NULL)
758 if (!BN_MONT_CTX_set(mont, m, ctx))
764 * If the size of the operands allow it, perform the optimized
765 * RSAZ exponentiation. For further information see
766 * crypto/bn/rsaz_exp.c and accompanying assembly modules.
768 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
769 && rsaz_avx2_eligible()) {
770 if (NULL == bn_wexpand(rr, 16))
772 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
779 } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
780 if (NULL == bn_wexpand(rr, 8))
782 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
791 /* Get the window size to use with size of p. */
792 window = BN_window_bits_for_ctime_exponent_size(bits);
793 #if defined(SPARC_T4_MONT)
794 if (window >= 5 && (top & 15) == 0 && top <= 64 &&
795 (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) ==
796 (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0]))
800 #if defined(OPENSSL_BN_ASM_MONT5)
802 window = 5; /* ~5% improvement for RSA2048 sign, and even
804 /* reserve space for mont->N.d[] copy */
805 powerbufLen += top * sizeof(mont->N.d[0]);
811 * Allocate a buffer large enough to hold all of the pre-computed powers
812 * of am, am itself and tmp.
814 numPowers = 1 << window;
815 powerbufLen += sizeof(m->d[0]) * (top * numPowers +
817 numPowers ? (2 * top) : numPowers));
819 if (powerbufLen < 3072)
821 alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
825 (unsigned char *)OPENSSL_malloc(powerbufLen +
826 MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
830 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
831 memset(powerbuf, 0, powerbufLen);
834 if (powerbufLen < 3072)
838 /* lay down tmp and am right after powers table */
839 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
841 tmp.top = am.top = 0;
842 tmp.dmax = am.dmax = top;
843 tmp.neg = am.neg = 0;
844 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
846 /* prepare a^0 in Montgomery domain */
847 #if 1 /* by Shay Gueron's suggestion */
848 if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
849 /* 2^(top*BN_BITS2) - m */
850 tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
851 for (i = 1; i < top; i++)
852 tmp.d[i] = (~m->d[i]) & BN_MASK2;
856 if (!bn_to_mont_fixed_top(&tmp, BN_value_one(), mont, ctx))
859 /* prepare a^1 in Montgomery domain */
860 if (a->neg || BN_ucmp(a, m) >= 0) {
861 if (!BN_mod(&am, a, m, ctx))
863 if (!bn_to_mont_fixed_top(&am, &am, mont, ctx))
865 } else if (!bn_to_mont_fixed_top(&am, a, mont, ctx))
868 #if defined(SPARC_T4_MONT)
870 typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np,
871 const BN_ULONG *n0, const void *table,
872 int power, int bits);
873 int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np,
874 const BN_ULONG *n0, const void *table,
875 int power, int bits);
876 int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np,
877 const BN_ULONG *n0, const void *table,
878 int power, int bits);
879 int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np,
880 const BN_ULONG *n0, const void *table,
881 int power, int bits);
882 int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np,
883 const BN_ULONG *n0, const void *table,
884 int power, int bits);
885 static const bn_pwr5_mont_f pwr5_funcs[4] = {
886 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
887 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
889 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
891 typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap,
892 const void *bp, const BN_ULONG *np,
894 int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp,
895 const BN_ULONG *np, const BN_ULONG *n0);
896 int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap,
897 const void *bp, const BN_ULONG *np,
899 int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap,
900 const void *bp, const BN_ULONG *np,
902 int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap,
903 const void *bp, const BN_ULONG *np,
905 static const bn_mul_mont_f mul_funcs[4] = {
906 bn_mul_mont_t4_8, bn_mul_mont_t4_16,
907 bn_mul_mont_t4_24, bn_mul_mont_t4_32
909 bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
911 void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap,
912 const void *bp, const BN_ULONG *np,
913 const BN_ULONG *n0, int num);
914 void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap,
915 const void *bp, const BN_ULONG *np,
916 const BN_ULONG *n0, int num);
917 void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap,
918 const void *table, const BN_ULONG *np,
919 const BN_ULONG *n0, int num, int power);
920 void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
921 void *table, size_t power);
922 void bn_gather5_t4(BN_ULONG *out, size_t num,
923 void *table, size_t power);
924 void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num);
926 BN_ULONG *np = mont->N.d, *n0 = mont->n0;
927 int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
931 * BN_to_montgomery can contaminate words above .top [in
932 * BN_DEBUG[_DEBUG] build]...
934 for (i = am.top; i < top; i++)
936 for (i = tmp.top; i < top; i++)
939 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
940 bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
941 if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) &&
942 !(*mul_worker) (tmp.d, am.d, am.d, np, n0))
943 bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
944 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
946 for (i = 3; i < 32; i++) {
947 /* Calculate a^i = a^(i-1) * a */
948 if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) &&
949 !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0))
950 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
951 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
954 /* switch to 64-bit domain */
955 np = alloca(top * sizeof(BN_ULONG));
957 bn_flip_t4(np, mont->N.d, top);
960 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
961 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
962 bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
965 * Scan the exponent one window at a time starting from the most
972 wvalue = bn_get_bits(p, bits + 1);
974 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
976 /* retry once and fall back */
977 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
981 wvalue >>= stride - 5;
983 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
984 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
985 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
986 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
987 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
988 bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
992 bn_flip_t4(tmp.d, tmp.d, top);
994 /* back to 32-bit domain */
996 bn_correct_top(&tmp);
997 OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
1000 #if defined(OPENSSL_BN_ASM_MONT5)
1001 if (window == 5 && top > 1) {
1003 * This optimization uses ideas from http://eprint.iacr.org/2011/239,
1004 * specifically optimization of cache-timing attack countermeasures
1005 * and pre-computation optimization.
1009 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
1010 * 512-bit RSA is hardly relevant, we omit it to spare size...
1012 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
1013 const void *table, const BN_ULONG *np,
1014 const BN_ULONG *n0, int num, int power);
1015 void bn_scatter5(const BN_ULONG *inp, size_t num,
1016 void *table, size_t power);
1017 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
1018 void bn_power5(BN_ULONG *rp, const BN_ULONG *ap,
1019 const void *table, const BN_ULONG *np,
1020 const BN_ULONG *n0, int num, int power);
1021 int bn_get_bits5(const BN_ULONG *ap, int off);
1022 int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap,
1023 const BN_ULONG *not_used, const BN_ULONG *np,
1024 const BN_ULONG *n0, int num);
1026 BN_ULONG *n0 = mont->n0, *np;
1029 * BN_to_montgomery can contaminate words above .top [in
1030 * BN_DEBUG[_DEBUG] build]...
1032 for (i = am.top; i < top; i++)
1034 for (i = tmp.top; i < top; i++)
1038 * copy mont->N.d[] to improve cache locality
1040 for (np = am.d + top, i = 0; i < top; i++)
1041 np[i] = mont->N.d[i];
1043 bn_scatter5(tmp.d, top, powerbuf, 0);
1044 bn_scatter5(am.d, am.top, powerbuf, 1);
1045 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
1046 bn_scatter5(tmp.d, top, powerbuf, 2);
1049 for (i = 3; i < 32; i++) {
1050 /* Calculate a^i = a^(i-1) * a */
1051 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1052 bn_scatter5(tmp.d, top, powerbuf, i);
1055 /* same as above, but uses squaring for 1/2 of operations */
1056 for (i = 4; i < 32; i *= 2) {
1057 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1058 bn_scatter5(tmp.d, top, powerbuf, i);
1060 for (i = 3; i < 8; i += 2) {
1062 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1063 bn_scatter5(tmp.d, top, powerbuf, i);
1064 for (j = 2 * i; j < 32; j *= 2) {
1065 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1066 bn_scatter5(tmp.d, top, powerbuf, j);
1069 for (; i < 16; i += 2) {
1070 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1071 bn_scatter5(tmp.d, top, powerbuf, i);
1072 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1073 bn_scatter5(tmp.d, top, powerbuf, 2 * i);
1075 for (; i < 32; i += 2) {
1076 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1077 bn_scatter5(tmp.d, top, powerbuf, i);
1081 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
1082 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1083 bn_gather5(tmp.d, top, powerbuf, wvalue);
1086 * Scan the exponent one window at a time starting from the most
1091 for (wvalue = 0, i = 0; i < 5; i++, bits--)
1092 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1094 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1095 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1096 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1097 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1098 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1099 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
1103 wvalue = bn_get_bits5(p->d, bits - 4);
1105 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue);
1109 ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np, n0, top);
1111 bn_correct_top(&tmp);
1113 if (!BN_copy(rr, &tmp))
1115 goto err; /* non-zero ret means it's not error */
1120 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window))
1122 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window))
1126 * If the window size is greater than 1, then calculate
1127 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1128 * powers could instead be computed as (a^(i/2))^2 to use the slight
1129 * performance advantage of sqr over mul).
1132 if (!bn_mul_mont_fixed_top(&tmp, &am, &am, mont, ctx))
1134 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2,
1137 for (i = 3; i < numPowers; i++) {
1138 /* Calculate a^i = a^(i-1) * a */
1139 if (!bn_mul_mont_fixed_top(&tmp, &am, &tmp, mont, ctx))
1141 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i,
1148 for (wvalue = 0, i = bits % window; i >= 0; i--, bits--)
1149 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1150 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue,
1155 * Scan the exponent one window at a time starting from the most
1159 wvalue = 0; /* The 'value' of the window */
1161 /* Scan the window, squaring the result as we go */
1162 for (i = 0; i < window; i++, bits--) {
1163 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &tmp, mont, ctx))
1165 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1169 * Fetch the appropriate pre-computed value from the pre-buf
1171 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
1175 /* Multiply the result into the intermediate result */
1176 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &am, mont, ctx))
1182 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
1183 * removes padding [if any] and makes return value suitable for public
1186 #if defined(SPARC_T4_MONT)
1187 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
1188 am.d[0] = 1; /* borrow am */
1189 for (i = 1; i < top; i++)
1191 if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
1195 if (!BN_from_montgomery(rr, &tmp, mont, ctx))
1199 if ((in_mont == NULL) && (mont != NULL))
1200 BN_MONT_CTX_free(mont);
1201 if (powerbuf != NULL) {
1202 OPENSSL_cleanse(powerbuf, powerbufLen);
1204 OPENSSL_free(powerbufFree);
1210 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1211 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1213 BN_MONT_CTX *mont = NULL;
1214 int b, bits, ret = 0;
1219 #define BN_MOD_MUL_WORD(r, w, m) \
1220 (BN_mul_word(r, (w)) && \
1221 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1222 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1224 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1225 * probably more overhead than always using BN_mod (which uses BN_copy if
1226 * a similar test returns true).
1229 * We can use BN_mod and do not need BN_nnmod because our accumulator is
1230 * never negative (the result of BN_mod does not depend on the sign of
1233 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1234 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1236 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1237 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1238 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1239 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1246 if (!BN_is_odd(m)) {
1247 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
1251 a %= m->d[0]; /* make sure that 'a' is reduced */
1253 bits = BN_num_bits(p);
1255 /* x**0 mod 1, or x**0 mod -1 is still zero. */
1256 if (BN_abs_is_word(m, 1)) {
1271 d = BN_CTX_get(ctx);
1272 r = BN_CTX_get(ctx);
1273 t = BN_CTX_get(ctx);
1274 if (d == NULL || r == NULL || t == NULL)
1277 if (in_mont != NULL)
1280 if ((mont = BN_MONT_CTX_new()) == NULL)
1282 if (!BN_MONT_CTX_set(mont, m, ctx))
1286 r_is_one = 1; /* except for Montgomery factor */
1290 /* The result is accumulated in the product r*w. */
1291 w = a; /* bit 'bits-1' of 'p' is always set */
1292 for (b = bits - 2; b >= 0; b--) {
1293 /* First, square r*w. */
1295 if ((next_w / w) != w) { /* overflow */
1297 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1301 if (!BN_MOD_MUL_WORD(r, w, m))
1308 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
1312 /* Second, multiply r*w by 'a' if exponent bit is set. */
1313 if (BN_is_bit_set(p, b)) {
1315 if ((next_w / a) != w) { /* overflow */
1317 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1321 if (!BN_MOD_MUL_WORD(r, w, m))
1330 /* Finally, set r:=r*w. */
1333 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1337 if (!BN_MOD_MUL_WORD(r, w, m))
1342 if (r_is_one) { /* can happen only if a == 1 */
1346 if (!BN_from_montgomery(rr, r, mont, ctx))
1351 if ((in_mont == NULL) && (mont != NULL))
1352 BN_MONT_CTX_free(mont);
1358 /* The old fallback, simple version :-) */
1359 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1360 const BIGNUM *m, BN_CTX *ctx)
1362 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
1365 /* Table of variables obtained from 'ctx' */
1366 BIGNUM *val[TABLE_SIZE];
1368 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1369 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
1370 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1371 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1372 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1376 bits = BN_num_bits(p);
1378 /* x**0 mod 1, or x**0 mod -1 is still zero. */
1379 if (BN_abs_is_word(m, 1)) {
1389 d = BN_CTX_get(ctx);
1390 val[0] = BN_CTX_get(ctx);
1394 if (!BN_nnmod(val[0], a, m, ctx))
1396 if (BN_is_zero(val[0])) {
1402 window = BN_window_bits_for_exponent_size(bits);
1404 if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1406 j = 1 << (window - 1);
1407 for (i = 1; i < j; i++) {
1408 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
1409 !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
1414 start = 1; /* This is used to avoid multiplication etc
1415 * when there is only the value '1' in the
1417 wvalue = 0; /* The 'value' of the window */
1418 wstart = bits - 1; /* The top bit of the window */
1419 wend = 0; /* The bottom bit of the window */
1425 if (BN_is_bit_set(p, wstart) == 0) {
1427 if (!BN_mod_mul(r, r, r, m, ctx))
1435 * We now have wstart on a 'set' bit, we now need to work out how bit
1436 * a window to do. To do this we need to scan forward until the last
1437 * set bit before the end of the window
1442 for (i = 1; i < window; i++) {
1445 if (BN_is_bit_set(p, wstart - i)) {
1446 wvalue <<= (i - wend);
1452 /* wend is the size of the current window */
1454 /* add the 'bytes above' */
1456 for (i = 0; i < j; i++) {
1457 if (!BN_mod_mul(r, r, r, m, ctx))
1461 /* wvalue will be an odd number < 2^window */
1462 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1465 /* move the 'window' down further */