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 is still zero. */
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 is still zero. */
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_montgomery(val[0], aa, mont, ctx))
479 window = BN_window_bits_for_exponent_size(bits);
481 if (!BN_mod_mul_montgomery(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_mod_mul_montgomery(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;
509 * Upper words will be zero if the corresponding words of 'm' were
510 * 0xfff[...], so decrement r->top accordingly.
515 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
518 if (BN_is_bit_set(p, wstart) == 0) {
520 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
529 * We now have wstart on a 'set' bit, we now need to work out how bit
530 * a window to do. To do this we need to scan forward until the last
531 * set bit before the end of the window
536 for (i = 1; i < window; i++) {
539 if (BN_is_bit_set(p, wstart - i)) {
540 wvalue <<= (i - wend);
546 /* wend is the size of the current window */
548 /* add the 'bytes above' */
550 for (i = 0; i < j; i++) {
551 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
555 /* wvalue will be an odd number < 2^window */
556 if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
559 /* move the 'window' down further */
566 #if defined(SPARC_T4_MONT)
567 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
568 j = mont->N.top; /* borrow j */
569 val[0]->d[0] = 1; /* borrow val[0] */
570 for (i = 1; i < j; i++)
573 if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
577 if (!BN_from_montgomery(rr, r, mont, ctx))
581 if ((in_mont == NULL) && (mont != NULL))
582 BN_MONT_CTX_free(mont);
588 #if defined(SPARC_T4_MONT)
589 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
594 wordpos = bitpos / BN_BITS2;
596 if (wordpos >= 0 && wordpos < a->top) {
597 ret = a->d[wordpos] & BN_MASK2;
600 if (++wordpos < a->top)
601 ret |= a->d[wordpos] << (BN_BITS2 - bitpos);
605 return ret & BN_MASK2;
610 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
611 * layout so that accessing any of these table values shows the same access
612 * pattern as far as cache lines are concerned. The following functions are
613 * used to transfer a BIGNUM from/to that table.
616 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
617 unsigned char *buf, int idx,
621 int width = 1 << window;
622 BN_ULONG *table = (BN_ULONG *)buf;
625 top = b->top; /* this works because 'buf' is explicitly
627 for (i = 0, j = idx; i < top; i++, j += width) {
634 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
635 unsigned char *buf, int idx,
639 int width = 1 << window;
640 volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
642 if (bn_wexpand(b, top) == NULL)
646 for (i = 0; i < top; i++, table += width) {
649 for (j = 0; j < width; j++) {
651 ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
657 int xstride = 1 << (window - 2);
658 BN_ULONG y0, y1, y2, y3;
660 i = idx >> (window - 2); /* equivalent of idx / xstride */
661 idx &= xstride - 1; /* equivalent of idx % xstride */
663 y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1);
664 y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1);
665 y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1);
666 y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1);
668 for (i = 0; i < top; i++, table += width) {
671 for (j = 0; j < xstride; j++) {
672 acc |= ( (table[j + 0 * xstride] & y0) |
673 (table[j + 1 * xstride] & y1) |
674 (table[j + 2 * xstride] & y2) |
675 (table[j + 3 * xstride] & y3) )
676 & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
689 * Given a pointer value, compute the next address that is a cache line
692 #define MOD_EXP_CTIME_ALIGN(x_) \
693 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
696 * This variant of BN_mod_exp_mont() uses fixed windows and the special
697 * precomputation memory layout to limit data-dependency to a minimum to
698 * protect secret exponents (cf. the hyper-threading timing attacks pointed
699 * out by Colin Percival,
700 * http://www.daemonology.net/hyperthreading-considered-harmful/)
702 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
703 const BIGNUM *m, BN_CTX *ctx,
704 BN_MONT_CTX *in_mont)
706 int i, bits, ret = 0, window, wvalue;
708 BN_MONT_CTX *mont = NULL;
711 unsigned char *powerbufFree = NULL;
713 unsigned char *powerbuf = NULL;
715 #if defined(SPARC_T4_MONT)
724 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
731 * Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak
732 * whether the top bits are zero.
734 bits = p->top * BN_BITS2;
736 /* x**0 mod 1 is still zero. */
749 * Allocate a montgomery context if it was not supplied by the caller. If
750 * this is not done, things will break in the montgomery part.
755 if ((mont = BN_MONT_CTX_new()) == NULL)
757 if (!BN_MONT_CTX_set(mont, m, ctx))
763 * If the size of the operands allow it, perform the optimized
764 * RSAZ exponentiation. For further information see
765 * crypto/bn/rsaz_exp.c and accompanying assembly modules.
767 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
768 && rsaz_avx2_eligible()) {
769 if (NULL == bn_wexpand(rr, 16))
771 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
778 } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
779 if (NULL == bn_wexpand(rr, 8))
781 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
790 /* Get the window size to use with size of p. */
791 window = BN_window_bits_for_ctime_exponent_size(bits);
792 #if defined(SPARC_T4_MONT)
793 if (window >= 5 && (top & 15) == 0 && top <= 64 &&
794 (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) ==
795 (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0]))
799 #if defined(OPENSSL_BN_ASM_MONT5)
801 window = 5; /* ~5% improvement for RSA2048 sign, and even
803 /* reserve space for mont->N.d[] copy */
804 powerbufLen += top * sizeof(mont->N.d[0]);
810 * Allocate a buffer large enough to hold all of the pre-computed powers
811 * of am, am itself and tmp.
813 numPowers = 1 << window;
814 powerbufLen += sizeof(m->d[0]) * (top * numPowers +
816 numPowers ? (2 * top) : numPowers));
818 if (powerbufLen < 3072)
820 alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
824 (unsigned char *)OPENSSL_malloc(powerbufLen +
825 MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
829 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
830 memset(powerbuf, 0, powerbufLen);
833 if (powerbufLen < 3072)
837 /* lay down tmp and am right after powers table */
838 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
840 tmp.top = am.top = 0;
841 tmp.dmax = am.dmax = top;
842 tmp.neg = am.neg = 0;
843 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
845 /* prepare a^0 in Montgomery domain */
846 #if 1 /* by Shay Gueron's suggestion */
847 if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
848 /* 2^(top*BN_BITS2) - m */
849 tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
850 for (i = 1; i < top; i++)
851 tmp.d[i] = (~m->d[i]) & BN_MASK2;
855 if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx))
858 /* prepare a^1 in Montgomery domain */
859 if (a->neg || BN_ucmp(a, m) >= 0) {
860 if (!BN_mod(&am, a, m, ctx))
862 if (!BN_to_montgomery(&am, &am, mont, ctx))
864 } else if (!BN_to_montgomery(&am, a, mont, ctx))
867 #if defined(SPARC_T4_MONT)
869 typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np,
870 const BN_ULONG *n0, const void *table,
871 int power, int bits);
872 int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np,
873 const BN_ULONG *n0, const void *table,
874 int power, int bits);
875 int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np,
876 const BN_ULONG *n0, const void *table,
877 int power, int bits);
878 int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np,
879 const BN_ULONG *n0, const void *table,
880 int power, int bits);
881 int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np,
882 const BN_ULONG *n0, const void *table,
883 int power, int bits);
884 static const bn_pwr5_mont_f pwr5_funcs[4] = {
885 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
886 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
888 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
890 typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap,
891 const void *bp, const BN_ULONG *np,
893 int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp,
894 const BN_ULONG *np, const BN_ULONG *n0);
895 int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap,
896 const void *bp, const BN_ULONG *np,
898 int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap,
899 const void *bp, const BN_ULONG *np,
901 int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap,
902 const void *bp, const BN_ULONG *np,
904 static const bn_mul_mont_f mul_funcs[4] = {
905 bn_mul_mont_t4_8, bn_mul_mont_t4_16,
906 bn_mul_mont_t4_24, bn_mul_mont_t4_32
908 bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
910 void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap,
911 const void *bp, const BN_ULONG *np,
912 const BN_ULONG *n0, int num);
913 void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap,
914 const void *bp, const BN_ULONG *np,
915 const BN_ULONG *n0, int num);
916 void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap,
917 const void *table, const BN_ULONG *np,
918 const BN_ULONG *n0, int num, int power);
919 void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
920 void *table, size_t power);
921 void bn_gather5_t4(BN_ULONG *out, size_t num,
922 void *table, size_t power);
923 void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num);
925 BN_ULONG *np = mont->N.d, *n0 = mont->n0;
926 int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
930 * BN_to_montgomery can contaminate words above .top [in
931 * BN_DEBUG[_DEBUG] build]...
933 for (i = am.top; i < top; i++)
935 for (i = tmp.top; i < top; i++)
938 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
939 bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
940 if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) &&
941 !(*mul_worker) (tmp.d, am.d, am.d, np, n0))
942 bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
943 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
945 for (i = 3; i < 32; i++) {
946 /* Calculate a^i = a^(i-1) * a */
947 if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) &&
948 !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0))
949 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
950 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
953 /* switch to 64-bit domain */
954 np = alloca(top * sizeof(BN_ULONG));
956 bn_flip_t4(np, mont->N.d, top);
959 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
960 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
961 bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
964 * Scan the exponent one window at a time starting from the most
971 wvalue = bn_get_bits(p, bits + 1);
973 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
975 /* retry once and fall back */
976 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
980 wvalue >>= stride - 5;
982 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
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_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
991 bn_flip_t4(tmp.d, tmp.d, top);
993 /* back to 32-bit domain */
995 bn_correct_top(&tmp);
996 OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
999 #if defined(OPENSSL_BN_ASM_MONT5)
1000 if (window == 5 && top > 1) {
1002 * This optimization uses ideas from http://eprint.iacr.org/2011/239,
1003 * specifically optimization of cache-timing attack countermeasures
1004 * and pre-computation optimization.
1008 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
1009 * 512-bit RSA is hardly relevant, we omit it to spare size...
1011 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
1012 const void *table, const BN_ULONG *np,
1013 const BN_ULONG *n0, int num, int power);
1014 void bn_scatter5(const BN_ULONG *inp, size_t num,
1015 void *table, size_t power);
1016 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
1017 void bn_power5(BN_ULONG *rp, const BN_ULONG *ap,
1018 const void *table, const BN_ULONG *np,
1019 const BN_ULONG *n0, int num, int power);
1020 int bn_get_bits5(const BN_ULONG *ap, int off);
1021 int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap,
1022 const BN_ULONG *not_used, const BN_ULONG *np,
1023 const BN_ULONG *n0, int num);
1025 BN_ULONG *n0 = mont->n0, *np;
1028 * BN_to_montgomery can contaminate words above .top [in
1029 * BN_DEBUG[_DEBUG] build]...
1031 for (i = am.top; i < top; i++)
1033 for (i = tmp.top; i < top; i++)
1037 * copy mont->N.d[] to improve cache locality
1039 for (np = am.d + top, i = 0; i < top; i++)
1040 np[i] = mont->N.d[i];
1042 bn_scatter5(tmp.d, top, powerbuf, 0);
1043 bn_scatter5(am.d, am.top, powerbuf, 1);
1044 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
1045 bn_scatter5(tmp.d, top, powerbuf, 2);
1048 for (i = 3; i < 32; i++) {
1049 /* Calculate a^i = a^(i-1) * a */
1050 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1051 bn_scatter5(tmp.d, top, powerbuf, i);
1054 /* same as above, but uses squaring for 1/2 of operations */
1055 for (i = 4; i < 32; i *= 2) {
1056 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1057 bn_scatter5(tmp.d, top, powerbuf, i);
1059 for (i = 3; i < 8; i += 2) {
1061 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1062 bn_scatter5(tmp.d, top, powerbuf, i);
1063 for (j = 2 * i; j < 32; j *= 2) {
1064 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1065 bn_scatter5(tmp.d, top, powerbuf, j);
1068 for (; i < 16; i += 2) {
1069 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1070 bn_scatter5(tmp.d, top, powerbuf, i);
1071 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1072 bn_scatter5(tmp.d, top, powerbuf, 2 * i);
1074 for (; i < 32; i += 2) {
1075 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1076 bn_scatter5(tmp.d, top, powerbuf, i);
1080 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
1081 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1082 bn_gather5(tmp.d, top, powerbuf, wvalue);
1085 * Scan the exponent one window at a time starting from the most
1090 for (wvalue = 0, i = 0; i < 5; i++, bits--)
1091 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1093 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
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_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
1102 wvalue = bn_get_bits5(p->d, bits - 4);
1104 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue);
1108 ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np, n0, top);
1110 bn_correct_top(&tmp);
1112 if (!BN_copy(rr, &tmp))
1114 goto err; /* non-zero ret means it's not error */
1119 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window))
1121 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window))
1125 * If the window size is greater than 1, then calculate
1126 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1127 * powers could instead be computed as (a^(i/2))^2 to use the slight
1128 * performance advantage of sqr over mul).
1131 if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx))
1133 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2,
1136 for (i = 3; i < numPowers; i++) {
1137 /* Calculate a^i = a^(i-1) * a */
1138 if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx))
1140 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i,
1147 for (wvalue = 0, i = bits % window; i >= 0; i--, bits--)
1148 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1149 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue,
1154 * Scan the exponent one window at a time starting from the most
1158 wvalue = 0; /* The 'value' of the window */
1160 /* Scan the window, squaring the result as we go */
1161 for (i = 0; i < window; i++, bits--) {
1162 if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx))
1164 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1168 * Fetch the appropriate pre-computed value from the pre-buf
1170 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
1174 /* Multiply the result into the intermediate result */
1175 if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx))
1180 /* Convert the final result from montgomery to standard format */
1181 #if defined(SPARC_T4_MONT)
1182 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
1183 am.d[0] = 1; /* borrow am */
1184 for (i = 1; i < top; i++)
1186 if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
1190 if (!BN_from_montgomery(rr, &tmp, mont, ctx))
1194 if ((in_mont == NULL) && (mont != NULL))
1195 BN_MONT_CTX_free(mont);
1196 if (powerbuf != NULL) {
1197 OPENSSL_cleanse(powerbuf, powerbufLen);
1199 OPENSSL_free(powerbufFree);
1205 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1206 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1208 BN_MONT_CTX *mont = NULL;
1209 int b, bits, ret = 0;
1214 #define BN_MOD_MUL_WORD(r, w, m) \
1215 (BN_mul_word(r, (w)) && \
1216 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1217 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1219 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1220 * probably more overhead than always using BN_mod (which uses BN_copy if
1221 * a similar test returns true).
1224 * We can use BN_mod and do not need BN_nnmod because our accumulator is
1225 * never negative (the result of BN_mod does not depend on the sign of
1228 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1229 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1231 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1232 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1233 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1234 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1241 if (!BN_is_odd(m)) {
1242 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
1246 a %= m->d[0]; /* make sure that 'a' is reduced */
1248 bits = BN_num_bits(p);
1250 /* x**0 mod 1 is still zero. */
1266 d = BN_CTX_get(ctx);
1267 r = BN_CTX_get(ctx);
1268 t = BN_CTX_get(ctx);
1269 if (d == NULL || r == NULL || t == NULL)
1272 if (in_mont != NULL)
1275 if ((mont = BN_MONT_CTX_new()) == NULL)
1277 if (!BN_MONT_CTX_set(mont, m, ctx))
1281 r_is_one = 1; /* except for Montgomery factor */
1285 /* The result is accumulated in the product r*w. */
1286 w = a; /* bit 'bits-1' of 'p' is always set */
1287 for (b = bits - 2; b >= 0; b--) {
1288 /* First, square r*w. */
1290 if ((next_w / w) != w) { /* overflow */
1292 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1296 if (!BN_MOD_MUL_WORD(r, w, m))
1303 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
1307 /* Second, multiply r*w by 'a' if exponent bit is set. */
1308 if (BN_is_bit_set(p, b)) {
1310 if ((next_w / a) != w) { /* overflow */
1312 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1316 if (!BN_MOD_MUL_WORD(r, w, m))
1325 /* Finally, set r:=r*w. */
1328 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1332 if (!BN_MOD_MUL_WORD(r, w, m))
1337 if (r_is_one) { /* can happen only if a == 1 */
1341 if (!BN_from_montgomery(rr, r, mont, ctx))
1346 if ((in_mont == NULL) && (mont != NULL))
1347 BN_MONT_CTX_free(mont);
1353 /* The old fallback, simple version :-) */
1354 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1355 const BIGNUM *m, BN_CTX *ctx)
1357 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
1360 /* Table of variables obtained from 'ctx' */
1361 BIGNUM *val[TABLE_SIZE];
1363 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1364 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
1365 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1366 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1367 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1371 bits = BN_num_bits(p);
1373 /* x**0 mod 1 is still zero. */
1384 d = BN_CTX_get(ctx);
1385 val[0] = BN_CTX_get(ctx);
1389 if (!BN_nnmod(val[0], a, m, ctx))
1391 if (BN_is_zero(val[0])) {
1397 window = BN_window_bits_for_exponent_size(bits);
1399 if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1401 j = 1 << (window - 1);
1402 for (i = 1; i < j; i++) {
1403 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
1404 !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
1409 start = 1; /* This is used to avoid multiplication etc
1410 * when there is only the value '1' in the
1412 wvalue = 0; /* The 'value' of the window */
1413 wstart = bits - 1; /* The top bit of the window */
1414 wend = 0; /* The bottom bit of the window */
1420 if (BN_is_bit_set(p, wstart) == 0) {
1422 if (!BN_mod_mul(r, r, r, m, ctx))
1430 * We now have wstart on a 'set' bit, we now need to work out how bit
1431 * a window to do. To do this we need to scan forward until the last
1432 * set bit before the end of the window
1437 for (i = 1; i < window; i++) {
1440 if (BN_is_bit_set(p, wstart - i)) {
1441 wvalue <<= (i - wend);
1447 /* wend is the size of the current window */
1449 /* add the 'bytes above' */
1451 for (i = 0; i < j; i++) {
1452 if (!BN_mod_mul(r, r, r, m, ctx))
1456 /* wvalue will be an odd number < 2^window */
1457 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1460 /* move the 'window' down further */