1 /* crypto/bn/bn_exp.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
58 /* ====================================================================
59 * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
65 * 1. Redistributions of source code must retain the above copyright
66 * notice, this list of conditions and the following disclaimer.
68 * 2. Redistributions in binary form must reproduce the above copyright
69 * notice, this list of conditions and the following disclaimer in
70 * the documentation and/or other materials provided with the
73 * 3. All advertising materials mentioning features or use of this
74 * software must display the following acknowledgment:
75 * "This product includes software developed by the OpenSSL Project
76 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
79 * endorse or promote products derived from this software without
80 * prior written permission. For written permission, please contact
81 * openssl-core@openssl.org.
83 * 5. Products derived from this software may not be called "OpenSSL"
84 * nor may "OpenSSL" appear in their names without prior written
85 * permission of the OpenSSL Project.
87 * 6. Redistributions of any form whatsoever must retain the following
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
95 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
103 * OF THE POSSIBILITY OF SUCH DAMAGE.
104 * ====================================================================
106 * This product includes cryptographic software written by Eric Young
107 * (eay@cryptsoft.com). This product includes software written by Tim
108 * Hudson (tjh@cryptsoft.com).
112 #include "cryptlib.h"
113 #include "constant_time_locl.h"
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_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
150 BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
155 if ((r == a) || (r == p))
156 rr = BN_CTX_get(ctx);
160 if (rr == NULL || v == NULL)
163 if (BN_copy(v, a) == NULL)
165 bits = BN_num_bits(p);
168 if (BN_copy(rr, a) == NULL)
175 for (i = 1; i < bits; i++) {
176 if (!BN_sqr(v, v, ctx))
178 if (BN_is_bit_set(p, i)) {
179 if (!BN_mul(rr, rr, v, ctx))
183 if (r != rr && BN_copy(r, rr) == NULL)
193 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
203 * For even modulus m = 2^k*m_odd, it might make sense to compute
204 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
205 * exponentiation for the odd part), using appropriate exponent
206 * reductions, and combine the results using the CRT.
208 * For now, we use Montgomery only if the modulus is odd; otherwise,
209 * exponentiation using the reciprocal-based quick remaindering
212 * (Timing obtained with expspeed.c [computations a^p mod m
213 * where a, p, m are of the same length: 256, 512, 1024, 2048,
214 * 4096, 8192 bits], compared to the running time of the
215 * standard algorithm:
217 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
218 * 55 .. 77 % [UltraSparc processor, but
219 * debug-solaris-sparcv8-gcc conf.]
221 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
222 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
224 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
225 * at 2048 and more bits, but at 512 and 1024 bits, it was
226 * slower even than the standard algorithm!
228 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
229 * should be obtained when the new Montgomery reduction code
230 * has been integrated into OpenSSL.)
234 #define MONT_EXP_WORD
239 * I have finally been able to take out this pre-condition of the top bit
240 * being set. It was caused by an error in BN_div with negatives. There
241 * was also another problem when for a^b%m a >= m. eay 07-May-97
243 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
246 # ifdef MONT_EXP_WORD
247 if (a->top == 1 && !a->neg
248 && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) {
249 BN_ULONG A = a->d[0];
250 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
253 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
258 ret = BN_mod_exp_recp(r, a, p, m, ctx);
262 ret = BN_mod_exp_simple(r, a, p, m, ctx);
270 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
271 const BIGNUM *m, BN_CTX *ctx)
273 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
276 /* Table of variables obtained from 'ctx' */
277 BIGNUM *val[TABLE_SIZE];
280 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
281 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
282 BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
286 bits = BN_num_bits(p);
288 /* x**0 mod 1 is still zero. */
299 aa = BN_CTX_get(ctx);
300 val[0] = BN_CTX_get(ctx);
304 BN_RECP_CTX_init(&recp);
306 /* ignore sign of 'm' */
310 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
313 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
317 if (!BN_nnmod(val[0], a, m, ctx))
319 if (BN_is_zero(val[0])) {
325 window = BN_window_bits_for_exponent_size(bits);
327 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
329 j = 1 << (window - 1);
330 for (i = 1; i < j; i++) {
331 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
332 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
337 start = 1; /* This is used to avoid multiplication etc
338 * when there is only the value '1' in the
340 wvalue = 0; /* The 'value' of the window */
341 wstart = bits - 1; /* The top bit of the window */
342 wend = 0; /* The bottom bit of the window */
348 if (BN_is_bit_set(p, wstart) == 0) {
350 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
358 * We now have wstart on a 'set' bit, we now need to work out how bit
359 * a window to do. To do this we need to scan forward until the last
360 * set bit before the end of the window
365 for (i = 1; i < window; i++) {
368 if (BN_is_bit_set(p, wstart - i)) {
369 wvalue <<= (i - wend);
375 /* wend is the size of the current window */
377 /* add the 'bytes above' */
379 for (i = 0; i < j; i++) {
380 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
384 /* wvalue will be an odd number < 2^window */
385 if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
388 /* move the 'window' down further */
398 BN_RECP_CTX_free(&recp);
403 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
404 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
406 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
410 /* Table of variables obtained from 'ctx' */
411 BIGNUM *val[TABLE_SIZE];
412 BN_MONT_CTX *mont = NULL;
414 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
415 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
423 BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
426 bits = BN_num_bits(p);
428 /* x**0 mod 1 is still zero. */
441 val[0] = BN_CTX_get(ctx);
442 if (!d || !r || !val[0])
446 * If this is not done, things will break in the montgomery part
452 if ((mont = BN_MONT_CTX_new()) == NULL)
454 if (!BN_MONT_CTX_set(mont, m, ctx))
458 if (a->neg || BN_ucmp(a, m) >= 0) {
459 if (!BN_nnmod(val[0], a, m, ctx))
464 if (BN_is_zero(aa)) {
469 if (!BN_to_montgomery(val[0], aa, mont, ctx))
472 window = BN_window_bits_for_exponent_size(bits);
474 if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx))
476 j = 1 << (window - 1);
477 for (i = 1; i < j; i++) {
478 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
479 !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx))
484 start = 1; /* This is used to avoid multiplication etc
485 * when there is only the value '1' in the
487 wvalue = 0; /* The 'value' of the window */
488 wstart = bits - 1; /* The top bit of the window */
489 wend = 0; /* The bottom bit of the window */
491 #if 1 /* by Shay Gueron's suggestion */
492 j = m->top; /* borrow j */
493 if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
494 if (bn_wexpand(r, j) == NULL)
496 /* 2^(top*BN_BITS2) - m */
497 r->d[0] = (0 - m->d[0]) & BN_MASK2;
498 for (i = 1; i < j; i++)
499 r->d[i] = (~m->d[i]) & BN_MASK2;
502 * Upper words will be zero if the corresponding words of 'm' were
503 * 0xfff[...], so decrement r->top accordingly.
508 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
511 if (BN_is_bit_set(p, wstart) == 0) {
513 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
522 * We now have wstart on a 'set' bit, we now need to work out how bit
523 * a window to do. To do this we need to scan forward until the last
524 * set bit before the end of the window
529 for (i = 1; i < window; i++) {
532 if (BN_is_bit_set(p, wstart - i)) {
533 wvalue <<= (i - wend);
539 /* wend is the size of the current window */
541 /* add the 'bytes above' */
543 for (i = 0; i < j; i++) {
544 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
548 /* wvalue will be an odd number < 2^window */
549 if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
552 /* move the 'window' down further */
559 #if defined(SPARC_T4_MONT)
560 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
561 j = mont->N.top; /* borrow j */
562 val[0]->d[0] = 1; /* borrow val[0] */
563 for (i = 1; i < j; i++)
566 if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
570 if (!BN_from_montgomery(rr, r, mont, ctx))
574 if ((in_mont == NULL) && (mont != NULL))
575 BN_MONT_CTX_free(mont);
581 #if defined(SPARC_T4_MONT)
582 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
587 wordpos = bitpos / BN_BITS2;
589 if (wordpos >= 0 && wordpos < a->top) {
590 ret = a->d[wordpos] & BN_MASK2;
593 if (++wordpos < a->top)
594 ret |= a->d[wordpos] << (BN_BITS2 - bitpos);
598 return ret & BN_MASK2;
603 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
604 * layout so that accessing any of these table values shows the same access
605 * pattern as far as cache lines are concerned. The following functions are
606 * used to transfer a BIGNUM from/to that table.
609 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
610 unsigned char *buf, int idx,
614 int width = 1 << window;
615 BN_ULONG *table = (BN_ULONG *)buf;
618 top = b->top; /* this works because 'buf' is explicitly
620 for (i = 0, j = idx; i < top; i++, j += width) {
627 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
628 unsigned char *buf, int idx,
632 int width = 1 << window;
633 volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
635 if (bn_wexpand(b, top) == NULL)
639 for (i = 0; i < top; i++, table += width) {
642 for (j = 0; j < width; j++) {
644 ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
650 int xstride = 1 << (window - 2);
651 BN_ULONG y0, y1, y2, y3;
653 i = idx >> (window - 2); /* equivalent of idx / xstride */
654 idx &= xstride - 1; /* equivalent of idx % xstride */
656 y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1);
657 y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1);
658 y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1);
659 y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1);
661 for (i = 0; i < top; i++, table += width) {
664 for (j = 0; j < xstride; j++) {
665 acc |= ( (table[j + 0 * xstride] & y0) |
666 (table[j + 1 * xstride] & y1) |
667 (table[j + 2 * xstride] & y2) |
668 (table[j + 3 * xstride] & y3) )
669 & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
682 * Given a pointer value, compute the next address that is a cache line
685 #define MOD_EXP_CTIME_ALIGN(x_) \
686 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
689 * This variant of BN_mod_exp_mont() uses fixed windows and the special
690 * precomputation memory layout to limit data-dependency to a minimum to
691 * protect secret exponents (cf. the hyper-threading timing attacks pointed
692 * out by Colin Percival,
693 * http://www.daemonology.net/hyperthreading-considered-harmful/)
695 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
696 const BIGNUM *m, BN_CTX *ctx,
697 BN_MONT_CTX *in_mont)
699 int i, bits, ret = 0, window, wvalue;
701 BN_MONT_CTX *mont = NULL;
704 unsigned char *powerbufFree = NULL;
706 unsigned char *powerbuf = NULL;
708 #if defined(SPARC_T4_MONT)
717 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
723 bits = BN_num_bits(p);
725 /* x**0 mod 1 is still zero. */
738 * Allocate a montgomery context if it was not supplied by the caller. If
739 * this is not done, things will break in the montgomery part.
744 if ((mont = BN_MONT_CTX_new()) == NULL)
746 if (!BN_MONT_CTX_set(mont, m, ctx))
752 * If the size of the operands allow it, perform the optimized
753 * RSAZ exponentiation. For further information see
754 * crypto/bn/rsaz_exp.c and accompanying assembly modules.
756 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
757 && rsaz_avx2_eligible()) {
758 if (NULL == bn_wexpand(rr, 16))
760 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
767 } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
768 if (NULL == bn_wexpand(rr, 8))
770 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
779 /* Get the window size to use with size of p. */
780 window = BN_window_bits_for_ctime_exponent_size(bits);
781 #if defined(SPARC_T4_MONT)
782 if (window >= 5 && (top & 15) == 0 && top <= 64 &&
783 (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) ==
784 (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0]))
788 #if defined(OPENSSL_BN_ASM_MONT5)
790 window = 5; /* ~5% improvement for RSA2048 sign, and even
792 /* reserve space for mont->N.d[] copy */
793 powerbufLen += top * sizeof(mont->N.d[0]);
799 * Allocate a buffer large enough to hold all of the pre-computed powers
800 * of am, am itself and tmp.
802 numPowers = 1 << window;
803 powerbufLen += sizeof(m->d[0]) * (top * numPowers +
805 numPowers ? (2 * top) : numPowers));
807 if (powerbufLen < 3072)
809 alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
813 (unsigned char *)OPENSSL_malloc(powerbufLen +
814 MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
818 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
819 memset(powerbuf, 0, powerbufLen);
822 if (powerbufLen < 3072)
826 /* lay down tmp and am right after powers table */
827 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
829 tmp.top = am.top = 0;
830 tmp.dmax = am.dmax = top;
831 tmp.neg = am.neg = 0;
832 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
834 /* prepare a^0 in Montgomery domain */
835 #if 1 /* by Shay Gueron's suggestion */
836 if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
837 /* 2^(top*BN_BITS2) - m */
838 tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
839 for (i = 1; i < top; i++)
840 tmp.d[i] = (~m->d[i]) & BN_MASK2;
844 if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx))
847 /* prepare a^1 in Montgomery domain */
848 if (a->neg || BN_ucmp(a, m) >= 0) {
849 if (!BN_mod(&am, a, m, ctx))
851 if (!BN_to_montgomery(&am, &am, mont, ctx))
853 } else if (!BN_to_montgomery(&am, a, mont, ctx))
856 #if defined(SPARC_T4_MONT)
858 typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np,
859 const BN_ULONG *n0, const void *table,
860 int power, int bits);
861 int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np,
862 const BN_ULONG *n0, const void *table,
863 int power, int bits);
864 int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np,
865 const BN_ULONG *n0, const void *table,
866 int power, int bits);
867 int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np,
868 const BN_ULONG *n0, const void *table,
869 int power, int bits);
870 int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np,
871 const BN_ULONG *n0, const void *table,
872 int power, int bits);
873 static const bn_pwr5_mont_f pwr5_funcs[4] = {
874 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
875 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
877 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
879 typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap,
880 const void *bp, const BN_ULONG *np,
882 int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp,
883 const BN_ULONG *np, const BN_ULONG *n0);
884 int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap,
885 const void *bp, const BN_ULONG *np,
887 int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap,
888 const void *bp, const BN_ULONG *np,
890 int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap,
891 const void *bp, const BN_ULONG *np,
893 static const bn_mul_mont_f mul_funcs[4] = {
894 bn_mul_mont_t4_8, bn_mul_mont_t4_16,
895 bn_mul_mont_t4_24, bn_mul_mont_t4_32
897 bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
899 void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap,
900 const void *bp, const BN_ULONG *np,
901 const BN_ULONG *n0, int num);
902 void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap,
903 const void *bp, const BN_ULONG *np,
904 const BN_ULONG *n0, int num);
905 void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap,
906 const void *table, const BN_ULONG *np,
907 const BN_ULONG *n0, int num, int power);
908 void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
909 void *table, size_t power);
910 void bn_gather5_t4(BN_ULONG *out, size_t num,
911 void *table, size_t power);
912 void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num);
914 BN_ULONG *np = mont->N.d, *n0 = mont->n0;
915 int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
919 * BN_to_montgomery can contaminate words above .top [in
920 * BN_DEBUG[_DEBUG] build]...
922 for (i = am.top; i < top; i++)
924 for (i = tmp.top; i < top; i++)
927 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
928 bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
929 if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) &&
930 !(*mul_worker) (tmp.d, am.d, am.d, np, n0))
931 bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
932 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
934 for (i = 3; i < 32; i++) {
935 /* Calculate a^i = a^(i-1) * a */
936 if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) &&
937 !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0))
938 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
939 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
942 /* switch to 64-bit domain */
943 np = alloca(top * sizeof(BN_ULONG));
945 bn_flip_t4(np, mont->N.d, top);
948 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
949 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
950 bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
953 * Scan the exponent one window at a time starting from the most
960 wvalue = bn_get_bits(p, bits + 1);
962 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
964 /* retry once and fall back */
965 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
969 wvalue >>= stride - 5;
971 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
972 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
973 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
974 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
975 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
976 bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
980 bn_flip_t4(tmp.d, tmp.d, top);
982 /* back to 32-bit domain */
984 bn_correct_top(&tmp);
985 OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
988 #if defined(OPENSSL_BN_ASM_MONT5)
989 if (window == 5 && top > 1) {
991 * This optimization uses ideas from http://eprint.iacr.org/2011/239,
992 * specifically optimization of cache-timing attack countermeasures
993 * and pre-computation optimization.
997 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
998 * 512-bit RSA is hardly relevant, we omit it to spare size...
1000 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
1001 const void *table, const BN_ULONG *np,
1002 const BN_ULONG *n0, int num, int power);
1003 void bn_scatter5(const BN_ULONG *inp, size_t num,
1004 void *table, size_t power);
1005 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
1006 void bn_power5(BN_ULONG *rp, const BN_ULONG *ap,
1007 const void *table, const BN_ULONG *np,
1008 const BN_ULONG *n0, int num, int power);
1009 int bn_get_bits5(const BN_ULONG *ap, int off);
1010 int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap,
1011 const BN_ULONG *not_used, const BN_ULONG *np,
1012 const BN_ULONG *n0, int num);
1014 BN_ULONG *n0 = mont->n0, *np;
1017 * BN_to_montgomery can contaminate words above .top [in
1018 * BN_DEBUG[_DEBUG] build]...
1020 for (i = am.top; i < top; i++)
1022 for (i = tmp.top; i < top; i++)
1026 * copy mont->N.d[] to improve cache locality
1028 for (np = am.d + top, i = 0; i < top; i++)
1029 np[i] = mont->N.d[i];
1031 bn_scatter5(tmp.d, top, powerbuf, 0);
1032 bn_scatter5(am.d, am.top, powerbuf, 1);
1033 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
1034 bn_scatter5(tmp.d, top, powerbuf, 2);
1037 for (i = 3; i < 32; i++) {
1038 /* Calculate a^i = a^(i-1) * a */
1039 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1040 bn_scatter5(tmp.d, top, powerbuf, i);
1043 /* same as above, but uses squaring for 1/2 of operations */
1044 for (i = 4; i < 32; i *= 2) {
1045 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1046 bn_scatter5(tmp.d, top, powerbuf, i);
1048 for (i = 3; i < 8; i += 2) {
1050 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1051 bn_scatter5(tmp.d, top, powerbuf, i);
1052 for (j = 2 * i; j < 32; j *= 2) {
1053 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1054 bn_scatter5(tmp.d, top, powerbuf, j);
1057 for (; i < 16; i += 2) {
1058 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1059 bn_scatter5(tmp.d, top, powerbuf, i);
1060 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1061 bn_scatter5(tmp.d, top, powerbuf, 2 * i);
1063 for (; i < 32; i += 2) {
1064 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
1065 bn_scatter5(tmp.d, top, powerbuf, i);
1069 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
1070 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1071 bn_gather5(tmp.d, top, powerbuf, wvalue);
1074 * Scan the exponent one window at a time starting from the most
1079 for (wvalue = 0, i = 0; i < 5; i++, bits--)
1080 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1082 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1083 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1084 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1085 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1086 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1087 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
1091 wvalue = bn_get_bits5(p->d, bits - 4);
1093 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue);
1097 ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np, n0, top);
1099 bn_correct_top(&tmp);
1101 if (!BN_copy(rr, &tmp))
1103 goto err; /* non-zero ret means it's not error */
1108 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window))
1110 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window))
1114 * If the window size is greater than 1, then calculate
1115 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1116 * powers could instead be computed as (a^(i/2))^2 to use the slight
1117 * performance advantage of sqr over mul).
1120 if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx))
1122 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2,
1125 for (i = 3; i < numPowers; i++) {
1126 /* Calculate a^i = a^(i-1) * a */
1127 if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx))
1129 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i,
1136 for (wvalue = 0, i = bits % window; i >= 0; i--, bits--)
1137 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1138 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue,
1143 * Scan the exponent one window at a time starting from the most
1147 wvalue = 0; /* The 'value' of the window */
1149 /* Scan the window, squaring the result as we go */
1150 for (i = 0; i < window; i++, bits--) {
1151 if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx))
1153 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1157 * Fetch the appropriate pre-computed value from the pre-buf
1159 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
1163 /* Multiply the result into the intermediate result */
1164 if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx))
1169 /* Convert the final result from montgomery to standard format */
1170 #if defined(SPARC_T4_MONT)
1171 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
1172 am.d[0] = 1; /* borrow am */
1173 for (i = 1; i < top; i++)
1175 if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
1179 if (!BN_from_montgomery(rr, &tmp, mont, ctx))
1183 if ((in_mont == NULL) && (mont != NULL))
1184 BN_MONT_CTX_free(mont);
1185 if (powerbuf != NULL) {
1186 OPENSSL_cleanse(powerbuf, powerbufLen);
1188 OPENSSL_free(powerbufFree);
1194 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1195 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1197 BN_MONT_CTX *mont = NULL;
1198 int b, bits, ret = 0;
1203 #define BN_MOD_MUL_WORD(r, w, m) \
1204 (BN_mul_word(r, (w)) && \
1205 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1206 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1208 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1209 * probably more overhead than always using BN_mod (which uses BN_copy if
1210 * a similar test returns true).
1213 * We can use BN_mod and do not need BN_nnmod because our accumulator is
1214 * never negative (the result of BN_mod does not depend on the sign of
1217 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1218 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1220 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
1221 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1222 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1229 if (!BN_is_odd(m)) {
1230 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
1234 a %= m->d[0]; /* make sure that 'a' is reduced */
1236 bits = BN_num_bits(p);
1238 /* x**0 mod 1 is still zero. */
1254 d = BN_CTX_get(ctx);
1255 r = BN_CTX_get(ctx);
1256 t = BN_CTX_get(ctx);
1257 if (d == NULL || r == NULL || t == NULL)
1260 if (in_mont != NULL)
1263 if ((mont = BN_MONT_CTX_new()) == NULL)
1265 if (!BN_MONT_CTX_set(mont, m, ctx))
1269 r_is_one = 1; /* except for Montgomery factor */
1273 /* The result is accumulated in the product r*w. */
1274 w = a; /* bit 'bits-1' of 'p' is always set */
1275 for (b = bits - 2; b >= 0; b--) {
1276 /* First, square r*w. */
1278 if ((next_w / w) != w) { /* overflow */
1280 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1284 if (!BN_MOD_MUL_WORD(r, w, m))
1291 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
1295 /* Second, multiply r*w by 'a' if exponent bit is set. */
1296 if (BN_is_bit_set(p, b)) {
1298 if ((next_w / a) != w) { /* overflow */
1300 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1304 if (!BN_MOD_MUL_WORD(r, w, m))
1313 /* Finally, set r:=r*w. */
1316 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1320 if (!BN_MOD_MUL_WORD(r, w, m))
1325 if (r_is_one) { /* can happen only if a == 1 */
1329 if (!BN_from_montgomery(rr, r, mont, ctx))
1334 if ((in_mont == NULL) && (mont != NULL))
1335 BN_MONT_CTX_free(mont);
1341 /* The old fallback, simple version :-) */
1342 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1343 const BIGNUM *m, BN_CTX *ctx)
1345 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
1348 /* Table of variables obtained from 'ctx' */
1349 BIGNUM *val[TABLE_SIZE];
1351 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
1352 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1353 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1357 bits = BN_num_bits(p);
1359 /* x**0 mod 1 is still zero. */
1370 d = BN_CTX_get(ctx);
1371 val[0] = BN_CTX_get(ctx);
1375 if (!BN_nnmod(val[0], a, m, ctx))
1377 if (BN_is_zero(val[0])) {
1383 window = BN_window_bits_for_exponent_size(bits);
1385 if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1387 j = 1 << (window - 1);
1388 for (i = 1; i < j; i++) {
1389 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
1390 !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
1395 start = 1; /* This is used to avoid multiplication etc
1396 * when there is only the value '1' in the
1398 wvalue = 0; /* The 'value' of the window */
1399 wstart = bits - 1; /* The top bit of the window */
1400 wend = 0; /* The bottom bit of the window */
1406 if (BN_is_bit_set(p, wstart) == 0) {
1408 if (!BN_mod_mul(r, r, r, m, ctx))
1416 * We now have wstart on a 'set' bit, we now need to work out how bit
1417 * a window to do. To do this we need to scan forward until the last
1418 * set bit before the end of the window
1423 for (i = 1; i < window; i++) {
1426 if (BN_is_bit_set(p, wstart - i)) {
1427 wvalue <<= (i - wend);
1433 /* wend is the size of the current window */
1435 /* add the 'bytes above' */
1437 for (i = 0; i < j; i++) {
1438 if (!BN_mod_mul(r, r, r, m, ctx))
1442 /* wvalue will be an odd number < 2^window */
1443 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1446 /* move the 'window' down further */