1 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
4 * This package is an SSL implementation written
5 * by Eric Young (eay@cryptsoft.com).
6 * The implementation was written so as to conform with Netscapes SSL.
8 * This library is free for commercial and non-commercial use as long as
9 * the following conditions are aheared to. The following conditions
10 * apply to all code found in this distribution, be it the RC4, RSA,
11 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
12 * included with this distribution is covered by the same copyright terms
13 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
15 * Copyright remains Eric Young's, and as such any Copyright notices in
16 * the code are not to be removed.
17 * If this package is used in a product, Eric Young should be given attribution
18 * as the author of the parts of the library used.
19 * This can be in the form of a textual message at program startup or
20 * in documentation (online or textual) provided with the package.
22 * Redistribution and use in source and binary forms, with or without
23 * modification, are permitted provided that the following conditions
25 * 1. Redistributions of source code must retain the copyright
26 * notice, this list of conditions and the following disclaimer.
27 * 2. Redistributions in binary form must reproduce the above copyright
28 * notice, this list of conditions and the following disclaimer in the
29 * documentation and/or other materials provided with the distribution.
30 * 3. All advertising materials mentioning features or use of this software
31 * must display the following acknowledgement:
32 * "This product includes cryptographic software written by
33 * Eric Young (eay@cryptsoft.com)"
34 * The word 'cryptographic' can be left out if the rouines from the library
35 * being used are not cryptographic related :-).
36 * 4. If you include any Windows specific code (or a derivative thereof) from
37 * the apps directory (application code) you must include an acknowledgement:
38 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
40 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
41 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
42 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
43 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
44 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
45 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
46 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
47 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
48 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
49 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
52 * The licence and distribution terms for any publically available version or
53 * derivative of this code cannot be changed. i.e. this code cannot simply be
54 * copied and put under another distribution licence
55 * [including the GNU Public Licence.]
57 /* ====================================================================
58 * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
60 * Redistribution and use in source and binary forms, with or without
61 * modification, are permitted provided that the following conditions
64 * 1. Redistributions of source code must retain the above copyright
65 * notice, this list of conditions and the following disclaimer.
67 * 2. Redistributions in binary form must reproduce the above copyright
68 * notice, this list of conditions and the following disclaimer in
69 * the documentation and/or other materials provided with the
72 * 3. All advertising materials mentioning features or use of this
73 * software must display the following acknowledgment:
74 * "This product includes software developed by the OpenSSL Project
75 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
77 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
78 * endorse or promote products derived from this software without
79 * prior written permission. For written permission, please contact
80 * openssl-core@openssl.org.
82 * 5. Products derived from this software may not be called "OpenSSL"
83 * nor may "OpenSSL" appear in their names without prior written
84 * permission of the OpenSSL Project.
86 * 6. Redistributions of any form whatsoever must retain the following
88 * "This product includes software developed by the OpenSSL Project
89 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
91 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
92 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
93 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
94 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
95 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
96 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
97 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
98 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
99 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
100 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
101 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
102 * OF THE POSSIBILITY OF SUCH DAMAGE.
103 * ====================================================================
105 * This product includes cryptographic software written by Eric Young
106 * (eay@cryptsoft.com). This product includes software written by Tim
107 * Hudson (tjh@cryptsoft.com).
111 #include "internal/cryptlib.h"
118 # define alloca _alloca
120 #elif defined(__GNUC__)
122 # define alloca(s) __builtin_alloca((s))
128 #include "rsaz_exp.h"
131 #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
132 # include "sparc_arch.h"
133 extern unsigned int OPENSSL_sparcv9cap_P[];
134 # define SPARC_T4_MONT
137 /* maximum precomputation table size for *variable* sliding windows */
138 #define TABLE_SIZE 32
140 /* this one works - simple but works */
141 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
143 int i, bits, ret = 0;
146 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
147 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
148 BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
153 if ((r == a) || (r == p))
154 rr = BN_CTX_get(ctx);
158 if (rr == NULL || v == NULL)
161 if (BN_copy(v, a) == NULL)
163 bits = BN_num_bits(p);
166 if (BN_copy(rr, a) == NULL)
173 for (i = 1; i < bits; i++) {
174 if (!BN_sqr(v, v, ctx))
176 if (BN_is_bit_set(p, i)) {
177 if (!BN_mul(rr, rr, v, ctx))
190 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
200 * For even modulus m = 2^k*m_odd, it might make sense to compute
201 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
202 * exponentiation for the odd part), using appropriate exponent
203 * reductions, and combine the results using the CRT.
205 * For now, we use Montgomery only if the modulus is odd; otherwise,
206 * exponentiation using the reciprocal-based quick remaindering
209 * (Timing obtained with expspeed.c [computations a^p mod m
210 * where a, p, m are of the same length: 256, 512, 1024, 2048,
211 * 4096, 8192 bits], compared to the running time of the
212 * standard algorithm:
214 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
215 * 55 .. 77 % [UltraSparc processor, but
216 * debug-solaris-sparcv8-gcc conf.]
218 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
219 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
221 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
222 * at 2048 and more bits, but at 512 and 1024 bits, it was
223 * slower even than the standard algorithm!
225 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
226 * should be obtained when the new Montgomery reduction code
227 * has been integrated into OpenSSL.)
231 #define MONT_EXP_WORD
236 * I have finally been able to take out this pre-condition of the top bit
237 * being set. It was caused by an error in BN_div with negatives. There
238 * was also another problem when for a^b%m a >= m. eay 07-May-97
240 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
243 # ifdef MONT_EXP_WORD
244 if (a->top == 1 && !a->neg
245 && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) {
246 BN_ULONG A = a->d[0];
247 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
250 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
255 ret = BN_mod_exp_recp(r, a, p, m, ctx);
259 ret = BN_mod_exp_simple(r, a, p, m, ctx);
267 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
268 const BIGNUM *m, BN_CTX *ctx)
270 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
273 /* Table of variables obtained from 'ctx' */
274 BIGNUM *val[TABLE_SIZE];
277 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
278 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
279 BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
283 bits = BN_num_bits(p);
285 /* x**0 mod 1 is still zero. */
296 aa = BN_CTX_get(ctx);
297 val[0] = BN_CTX_get(ctx);
301 BN_RECP_CTX_init(&recp);
303 /* ignore sign of 'm' */
307 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
310 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
314 if (!BN_nnmod(val[0], a, m, ctx))
316 if (BN_is_zero(val[0])) {
322 window = BN_window_bits_for_exponent_size(bits);
324 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
326 j = 1 << (window - 1);
327 for (i = 1; i < j; i++) {
328 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
329 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
334 start = 1; /* This is used to avoid multiplication etc
335 * when there is only the value '1' in the
337 wvalue = 0; /* The 'value' of the window */
338 wstart = bits - 1; /* The top bit of the window */
339 wend = 0; /* The bottom bit of the window */
345 if (BN_is_bit_set(p, wstart) == 0) {
347 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
355 * We now have wstart on a 'set' bit, we now need to work out how bit
356 * a window to do. To do this we need to scan forward until the last
357 * set bit before the end of the window
362 for (i = 1; i < window; i++) {
365 if (BN_is_bit_set(p, wstart - i)) {
366 wvalue <<= (i - wend);
372 /* wend is the size of the current window */
374 /* add the 'bytes above' */
376 for (i = 0; i < j; i++) {
377 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
381 /* wvalue will be an odd number < 2^window */
382 if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
385 /* move the 'window' down further */
395 BN_RECP_CTX_free(&recp);
400 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
401 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
403 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
407 /* Table of variables obtained from 'ctx' */
408 BIGNUM *val[TABLE_SIZE];
409 BN_MONT_CTX *mont = NULL;
411 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
412 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
420 BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
423 bits = BN_num_bits(p);
425 /* x**0 mod 1 is still zero. */
438 val[0] = BN_CTX_get(ctx);
439 if (!d || !r || !val[0])
443 * If this is not done, things will break in the montgomery part
449 if ((mont = BN_MONT_CTX_new()) == NULL)
451 if (!BN_MONT_CTX_set(mont, m, ctx))
455 if (a->neg || BN_ucmp(a, m) >= 0) {
456 if (!BN_nnmod(val[0], a, m, ctx))
461 if (BN_is_zero(aa)) {
466 if (!BN_to_montgomery(val[0], aa, mont, ctx))
469 window = BN_window_bits_for_exponent_size(bits);
471 if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx))
473 j = 1 << (window - 1);
474 for (i = 1; i < j; i++) {
475 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
476 !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx))
481 start = 1; /* This is used to avoid multiplication etc
482 * when there is only the value '1' in the
484 wvalue = 0; /* The 'value' of the window */
485 wstart = bits - 1; /* The top bit of the window */
486 wend = 0; /* The bottom bit of the window */
488 #if 1 /* by Shay Gueron's suggestion */
489 j = m->top; /* borrow j */
490 if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
491 if (bn_wexpand(r, j) == NULL)
493 /* 2^(top*BN_BITS2) - m */
494 r->d[0] = (0 - m->d[0]) & BN_MASK2;
495 for (i = 1; i < j; i++)
496 r->d[i] = (~m->d[i]) & BN_MASK2;
499 * Upper words will be zero if the corresponding words of 'm' were
500 * 0xfff[...], so decrement r->top accordingly.
505 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
508 if (BN_is_bit_set(p, wstart) == 0) {
510 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
519 * We now have wstart on a 'set' bit, we now need to work out how bit
520 * a window to do. To do this we need to scan forward until the last
521 * set bit before the end of the window
526 for (i = 1; i < window; i++) {
529 if (BN_is_bit_set(p, wstart - i)) {
530 wvalue <<= (i - wend);
536 /* wend is the size of the current window */
538 /* add the 'bytes above' */
540 for (i = 0; i < j; i++) {
541 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
545 /* wvalue will be an odd number < 2^window */
546 if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
549 /* move the 'window' down further */
556 #if defined(SPARC_T4_MONT)
557 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
558 j = mont->N.top; /* borrow j */
559 val[0]->d[0] = 1; /* borrow val[0] */
560 for (i = 1; i < j; i++)
563 if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
567 if (!BN_from_montgomery(rr, r, mont, ctx))
572 BN_MONT_CTX_free(mont);
578 #if defined(SPARC_T4_MONT)
579 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
584 wordpos = bitpos / BN_BITS2;
586 if (wordpos >= 0 && wordpos < a->top) {
587 ret = a->d[wordpos] & BN_MASK2;
590 if (++wordpos < a->top)
591 ret |= a->d[wordpos] << (BN_BITS2 - bitpos);
595 return ret & BN_MASK2;
600 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
601 * layout so that accessing any of these table values shows the same access
602 * pattern as far as cache lines are concerned. The following functions are
603 * used to transfer a BIGNUM from/to that table.
606 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
607 unsigned char *buf, int idx,
613 top = b->top; /* this works because 'buf' is explicitly
615 for (i = 0, j = idx; i < top * sizeof b->d[0]; i++, j += width) {
616 buf[j] = ((unsigned char *)b->d)[i];
622 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
623 unsigned char *buf, int idx,
628 if (bn_wexpand(b, top) == NULL)
631 for (i = 0, j = idx; i < top * sizeof b->d[0]; i++, j += width) {
632 ((unsigned char *)b->d)[i] = buf[j];
641 * Given a pointer value, compute the next address that is a cache line
644 #define MOD_EXP_CTIME_ALIGN(x_) \
645 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
648 * This variant of BN_mod_exp_mont() uses fixed windows and the special
649 * precomputation memory layout to limit data-dependency to a minimum to
650 * protect secret exponents (cf. the hyper-threading timing attacks pointed
651 * out by Colin Percival,
652 * http://www.daemonology.net/hyperthreading-considered-harmful/)
654 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
655 const BIGNUM *m, BN_CTX *ctx,
656 BN_MONT_CTX *in_mont)
658 int i, bits, ret = 0, window, wvalue;
660 BN_MONT_CTX *mont = NULL;
663 unsigned char *powerbufFree = NULL;
665 unsigned char *powerbuf = NULL;
667 #if defined(SPARC_T4_MONT)
676 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
682 bits = BN_num_bits(p);
684 /* x**0 mod 1 is still zero. */
697 * Allocate a montgomery context if it was not supplied by the caller. If
698 * this is not done, things will break in the montgomery part.
703 if ((mont = BN_MONT_CTX_new()) == NULL)
705 if (!BN_MONT_CTX_set(mont, m, ctx))
711 * If the size of the operands allow it, perform the optimized
712 * RSAZ exponentiation. For further information see
713 * crypto/bn/rsaz_exp.c and accompanying assembly modules.
715 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
716 && rsaz_avx2_eligible()) {
717 if (NULL == bn_wexpand(rr, 16))
719 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
726 } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
727 if (NULL == bn_wexpand(rr, 8))
729 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
738 /* Get the window size to use with size of p. */
739 window = BN_window_bits_for_ctime_exponent_size(bits);
740 #if defined(SPARC_T4_MONT)
741 if (window >= 5 && (top & 15) == 0 && top <= 64 &&
742 (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) ==
743 (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0]))
747 #if defined(OPENSSL_BN_ASM_MONT5)
749 window = 5; /* ~5% improvement for RSA2048 sign, and even
752 powerbufLen += 2 * top * sizeof(m->d[0]);
758 * Allocate a buffer large enough to hold all of the pre-computed powers
759 * of am, am itself and tmp.
761 numPowers = 1 << window;
762 powerbufLen += sizeof(m->d[0]) * (top * numPowers +
764 numPowers ? (2 * top) : numPowers));
766 if (powerbufLen < 3072)
768 alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
772 OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
776 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
777 memset(powerbuf, 0, powerbufLen);
780 if (powerbufLen < 3072)
784 /* lay down tmp and am right after powers table */
785 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
787 tmp.top = am.top = 0;
788 tmp.dmax = am.dmax = top;
789 tmp.neg = am.neg = 0;
790 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
792 /* prepare a^0 in Montgomery domain */
793 #if 1 /* by Shay Gueron's suggestion */
794 if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
795 /* 2^(top*BN_BITS2) - m */
796 tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
797 for (i = 1; i < top; i++)
798 tmp.d[i] = (~m->d[i]) & BN_MASK2;
802 if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx))
805 /* prepare a^1 in Montgomery domain */
806 if (a->neg || BN_ucmp(a, m) >= 0) {
807 if (!BN_mod(&am, a, m, ctx))
809 if (!BN_to_montgomery(&am, &am, mont, ctx))
811 } else if (!BN_to_montgomery(&am, a, mont, ctx))
814 #if defined(SPARC_T4_MONT)
816 typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np,
817 const BN_ULONG *n0, const void *table,
818 int power, int bits);
819 int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np,
820 const BN_ULONG *n0, const void *table,
821 int power, int bits);
822 int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np,
823 const BN_ULONG *n0, const void *table,
824 int power, int bits);
825 int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np,
826 const BN_ULONG *n0, const void *table,
827 int power, int bits);
828 int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np,
829 const BN_ULONG *n0, const void *table,
830 int power, int bits);
831 static const bn_pwr5_mont_f pwr5_funcs[4] = {
832 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
833 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
835 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
837 typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap,
838 const void *bp, const BN_ULONG *np,
840 int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp,
841 const BN_ULONG *np, const BN_ULONG *n0);
842 int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap,
843 const void *bp, const BN_ULONG *np,
845 int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap,
846 const void *bp, const BN_ULONG *np,
848 int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap,
849 const void *bp, const BN_ULONG *np,
851 static const bn_mul_mont_f mul_funcs[4] = {
852 bn_mul_mont_t4_8, bn_mul_mont_t4_16,
853 bn_mul_mont_t4_24, bn_mul_mont_t4_32
855 bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
857 void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap,
858 const void *bp, const BN_ULONG *np,
859 const BN_ULONG *n0, int num);
860 void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap,
861 const void *bp, const BN_ULONG *np,
862 const BN_ULONG *n0, int num);
863 void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap,
864 const void *table, const BN_ULONG *np,
865 const BN_ULONG *n0, int num, int power);
866 void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
867 void *table, size_t power);
868 void bn_gather5_t4(BN_ULONG *out, size_t num,
869 void *table, size_t power);
870 void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num);
872 BN_ULONG *np = mont->N.d, *n0 = mont->n0;
873 int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
877 * BN_to_montgomery can contaminate words above .top [in
878 * BN_DEBUG[_DEBUG] build]...
880 for (i = am.top; i < top; i++)
882 for (i = tmp.top; i < top; i++)
885 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
886 bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
887 if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) &&
888 !(*mul_worker) (tmp.d, am.d, am.d, np, n0))
889 bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
890 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
892 for (i = 3; i < 32; i++) {
893 /* Calculate a^i = a^(i-1) * a */
894 if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) &&
895 !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0))
896 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
897 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
900 /* switch to 64-bit domain */
901 np = alloca(top * sizeof(BN_ULONG));
903 bn_flip_t4(np, mont->N.d, top);
906 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
907 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
908 bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
911 * Scan the exponent one window at a time starting from the most
918 wvalue = bn_get_bits(p, bits + 1);
920 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
922 /* retry once and fall back */
923 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
927 wvalue >>= stride - 5;
929 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
930 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
931 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
932 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
933 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
934 bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
938 bn_flip_t4(tmp.d, tmp.d, top);
940 /* back to 32-bit domain */
942 bn_correct_top(&tmp);
943 OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
946 #if defined(OPENSSL_BN_ASM_MONT5)
947 if (window == 5 && top > 1) {
949 * This optimization uses ideas from http://eprint.iacr.org/2011/239,
950 * specifically optimization of cache-timing attack countermeasures
951 * and pre-computation optimization.
955 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
956 * 512-bit RSA is hardly relevant, we omit it to spare size...
958 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
959 const void *table, const BN_ULONG *np,
960 const BN_ULONG *n0, int num, int power);
961 void bn_scatter5(const BN_ULONG *inp, size_t num,
962 void *table, size_t power);
963 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
964 void bn_power5(BN_ULONG *rp, const BN_ULONG *ap,
965 const void *table, const BN_ULONG *np,
966 const BN_ULONG *n0, int num, int power);
967 int bn_get_bits5(const BN_ULONG *ap, int off);
968 int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap,
969 const BN_ULONG *not_used, const BN_ULONG *np,
970 const BN_ULONG *n0, int num);
972 BN_ULONG *np = mont->N.d, *n0 = mont->n0, *np2;
975 * BN_to_montgomery can contaminate words above .top [in
976 * BN_DEBUG[_DEBUG] build]...
978 for (i = am.top; i < top; i++)
980 for (i = tmp.top; i < top; i++)
986 for (np2 = am.d + top, i = 0; i < top; i++)
989 bn_scatter5(tmp.d, top, powerbuf, 0);
990 bn_scatter5(am.d, am.top, powerbuf, 1);
991 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
992 bn_scatter5(tmp.d, top, powerbuf, 2);
995 for (i = 3; i < 32; i++) {
996 /* Calculate a^i = a^(i-1) * a */
997 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np2, n0, top, i - 1);
998 bn_scatter5(tmp.d, top, powerbuf, i);
1001 /* same as above, but uses squaring for 1/2 of operations */
1002 for (i = 4; i < 32; i *= 2) {
1003 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1004 bn_scatter5(tmp.d, top, powerbuf, i);
1006 for (i = 3; i < 8; i += 2) {
1008 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np2, n0, top, i - 1);
1009 bn_scatter5(tmp.d, top, powerbuf, i);
1010 for (j = 2 * i; j < 32; j *= 2) {
1011 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1012 bn_scatter5(tmp.d, top, powerbuf, j);
1015 for (; i < 16; i += 2) {
1016 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np2, n0, top, i - 1);
1017 bn_scatter5(tmp.d, top, powerbuf, i);
1018 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1019 bn_scatter5(tmp.d, top, powerbuf, 2 * i);
1021 for (; i < 32; i += 2) {
1022 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np2, n0, top, i - 1);
1023 bn_scatter5(tmp.d, top, powerbuf, i);
1027 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
1028 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1029 bn_gather5(tmp.d, top, powerbuf, wvalue);
1032 * Scan the exponent one window at a time starting from the most
1037 for (wvalue = 0, i = 0; i < 5; i++, bits--)
1038 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1040 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1041 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1042 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1043 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1044 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1045 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
1049 wvalue = bn_get_bits5(p->d, bits - 4);
1051 bn_power5(tmp.d, tmp.d, powerbuf, np2, n0, top, wvalue);
1055 ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np2, n0, top);
1057 bn_correct_top(&tmp);
1059 if (!BN_copy(rr, &tmp))
1061 goto err; /* non-zero ret means it's not error */
1066 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, numPowers))
1068 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, numPowers))
1072 * If the window size is greater than 1, then calculate
1073 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1074 * powers could instead be computed as (a^(i/2))^2 to use the slight
1075 * performance advantage of sqr over mul).
1078 if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx))
1080 if (!MOD_EXP_CTIME_COPY_TO_PREBUF
1081 (&tmp, top, powerbuf, 2, numPowers))
1083 for (i = 3; i < numPowers; i++) {
1084 /* Calculate a^i = a^(i-1) * a */
1085 if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx))
1087 if (!MOD_EXP_CTIME_COPY_TO_PREBUF
1088 (&tmp, top, powerbuf, i, numPowers))
1094 for (wvalue = 0, i = bits % window; i >= 0; i--, bits--)
1095 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1096 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF
1097 (&tmp, top, powerbuf, wvalue, numPowers))
1101 * Scan the exponent one window at a time starting from the most
1105 wvalue = 0; /* The 'value' of the window */
1107 /* Scan the window, squaring the result as we go */
1108 for (i = 0; i < window; i++, bits--) {
1109 if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx))
1111 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1115 * Fetch the appropriate pre-computed value from the pre-buf
1117 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF
1118 (&am, top, powerbuf, wvalue, numPowers))
1121 /* Multiply the result into the intermediate result */
1122 if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx))
1127 /* Convert the final result from montgomery to standard format */
1128 #if defined(SPARC_T4_MONT)
1129 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
1130 am.d[0] = 1; /* borrow am */
1131 for (i = 1; i < top; i++)
1133 if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
1137 if (!BN_from_montgomery(rr, &tmp, mont, ctx))
1141 if (in_mont == NULL)
1142 BN_MONT_CTX_free(mont);
1143 if (powerbuf != NULL) {
1144 OPENSSL_cleanse(powerbuf, powerbufLen);
1145 OPENSSL_free(powerbufFree);
1151 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1152 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1154 BN_MONT_CTX *mont = NULL;
1155 int b, bits, ret = 0;
1160 #define BN_MOD_MUL_WORD(r, w, m) \
1161 (BN_mul_word(r, (w)) && \
1162 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1163 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1165 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1166 * probably more overhead than always using BN_mod (which uses BN_copy if
1167 * a similar test returns true).
1170 * We can use BN_mod and do not need BN_nnmod because our accumulator is
1171 * never negative (the result of BN_mod does not depend on the sign of
1174 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1175 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1177 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
1178 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1179 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1186 if (!BN_is_odd(m)) {
1187 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
1191 a %= m->d[0]; /* make sure that 'a' is reduced */
1193 bits = BN_num_bits(p);
1195 /* x**0 mod 1 is still zero. */
1211 d = BN_CTX_get(ctx);
1212 r = BN_CTX_get(ctx);
1213 t = BN_CTX_get(ctx);
1214 if (d == NULL || r == NULL || t == NULL)
1217 if (in_mont != NULL)
1220 if ((mont = BN_MONT_CTX_new()) == NULL)
1222 if (!BN_MONT_CTX_set(mont, m, ctx))
1226 r_is_one = 1; /* except for Montgomery factor */
1230 /* The result is accumulated in the product r*w. */
1231 w = a; /* bit 'bits-1' of 'p' is always set */
1232 for (b = bits - 2; b >= 0; b--) {
1233 /* First, square r*w. */
1235 if ((next_w / w) != w) { /* overflow */
1237 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1241 if (!BN_MOD_MUL_WORD(r, w, m))
1248 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
1252 /* Second, multiply r*w by 'a' if exponent bit is set. */
1253 if (BN_is_bit_set(p, b)) {
1255 if ((next_w / a) != w) { /* overflow */
1257 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1261 if (!BN_MOD_MUL_WORD(r, w, m))
1270 /* Finally, set r:=r*w. */
1273 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1277 if (!BN_MOD_MUL_WORD(r, w, m))
1282 if (r_is_one) { /* can happen only if a == 1 */
1286 if (!BN_from_montgomery(rr, r, mont, ctx))
1291 if (in_mont == NULL)
1292 BN_MONT_CTX_free(mont);
1298 /* The old fallback, simple version :-) */
1299 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1300 const BIGNUM *m, BN_CTX *ctx)
1302 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
1305 /* Table of variables obtained from 'ctx' */
1306 BIGNUM *val[TABLE_SIZE];
1308 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
1309 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1310 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1314 bits = BN_num_bits(p);
1316 /* x**0 mod 1 is still zero. */
1327 d = BN_CTX_get(ctx);
1328 val[0] = BN_CTX_get(ctx);
1332 if (!BN_nnmod(val[0], a, m, ctx))
1334 if (BN_is_zero(val[0])) {
1340 window = BN_window_bits_for_exponent_size(bits);
1342 if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1344 j = 1 << (window - 1);
1345 for (i = 1; i < j; i++) {
1346 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
1347 !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
1352 start = 1; /* This is used to avoid multiplication etc
1353 * when there is only the value '1' in the
1355 wvalue = 0; /* The 'value' of the window */
1356 wstart = bits - 1; /* The top bit of the window */
1357 wend = 0; /* The bottom bit of the window */
1363 if (BN_is_bit_set(p, wstart) == 0) {
1365 if (!BN_mod_mul(r, r, r, m, ctx))
1373 * We now have wstart on a 'set' bit, we now need to work out how bit
1374 * a window to do. To do this we need to scan forward until the last
1375 * set bit before the end of the window
1380 for (i = 1; i < window; i++) {
1383 if (BN_is_bit_set(p, wstart - i)) {
1384 wvalue <<= (i - wend);
1390 /* wend is the size of the current window */
1392 /* add the 'bytes above' */
1394 for (i = 0; i < j; i++) {
1395 if (!BN_mod_mul(r, r, r, m, ctx))
1399 /* wvalue will be an odd number < 2^window */
1400 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1403 /* move the 'window' down further */