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 "internal/cryptlib.h"
119 # define alloca _alloca
121 #elif defined(__GNUC__)
123 # define alloca(s) __builtin_alloca((s))
129 #include "rsaz_exp.h"
132 #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
133 # include "sparc_arch.h"
134 extern unsigned int OPENSSL_sparcv9cap_P[];
135 # define SPARC_T4_MONT
138 /* maximum precomputation table size for *variable* sliding windows */
139 #define TABLE_SIZE 32
141 /* this one works - simple but works */
142 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
144 int i, bits, ret = 0;
147 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
148 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
149 BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
154 if ((r == a) || (r == p))
155 rr = BN_CTX_get(ctx);
159 if (rr == NULL || v == NULL)
162 if (BN_copy(v, a) == NULL)
164 bits = BN_num_bits(p);
167 if (BN_copy(rr, a) == NULL)
174 for (i = 1; i < bits; i++) {
175 if (!BN_sqr(v, v, ctx))
177 if (BN_is_bit_set(p, i)) {
178 if (!BN_mul(rr, rr, v, ctx))
191 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
201 * For even modulus m = 2^k*m_odd, it might make sense to compute
202 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
203 * exponentiation for the odd part), using appropriate exponent
204 * reductions, and combine the results using the CRT.
206 * For now, we use Montgomery only if the modulus is odd; otherwise,
207 * exponentiation using the reciprocal-based quick remaindering
210 * (Timing obtained with expspeed.c [computations a^p mod m
211 * where a, p, m are of the same length: 256, 512, 1024, 2048,
212 * 4096, 8192 bits], compared to the running time of the
213 * standard algorithm:
215 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
216 * 55 .. 77 % [UltraSparc processor, but
217 * debug-solaris-sparcv8-gcc conf.]
219 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
220 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
222 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
223 * at 2048 and more bits, but at 512 and 1024 bits, it was
224 * slower even than the standard algorithm!
226 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
227 * should be obtained when the new Montgomery reduction code
228 * has been integrated into OpenSSL.)
232 #define MONT_EXP_WORD
237 * I have finally been able to take out this pre-condition of the top bit
238 * being set. It was caused by an error in BN_div with negatives. There
239 * was also another problem when for a^b%m a >= m. eay 07-May-97
241 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
244 # ifdef MONT_EXP_WORD
245 if (a->top == 1 && !a->neg
246 && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)) {
247 BN_ULONG A = a->d[0];
248 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
251 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
256 ret = BN_mod_exp_recp(r, a, p, m, ctx);
260 ret = BN_mod_exp_simple(r, a, p, m, ctx);
268 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
269 const BIGNUM *m, BN_CTX *ctx)
271 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
274 /* Table of variables obtained from 'ctx' */
275 BIGNUM *val[TABLE_SIZE];
278 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
279 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
280 BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
284 bits = BN_num_bits(p);
286 /* x**0 mod 1 is still zero. */
297 aa = BN_CTX_get(ctx);
298 val[0] = BN_CTX_get(ctx);
302 BN_RECP_CTX_init(&recp);
304 /* ignore sign of 'm' */
308 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
311 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
315 if (!BN_nnmod(val[0], a, m, ctx))
317 if (BN_is_zero(val[0])) {
323 window = BN_window_bits_for_exponent_size(bits);
325 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
327 j = 1 << (window - 1);
328 for (i = 1; i < j; i++) {
329 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
330 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
335 start = 1; /* This is used to avoid multiplication etc
336 * when there is only the value '1' in the
338 wvalue = 0; /* The 'value' of the window */
339 wstart = bits - 1; /* The top bit of the window */
340 wend = 0; /* The bottom bit of the window */
346 if (BN_is_bit_set(p, wstart) == 0) {
348 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
356 * We now have wstart on a 'set' bit, we now need to work out how bit
357 * a window to do. To do this we need to scan forward until the last
358 * set bit before the end of the window
363 for (i = 1; i < window; i++) {
366 if (BN_is_bit_set(p, wstart - i)) {
367 wvalue <<= (i - wend);
373 /* wend is the size of the current window */
375 /* add the 'bytes above' */
377 for (i = 0; i < j; i++) {
378 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
382 /* wvalue will be an odd number < 2^window */
383 if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
386 /* move the 'window' down further */
396 BN_RECP_CTX_free(&recp);
401 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
402 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
404 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
408 /* Table of variables obtained from 'ctx' */
409 BIGNUM *val[TABLE_SIZE];
410 BN_MONT_CTX *mont = NULL;
412 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
413 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
421 BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
424 bits = BN_num_bits(p);
426 /* x**0 mod 1 is still zero. */
439 val[0] = BN_CTX_get(ctx);
440 if (!d || !r || !val[0])
444 * If this is not done, things will break in the montgomery part
450 if ((mont = BN_MONT_CTX_new()) == NULL)
452 if (!BN_MONT_CTX_set(mont, m, ctx))
456 if (a->neg || BN_ucmp(a, m) >= 0) {
457 if (!BN_nnmod(val[0], a, m, ctx))
462 if (BN_is_zero(aa)) {
467 if (!BN_to_montgomery(val[0], aa, mont, ctx))
470 window = BN_window_bits_for_exponent_size(bits);
472 if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx))
474 j = 1 << (window - 1);
475 for (i = 1; i < j; i++) {
476 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
477 !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx))
482 start = 1; /* This is used to avoid multiplication etc
483 * when there is only the value '1' in the
485 wvalue = 0; /* The 'value' of the window */
486 wstart = bits - 1; /* The top bit of the window */
487 wend = 0; /* The bottom bit of the window */
489 #if 1 /* by Shay Gueron's suggestion */
490 j = m->top; /* borrow j */
491 if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
492 if (bn_wexpand(r, j) == NULL)
494 /* 2^(top*BN_BITS2) - m */
495 r->d[0] = (0 - m->d[0]) & BN_MASK2;
496 for (i = 1; i < j; i++)
497 r->d[i] = (~m->d[i]) & BN_MASK2;
500 * Upper words will be zero if the corresponding words of 'm' were
501 * 0xfff[...], so decrement r->top accordingly.
506 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
509 if (BN_is_bit_set(p, wstart) == 0) {
511 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
520 * We now have wstart on a 'set' bit, we now need to work out how bit
521 * a window to do. To do this we need to scan forward until the last
522 * set bit before the end of the window
527 for (i = 1; i < window; i++) {
530 if (BN_is_bit_set(p, wstart - i)) {
531 wvalue <<= (i - wend);
537 /* wend is the size of the current window */
539 /* add the 'bytes above' */
541 for (i = 0; i < j; i++) {
542 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
546 /* wvalue will be an odd number < 2^window */
547 if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
550 /* move the 'window' down further */
557 #if defined(SPARC_T4_MONT)
558 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
559 j = mont->N.top; /* borrow j */
560 val[0]->d[0] = 1; /* borrow val[0] */
561 for (i = 1; i < j; i++)
564 if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
568 if (!BN_from_montgomery(rr, r, mont, ctx))
573 BN_MONT_CTX_free(mont);
579 #if defined(SPARC_T4_MONT)
580 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
585 wordpos = bitpos / BN_BITS2;
587 if (wordpos >= 0 && wordpos < a->top) {
588 ret = a->d[wordpos] & BN_MASK2;
591 if (++wordpos < a->top)
592 ret |= a->d[wordpos] << (BN_BITS2 - bitpos);
596 return ret & BN_MASK2;
601 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
602 * layout so that accessing any of these table values shows the same access
603 * pattern as far as cache lines are concerned. The following functions are
604 * used to transfer a BIGNUM from/to that table.
607 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
608 unsigned char *buf, int idx,
614 top = b->top; /* this works because 'buf' is explicitly
616 for (i = 0, j = idx; i < top * sizeof b->d[0]; i++, j += width) {
617 buf[j] = ((unsigned char *)b->d)[i];
623 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
624 unsigned char *buf, int idx,
629 if (bn_wexpand(b, top) == NULL)
632 for (i = 0, j = idx; i < top * sizeof b->d[0]; i++, j += width) {
633 ((unsigned char *)b->d)[i] = buf[j];
642 * Given a pointer value, compute the next address that is a cache line
645 #define MOD_EXP_CTIME_ALIGN(x_) \
646 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
649 * This variant of BN_mod_exp_mont() uses fixed windows and the special
650 * precomputation memory layout to limit data-dependency to a minimum to
651 * protect secret exponents (cf. the hyper-threading timing attacks pointed
652 * out by Colin Percival,
653 * http://www.daemonology.net/hyperthreading-considered-harmful/)
655 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
656 const BIGNUM *m, BN_CTX *ctx,
657 BN_MONT_CTX *in_mont)
659 int i, bits, ret = 0, window, wvalue;
661 BN_MONT_CTX *mont = NULL;
664 unsigned char *powerbufFree = NULL;
666 unsigned char *powerbuf = NULL;
668 #if defined(SPARC_T4_MONT)
677 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
683 bits = BN_num_bits(p);
685 /* x**0 mod 1 is still zero. */
698 * Allocate a montgomery context if it was not supplied by the caller. If
699 * this is not done, things will break in the montgomery part.
704 if ((mont = BN_MONT_CTX_new()) == NULL)
706 if (!BN_MONT_CTX_set(mont, m, ctx))
712 * If the size of the operands allow it, perform the optimized
713 * RSAZ exponentiation. For further information see
714 * crypto/bn/rsaz_exp.c and accompanying assembly modules.
716 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
717 && rsaz_avx2_eligible()) {
718 if (NULL == bn_wexpand(rr, 16))
720 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
727 } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
728 if (NULL == bn_wexpand(rr, 8))
730 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
739 /* Get the window size to use with size of p. */
740 window = BN_window_bits_for_ctime_exponent_size(bits);
741 #if defined(SPARC_T4_MONT)
742 if (window >= 5 && (top & 15) == 0 && top <= 64 &&
743 (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) ==
744 (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0]))
748 #if defined(OPENSSL_BN_ASM_MONT5)
750 window = 5; /* ~5% improvement for RSA2048 sign, and even
753 powerbufLen += 2 * top * sizeof(m->d[0]);
759 * Allocate a buffer large enough to hold all of the pre-computed powers
760 * of am, am itself and tmp.
762 numPowers = 1 << window;
763 powerbufLen += sizeof(m->d[0]) * (top * numPowers +
765 numPowers ? (2 * top) : numPowers));
767 if (powerbufLen < 3072)
769 alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
773 OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
777 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
778 memset(powerbuf, 0, powerbufLen);
781 if (powerbufLen < 3072)
785 /* lay down tmp and am right after powers table */
786 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
788 tmp.top = am.top = 0;
789 tmp.dmax = am.dmax = top;
790 tmp.neg = am.neg = 0;
791 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
793 /* prepare a^0 in Montgomery domain */
794 #if 1 /* by Shay Gueron's suggestion */
795 if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
796 /* 2^(top*BN_BITS2) - m */
797 tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
798 for (i = 1; i < top; i++)
799 tmp.d[i] = (~m->d[i]) & BN_MASK2;
803 if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx))
806 /* prepare a^1 in Montgomery domain */
807 if (a->neg || BN_ucmp(a, m) >= 0) {
808 if (!BN_mod(&am, a, m, ctx))
810 if (!BN_to_montgomery(&am, &am, mont, ctx))
812 } else if (!BN_to_montgomery(&am, a, mont, ctx))
815 #if defined(SPARC_T4_MONT)
817 typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np,
818 const BN_ULONG *n0, const void *table,
819 int power, int bits);
820 int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np,
821 const BN_ULONG *n0, const void *table,
822 int power, int bits);
823 int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np,
824 const BN_ULONG *n0, const void *table,
825 int power, int bits);
826 int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np,
827 const BN_ULONG *n0, const void *table,
828 int power, int bits);
829 int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np,
830 const BN_ULONG *n0, const void *table,
831 int power, int bits);
832 static const bn_pwr5_mont_f pwr5_funcs[4] = {
833 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
834 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
836 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
838 typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap,
839 const void *bp, const BN_ULONG *np,
841 int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp,
842 const BN_ULONG *np, const BN_ULONG *n0);
843 int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap,
844 const void *bp, const BN_ULONG *np,
846 int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap,
847 const void *bp, const BN_ULONG *np,
849 int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap,
850 const void *bp, const BN_ULONG *np,
852 static const bn_mul_mont_f mul_funcs[4] = {
853 bn_mul_mont_t4_8, bn_mul_mont_t4_16,
854 bn_mul_mont_t4_24, bn_mul_mont_t4_32
856 bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
858 void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap,
859 const void *bp, const BN_ULONG *np,
860 const BN_ULONG *n0, int num);
861 void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap,
862 const void *bp, const BN_ULONG *np,
863 const BN_ULONG *n0, int num);
864 void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap,
865 const void *table, const BN_ULONG *np,
866 const BN_ULONG *n0, int num, int power);
867 void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
868 void *table, size_t power);
869 void bn_gather5_t4(BN_ULONG *out, size_t num,
870 void *table, size_t power);
871 void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num);
873 BN_ULONG *np = mont->N.d, *n0 = mont->n0;
874 int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
878 * BN_to_montgomery can contaminate words above .top [in
879 * BN_DEBUG[_DEBUG] build]...
881 for (i = am.top; i < top; i++)
883 for (i = tmp.top; i < top; i++)
886 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
887 bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
888 if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) &&
889 !(*mul_worker) (tmp.d, am.d, am.d, np, n0))
890 bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
891 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
893 for (i = 3; i < 32; i++) {
894 /* Calculate a^i = a^(i-1) * a */
895 if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) &&
896 !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0))
897 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
898 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
901 /* switch to 64-bit domain */
902 np = alloca(top * sizeof(BN_ULONG));
904 bn_flip_t4(np, mont->N.d, top);
907 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
908 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
909 bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
912 * Scan the exponent one window at a time starting from the most
919 wvalue = bn_get_bits(p, bits + 1);
921 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
923 /* retry once and fall back */
924 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
928 wvalue >>= stride - 5;
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_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
935 bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
939 bn_flip_t4(tmp.d, tmp.d, top);
941 /* back to 32-bit domain */
943 bn_correct_top(&tmp);
944 OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
947 #if defined(OPENSSL_BN_ASM_MONT5)
948 if (window == 5 && top > 1) {
950 * This optimization uses ideas from http://eprint.iacr.org/2011/239,
951 * specifically optimization of cache-timing attack countermeasures
952 * and pre-computation optimization.
956 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
957 * 512-bit RSA is hardly relevant, we omit it to spare size...
959 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
960 const void *table, const BN_ULONG *np,
961 const BN_ULONG *n0, int num, int power);
962 void bn_scatter5(const BN_ULONG *inp, size_t num,
963 void *table, size_t power);
964 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
965 void bn_power5(BN_ULONG *rp, const BN_ULONG *ap,
966 const void *table, const BN_ULONG *np,
967 const BN_ULONG *n0, int num, int power);
968 int bn_get_bits5(const BN_ULONG *ap, int off);
969 int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap,
970 const BN_ULONG *not_used, const BN_ULONG *np,
971 const BN_ULONG *n0, int num);
973 BN_ULONG *np = mont->N.d, *n0 = mont->n0, *np2;
976 * BN_to_montgomery can contaminate words above .top [in
977 * BN_DEBUG[_DEBUG] build]...
979 for (i = am.top; i < top; i++)
981 for (i = tmp.top; i < top; i++)
987 for (np2 = am.d + top, i = 0; i < top; i++)
990 bn_scatter5(tmp.d, top, powerbuf, 0);
991 bn_scatter5(am.d, am.top, powerbuf, 1);
992 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
993 bn_scatter5(tmp.d, top, powerbuf, 2);
996 for (i = 3; i < 32; i++) {
997 /* Calculate a^i = a^(i-1) * a */
998 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np2, n0, top, i - 1);
999 bn_scatter5(tmp.d, top, powerbuf, i);
1002 /* same as above, but uses squaring for 1/2 of operations */
1003 for (i = 4; i < 32; i *= 2) {
1004 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1005 bn_scatter5(tmp.d, top, powerbuf, i);
1007 for (i = 3; i < 8; i += 2) {
1009 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np2, n0, top, i - 1);
1010 bn_scatter5(tmp.d, top, powerbuf, i);
1011 for (j = 2 * i; j < 32; j *= 2) {
1012 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1013 bn_scatter5(tmp.d, top, powerbuf, j);
1016 for (; i < 16; i += 2) {
1017 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np2, n0, top, i - 1);
1018 bn_scatter5(tmp.d, top, powerbuf, i);
1019 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1020 bn_scatter5(tmp.d, top, powerbuf, 2 * i);
1022 for (; i < 32; i += 2) {
1023 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np2, n0, top, i - 1);
1024 bn_scatter5(tmp.d, top, powerbuf, i);
1028 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
1029 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1030 bn_gather5(tmp.d, top, powerbuf, wvalue);
1033 * Scan the exponent one window at a time starting from the most
1038 for (wvalue = 0, i = 0; i < 5; i++, bits--)
1039 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
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(tmp.d, tmp.d, tmp.d, np, n0, top);
1046 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
1050 wvalue = bn_get_bits5(p->d, bits - 4);
1052 bn_power5(tmp.d, tmp.d, powerbuf, np2, n0, top, wvalue);
1056 ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np2, n0, top);
1058 bn_correct_top(&tmp);
1060 if (!BN_copy(rr, &tmp))
1062 goto err; /* non-zero ret means it's not error */
1067 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, numPowers))
1069 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, numPowers))
1073 * If the window size is greater than 1, then calculate
1074 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1075 * powers could instead be computed as (a^(i/2))^2 to use the slight
1076 * performance advantage of sqr over mul).
1079 if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx))
1081 if (!MOD_EXP_CTIME_COPY_TO_PREBUF
1082 (&tmp, top, powerbuf, 2, numPowers))
1084 for (i = 3; i < numPowers; i++) {
1085 /* Calculate a^i = a^(i-1) * a */
1086 if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx))
1088 if (!MOD_EXP_CTIME_COPY_TO_PREBUF
1089 (&tmp, top, powerbuf, i, numPowers))
1095 for (wvalue = 0, i = bits % window; i >= 0; i--, bits--)
1096 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1097 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF
1098 (&tmp, top, powerbuf, wvalue, numPowers))
1102 * Scan the exponent one window at a time starting from the most
1106 wvalue = 0; /* The 'value' of the window */
1108 /* Scan the window, squaring the result as we go */
1109 for (i = 0; i < window; i++, bits--) {
1110 if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx))
1112 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1116 * Fetch the appropriate pre-computed value from the pre-buf
1118 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF
1119 (&am, top, powerbuf, wvalue, numPowers))
1122 /* Multiply the result into the intermediate result */
1123 if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx))
1128 /* Convert the final result from montgomery to standard format */
1129 #if defined(SPARC_T4_MONT)
1130 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
1131 am.d[0] = 1; /* borrow am */
1132 for (i = 1; i < top; i++)
1134 if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
1138 if (!BN_from_montgomery(rr, &tmp, mont, ctx))
1142 if (in_mont == NULL)
1143 BN_MONT_CTX_free(mont);
1144 if (powerbuf != NULL) {
1145 OPENSSL_cleanse(powerbuf, powerbufLen);
1146 OPENSSL_free(powerbufFree);
1152 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1153 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1155 BN_MONT_CTX *mont = NULL;
1156 int b, bits, ret = 0;
1161 #define BN_MOD_MUL_WORD(r, w, m) \
1162 (BN_mul_word(r, (w)) && \
1163 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1164 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1166 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1167 * probably more overhead than always using BN_mod (which uses BN_copy if
1168 * a similar test returns true).
1171 * We can use BN_mod and do not need BN_nnmod because our accumulator is
1172 * never negative (the result of BN_mod does not depend on the sign of
1175 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1176 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1178 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
1179 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1180 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1187 if (!BN_is_odd(m)) {
1188 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
1192 a %= m->d[0]; /* make sure that 'a' is reduced */
1194 bits = BN_num_bits(p);
1196 /* x**0 mod 1 is still zero. */
1212 d = BN_CTX_get(ctx);
1213 r = BN_CTX_get(ctx);
1214 t = BN_CTX_get(ctx);
1215 if (d == NULL || r == NULL || t == NULL)
1218 if (in_mont != NULL)
1221 if ((mont = BN_MONT_CTX_new()) == NULL)
1223 if (!BN_MONT_CTX_set(mont, m, ctx))
1227 r_is_one = 1; /* except for Montgomery factor */
1231 /* The result is accumulated in the product r*w. */
1232 w = a; /* bit 'bits-1' of 'p' is always set */
1233 for (b = bits - 2; b >= 0; b--) {
1234 /* First, square r*w. */
1236 if ((next_w / w) != w) { /* overflow */
1238 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1242 if (!BN_MOD_MUL_WORD(r, w, m))
1249 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
1253 /* Second, multiply r*w by 'a' if exponent bit is set. */
1254 if (BN_is_bit_set(p, b)) {
1256 if ((next_w / a) != w) { /* overflow */
1258 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1262 if (!BN_MOD_MUL_WORD(r, w, m))
1271 /* Finally, set r:=r*w. */
1274 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1278 if (!BN_MOD_MUL_WORD(r, w, m))
1283 if (r_is_one) { /* can happen only if a == 1 */
1287 if (!BN_from_montgomery(rr, r, mont, ctx))
1292 if (in_mont == NULL)
1293 BN_MONT_CTX_free(mont);
1299 /* The old fallback, simple version :-) */
1300 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1301 const BIGNUM *m, BN_CTX *ctx)
1303 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
1306 /* Table of variables obtained from 'ctx' */
1307 BIGNUM *val[TABLE_SIZE];
1309 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0) {
1310 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1311 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1315 bits = BN_num_bits(p);
1317 /* x**0 mod 1 is still zero. */
1328 d = BN_CTX_get(ctx);
1329 val[0] = BN_CTX_get(ctx);
1333 if (!BN_nnmod(val[0], a, m, ctx))
1335 if (BN_is_zero(val[0])) {
1341 window = BN_window_bits_for_exponent_size(bits);
1343 if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1345 j = 1 << (window - 1);
1346 for (i = 1; i < j; i++) {
1347 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
1348 !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
1353 start = 1; /* This is used to avoid multiplication etc
1354 * when there is only the value '1' in the
1356 wvalue = 0; /* The 'value' of the window */
1357 wstart = bits - 1; /* The top bit of the window */
1358 wend = 0; /* The bottom bit of the window */
1364 if (BN_is_bit_set(p, wstart) == 0) {
1366 if (!BN_mod_mul(r, r, r, m, ctx))
1374 * We now have wstart on a 'set' bit, we now need to work out how bit
1375 * a window to do. To do this we need to scan forward until the last
1376 * set bit before the end of the window
1381 for (i = 1; i < window; i++) {
1384 if (BN_is_bit_set(p, wstart - i)) {
1385 wvalue <<= (i - wend);
1391 /* wend is the size of the current window */
1393 /* add the 'bytes above' */
1395 for (i = 0; i < j; i++) {
1396 if (!BN_mod_mul(r, r, r, m, ctx))
1400 /* wvalue will be an odd number < 2^window */
1401 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1404 /* move the 'window' down further */