2 * Copyright 1995-2018 The OpenSSL Project Authors. All Rights Reserved.
4 * Licensed under the Apache License 2.0 (the "License"). You may not use
5 * this file except in compliance with the License. You can obtain a copy
6 * in the file LICENSE in the source distribution or at
7 * https://www.openssl.org/source/license.html
10 #include "internal/cryptlib.h"
11 #include "internal/constant_time.h"
18 # define alloca _alloca
20 #elif defined(__GNUC__)
22 # define alloca(s) __builtin_alloca((s))
31 #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
32 # include "sparc_arch.h"
33 extern unsigned int OPENSSL_sparcv9cap_P[];
34 # define SPARC_T4_MONT
37 /* maximum precomputation table size for *variable* sliding windows */
40 /* this one works - simple but works */
41 int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
46 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
47 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0) {
48 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
49 BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
54 rr = ((r == a) || (r == p)) ? BN_CTX_get(ctx) : r;
56 if (rr == NULL || v == NULL)
59 if (BN_copy(v, a) == NULL)
61 bits = BN_num_bits(p);
64 if (BN_copy(rr, a) == NULL)
71 for (i = 1; i < bits; i++) {
72 if (!BN_sqr(v, v, ctx))
74 if (BN_is_bit_set(p, i)) {
75 if (!BN_mul(rr, rr, v, ctx))
79 if (r != rr && BN_copy(r, rr) == NULL)
89 int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
99 * For even modulus m = 2^k*m_odd, it might make sense to compute
100 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
101 * exponentiation for the odd part), using appropriate exponent
102 * reductions, and combine the results using the CRT.
104 * For now, we use Montgomery only if the modulus is odd; otherwise,
105 * exponentiation using the reciprocal-based quick remaindering
108 * (Timing obtained with expspeed.c [computations a^p mod m
109 * where a, p, m are of the same length: 256, 512, 1024, 2048,
110 * 4096, 8192 bits], compared to the running time of the
111 * standard algorithm:
113 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
114 * 55 .. 77 % [UltraSparc processor, but
115 * debug-solaris-sparcv8-gcc conf.]
117 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
118 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
120 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
121 * at 2048 and more bits, but at 512 and 1024 bits, it was
122 * slower even than the standard algorithm!
124 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
125 * should be obtained when the new Montgomery reduction code
126 * has been integrated into OpenSSL.)
130 #define MONT_EXP_WORD
135 # ifdef MONT_EXP_WORD
136 if (a->top == 1 && !a->neg
137 && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)
138 && (BN_get_flags(a, BN_FLG_CONSTTIME) == 0)
139 && (BN_get_flags(m, BN_FLG_CONSTTIME) == 0)) {
140 BN_ULONG A = a->d[0];
141 ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
144 ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
149 ret = BN_mod_exp_recp(r, a, p, m, ctx);
153 ret = BN_mod_exp_simple(r, a, p, m, ctx);
161 int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
162 const BIGNUM *m, BN_CTX *ctx)
164 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
167 /* Table of variables obtained from 'ctx' */
168 BIGNUM *val[TABLE_SIZE];
171 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
172 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
173 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
174 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
175 BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
179 bits = BN_num_bits(p);
181 /* x**0 mod 1, or x**0 mod -1 is still zero. */
182 if (BN_abs_is_word(m, 1)) {
192 aa = BN_CTX_get(ctx);
193 val[0] = BN_CTX_get(ctx);
197 BN_RECP_CTX_init(&recp);
199 /* ignore sign of 'm' */
203 if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
206 if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
210 if (!BN_nnmod(val[0], a, m, ctx))
212 if (BN_is_zero(val[0])) {
218 window = BN_window_bits_for_exponent_size(bits);
220 if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
222 j = 1 << (window - 1);
223 for (i = 1; i < j; i++) {
224 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
225 !BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
230 start = 1; /* This is used to avoid multiplication etc
231 * when there is only the value '1' in the
233 wvalue = 0; /* The 'value' of the window */
234 wstart = bits - 1; /* The top bit of the window */
235 wend = 0; /* The bottom bit of the window */
241 if (BN_is_bit_set(p, wstart) == 0) {
243 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
251 * We now have wstart on a 'set' bit, we now need to work out how bit
252 * a window to do. To do this we need to scan forward until the last
253 * set bit before the end of the window
258 for (i = 1; i < window; i++) {
261 if (BN_is_bit_set(p, wstart - i)) {
262 wvalue <<= (i - wend);
268 /* wend is the size of the current window */
270 /* add the 'bytes above' */
272 for (i = 0; i < j; i++) {
273 if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
277 /* wvalue will be an odd number < 2^window */
278 if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
281 /* move the 'window' down further */
291 BN_RECP_CTX_free(&recp);
296 int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
297 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
299 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
303 /* Table of variables obtained from 'ctx' */
304 BIGNUM *val[TABLE_SIZE];
305 BN_MONT_CTX *mont = NULL;
307 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
308 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
309 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
310 return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
318 BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
321 bits = BN_num_bits(p);
323 /* x**0 mod 1, or x**0 mod -1 is still zero. */
324 if (BN_abs_is_word(m, 1)) {
336 val[0] = BN_CTX_get(ctx);
341 * If this is not done, things will break in the montgomery part
347 if ((mont = BN_MONT_CTX_new()) == NULL)
349 if (!BN_MONT_CTX_set(mont, m, ctx))
353 if (a->neg || BN_ucmp(a, m) >= 0) {
354 if (!BN_nnmod(val[0], a, m, ctx))
359 if (!bn_to_mont_fixed_top(val[0], aa, mont, ctx))
362 window = BN_window_bits_for_exponent_size(bits);
364 if (!bn_mul_mont_fixed_top(d, val[0], val[0], mont, ctx))
366 j = 1 << (window - 1);
367 for (i = 1; i < j; i++) {
368 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
369 !bn_mul_mont_fixed_top(val[i], val[i - 1], d, mont, ctx))
374 start = 1; /* This is used to avoid multiplication etc
375 * when there is only the value '1' in the
377 wvalue = 0; /* The 'value' of the window */
378 wstart = bits - 1; /* The top bit of the window */
379 wend = 0; /* The bottom bit of the window */
381 #if 1 /* by Shay Gueron's suggestion */
382 j = m->top; /* borrow j */
383 if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
384 if (bn_wexpand(r, j) == NULL)
386 /* 2^(top*BN_BITS2) - m */
387 r->d[0] = (0 - m->d[0]) & BN_MASK2;
388 for (i = 1; i < j; i++)
389 r->d[i] = (~m->d[i]) & BN_MASK2;
391 r->flags |= BN_FLG_FIXED_TOP;
394 if (!bn_to_mont_fixed_top(r, BN_value_one(), mont, ctx))
397 if (BN_is_bit_set(p, wstart) == 0) {
399 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx))
408 * We now have wstart on a 'set' bit, we now need to work out how bit
409 * a window to do. To do this we need to scan forward until the last
410 * set bit before the end of the window
415 for (i = 1; i < window; i++) {
418 if (BN_is_bit_set(p, wstart - i)) {
419 wvalue <<= (i - wend);
425 /* wend is the size of the current window */
427 /* add the 'bytes above' */
429 for (i = 0; i < j; i++) {
430 if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx))
434 /* wvalue will be an odd number < 2^window */
435 if (!bn_mul_mont_fixed_top(r, r, val[wvalue >> 1], mont, ctx))
438 /* move the 'window' down further */
446 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
447 * removes padding [if any] and makes return value suitable for public
450 #if defined(SPARC_T4_MONT)
451 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
452 j = mont->N.top; /* borrow j */
453 val[0]->d[0] = 1; /* borrow val[0] */
454 for (i = 1; i < j; i++)
457 if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
461 if (!BN_from_montgomery(rr, r, mont, ctx))
466 BN_MONT_CTX_free(mont);
472 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
477 wordpos = bitpos / BN_BITS2;
479 if (wordpos >= 0 && wordpos < a->top) {
480 ret = a->d[wordpos] & BN_MASK2;
483 if (++wordpos < a->top)
484 ret |= a->d[wordpos] << (BN_BITS2 - bitpos);
488 return ret & BN_MASK2;
492 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
493 * layout so that accessing any of these table values shows the same access
494 * pattern as far as cache lines are concerned. The following functions are
495 * used to transfer a BIGNUM from/to that table.
498 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
499 unsigned char *buf, int idx,
503 int width = 1 << window;
504 BN_ULONG *table = (BN_ULONG *)buf;
507 top = b->top; /* this works because 'buf' is explicitly
509 for (i = 0, j = idx; i < top; i++, j += width) {
516 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
517 unsigned char *buf, int idx,
521 int width = 1 << window;
523 * We declare table 'volatile' in order to discourage compiler
524 * from reordering loads from the table. Concern is that if
525 * reordered in specific manner loads might give away the
526 * information we are trying to conceal. Some would argue that
527 * compiler can reorder them anyway, but it can as well be
528 * argued that doing so would be violation of standard...
530 volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
532 if (bn_wexpand(b, top) == NULL)
536 for (i = 0; i < top; i++, table += width) {
539 for (j = 0; j < width; j++) {
541 ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
547 int xstride = 1 << (window - 2);
548 BN_ULONG y0, y1, y2, y3;
550 i = idx >> (window - 2); /* equivalent of idx / xstride */
551 idx &= xstride - 1; /* equivalent of idx % xstride */
553 y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1);
554 y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1);
555 y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1);
556 y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1);
558 for (i = 0; i < top; i++, table += width) {
561 for (j = 0; j < xstride; j++) {
562 acc |= ( (table[j + 0 * xstride] & y0) |
563 (table[j + 1 * xstride] & y1) |
564 (table[j + 2 * xstride] & y2) |
565 (table[j + 3 * xstride] & y3) )
566 & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
574 b->flags |= BN_FLG_FIXED_TOP;
579 * Given a pointer value, compute the next address that is a cache line
582 #define MOD_EXP_CTIME_ALIGN(x_) \
583 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
586 * This variant of BN_mod_exp_mont() uses fixed windows and the special
587 * precomputation memory layout to limit data-dependency to a minimum to
588 * protect secret exponents (cf. the hyper-threading timing attacks pointed
589 * out by Colin Percival,
590 * http://www.daemonology.net/hyperthreading-considered-harmful/)
592 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
593 const BIGNUM *m, BN_CTX *ctx,
594 BN_MONT_CTX *in_mont)
596 int i, bits, ret = 0, window, wvalue, wmask, window0;
598 BN_MONT_CTX *mont = NULL;
601 unsigned char *powerbufFree = NULL;
603 unsigned char *powerbuf = NULL;
605 #if defined(SPARC_T4_MONT)
614 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
621 * Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak
622 * whether the top bits are zero.
624 bits = p->top * BN_BITS2;
626 /* x**0 mod 1, or x**0 mod -1 is still zero. */
627 if (BN_abs_is_word(m, 1)) {
639 * Allocate a montgomery context if it was not supplied by the caller. If
640 * this is not done, things will break in the montgomery part.
645 if ((mont = BN_MONT_CTX_new()) == NULL)
647 if (!BN_MONT_CTX_set(mont, m, ctx))
651 if (a->neg || BN_ucmp(a, m) >= 0) {
652 BIGNUM *reduced = BN_CTX_get(ctx);
654 || !BN_nnmod(reduced, a, m, ctx)) {
662 * If the size of the operands allow it, perform the optimized
663 * RSAZ exponentiation. For further information see
664 * crypto/bn/rsaz_exp.c and accompanying assembly modules.
666 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
667 && rsaz_avx2_eligible()) {
668 if (NULL == bn_wexpand(rr, 16))
670 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
677 } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
678 if (NULL == bn_wexpand(rr, 8))
680 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
689 /* Get the window size to use with size of p. */
690 window = BN_window_bits_for_ctime_exponent_size(bits);
691 #if defined(SPARC_T4_MONT)
692 if (window >= 5 && (top & 15) == 0 && top <= 64 &&
693 (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) ==
694 (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0]))
698 #if defined(OPENSSL_BN_ASM_MONT5)
700 window = 5; /* ~5% improvement for RSA2048 sign, and even
702 /* reserve space for mont->N.d[] copy */
703 powerbufLen += top * sizeof(mont->N.d[0]);
709 * Allocate a buffer large enough to hold all of the pre-computed powers
710 * of am, am itself and tmp.
712 numPowers = 1 << window;
713 powerbufLen += sizeof(m->d[0]) * (top * numPowers +
715 numPowers ? (2 * top) : numPowers));
717 if (powerbufLen < 3072)
719 alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
723 OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
727 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
728 memset(powerbuf, 0, powerbufLen);
731 if (powerbufLen < 3072)
735 /* lay down tmp and am right after powers table */
736 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
738 tmp.top = am.top = 0;
739 tmp.dmax = am.dmax = top;
740 tmp.neg = am.neg = 0;
741 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
743 /* prepare a^0 in Montgomery domain */
744 #if 1 /* by Shay Gueron's suggestion */
745 if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
746 /* 2^(top*BN_BITS2) - m */
747 tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
748 for (i = 1; i < top; i++)
749 tmp.d[i] = (~m->d[i]) & BN_MASK2;
753 if (!bn_to_mont_fixed_top(&tmp, BN_value_one(), mont, ctx))
756 /* prepare a^1 in Montgomery domain */
757 if (!bn_to_mont_fixed_top(&am, a, mont, ctx))
760 #if defined(SPARC_T4_MONT)
762 typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np,
763 const BN_ULONG *n0, const void *table,
764 int power, int bits);
765 int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np,
766 const BN_ULONG *n0, const void *table,
767 int power, int bits);
768 int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np,
769 const BN_ULONG *n0, const void *table,
770 int power, int bits);
771 int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np,
772 const BN_ULONG *n0, const void *table,
773 int power, int bits);
774 int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np,
775 const BN_ULONG *n0, const void *table,
776 int power, int bits);
777 static const bn_pwr5_mont_f pwr5_funcs[4] = {
778 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
779 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
781 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
783 typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap,
784 const void *bp, const BN_ULONG *np,
786 int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp,
787 const BN_ULONG *np, const BN_ULONG *n0);
788 int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap,
789 const void *bp, const BN_ULONG *np,
791 int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap,
792 const void *bp, const BN_ULONG *np,
794 int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap,
795 const void *bp, const BN_ULONG *np,
797 static const bn_mul_mont_f mul_funcs[4] = {
798 bn_mul_mont_t4_8, bn_mul_mont_t4_16,
799 bn_mul_mont_t4_24, bn_mul_mont_t4_32
801 bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
803 void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap,
804 const void *bp, const BN_ULONG *np,
805 const BN_ULONG *n0, int num);
806 void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap,
807 const void *bp, const BN_ULONG *np,
808 const BN_ULONG *n0, int num);
809 void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap,
810 const void *table, const BN_ULONG *np,
811 const BN_ULONG *n0, int num, int power);
812 void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
813 void *table, size_t power);
814 void bn_gather5_t4(BN_ULONG *out, size_t num,
815 void *table, size_t power);
816 void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num);
818 BN_ULONG *np = mont->N.d, *n0 = mont->n0;
819 int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
823 * BN_to_montgomery can contaminate words above .top [in
824 * BN_DEBUG[_DEBUG] build]...
826 for (i = am.top; i < top; i++)
828 for (i = tmp.top; i < top; i++)
831 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
832 bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
833 if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) &&
834 !(*mul_worker) (tmp.d, am.d, am.d, np, n0))
835 bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
836 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
838 for (i = 3; i < 32; i++) {
839 /* Calculate a^i = a^(i-1) * a */
840 if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) &&
841 !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0))
842 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
843 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
846 /* switch to 64-bit domain */
847 np = alloca(top * sizeof(BN_ULONG));
849 bn_flip_t4(np, mont->N.d, top);
852 * The exponent may not have a whole number of fixed-size windows.
853 * To simplify the main loop, the initial window has between 1 and
854 * full-window-size bits such that what remains is always a whole
857 window0 = (bits - 1) % 5 + 1;
858 wmask = (1 << window0) - 1;
860 wvalue = bn_get_bits(p, bits) & wmask;
861 bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
864 * Scan the exponent one window at a time starting from the most
871 wvalue = bn_get_bits(p, bits);
873 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
875 /* retry once and fall back */
876 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
880 wvalue >>= stride - 5;
882 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
883 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
884 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
885 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
886 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
887 bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
891 bn_flip_t4(tmp.d, tmp.d, top);
893 /* back to 32-bit domain */
895 bn_correct_top(&tmp);
896 OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
899 #if defined(OPENSSL_BN_ASM_MONT5)
900 if (window == 5 && top > 1) {
902 * This optimization uses ideas from http://eprint.iacr.org/2011/239,
903 * specifically optimization of cache-timing attack countermeasures
904 * and pre-computation optimization.
908 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
909 * 512-bit RSA is hardly relevant, we omit it to spare size...
911 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
912 const void *table, const BN_ULONG *np,
913 const BN_ULONG *n0, int num, int power);
914 void bn_scatter5(const BN_ULONG *inp, size_t num,
915 void *table, size_t power);
916 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
917 void bn_power5(BN_ULONG *rp, const BN_ULONG *ap,
918 const void *table, const BN_ULONG *np,
919 const BN_ULONG *n0, int num, int power);
920 int bn_get_bits5(const BN_ULONG *ap, int off);
921 int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap,
922 const BN_ULONG *not_used, const BN_ULONG *np,
923 const BN_ULONG *n0, int num);
925 BN_ULONG *n0 = mont->n0, *np;
928 * BN_to_montgomery can contaminate words above .top [in
929 * BN_DEBUG[_DEBUG] build]...
931 for (i = am.top; i < top; i++)
933 for (i = tmp.top; i < top; i++)
937 * copy mont->N.d[] to improve cache locality
939 for (np = am.d + top, i = 0; i < top; i++)
940 np[i] = mont->N.d[i];
942 bn_scatter5(tmp.d, top, powerbuf, 0);
943 bn_scatter5(am.d, am.top, powerbuf, 1);
944 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
945 bn_scatter5(tmp.d, top, powerbuf, 2);
948 for (i = 3; i < 32; i++) {
949 /* Calculate a^i = a^(i-1) * a */
950 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
951 bn_scatter5(tmp.d, top, powerbuf, i);
954 /* same as above, but uses squaring for 1/2 of operations */
955 for (i = 4; i < 32; i *= 2) {
956 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
957 bn_scatter5(tmp.d, top, powerbuf, i);
959 for (i = 3; i < 8; i += 2) {
961 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
962 bn_scatter5(tmp.d, top, powerbuf, i);
963 for (j = 2 * i; j < 32; j *= 2) {
964 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
965 bn_scatter5(tmp.d, top, powerbuf, j);
968 for (; i < 16; i += 2) {
969 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
970 bn_scatter5(tmp.d, top, powerbuf, i);
971 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
972 bn_scatter5(tmp.d, top, powerbuf, 2 * i);
974 for (; i < 32; i += 2) {
975 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
976 bn_scatter5(tmp.d, top, powerbuf, i);
980 * The exponent may not have a whole number of fixed-size windows.
981 * To simplify the main loop, the initial window has between 1 and
982 * full-window-size bits such that what remains is always a whole
985 window0 = (bits - 1) % 5 + 1;
986 wmask = (1 << window0) - 1;
988 wvalue = bn_get_bits(p, bits) & wmask;
989 bn_gather5(tmp.d, top, powerbuf, wvalue);
992 * Scan the exponent one window at a time starting from the most
997 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
998 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
999 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1000 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1001 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
1002 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
1003 bn_get_bits5(p->d, bits -= 5));
1007 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top,
1008 bn_get_bits5(p->d, bits -= 5));
1012 ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np, n0, top);
1014 bn_correct_top(&tmp);
1016 if (!BN_copy(rr, &tmp))
1018 goto err; /* non-zero ret means it's not error */
1023 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window))
1025 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window))
1029 * If the window size is greater than 1, then calculate
1030 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1031 * powers could instead be computed as (a^(i/2))^2 to use the slight
1032 * performance advantage of sqr over mul).
1035 if (!bn_mul_mont_fixed_top(&tmp, &am, &am, mont, ctx))
1037 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2,
1040 for (i = 3; i < numPowers; i++) {
1041 /* Calculate a^i = a^(i-1) * a */
1042 if (!bn_mul_mont_fixed_top(&tmp, &am, &tmp, mont, ctx))
1044 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i,
1051 * The exponent may not have a whole number of fixed-size windows.
1052 * To simplify the main loop, the initial window has between 1 and
1053 * full-window-size bits such that what remains is always a whole
1056 window0 = (bits - 1) % window + 1;
1057 wmask = (1 << window0) - 1;
1059 wvalue = bn_get_bits(p, bits) & wmask;
1060 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue,
1064 wmask = (1 << window) - 1;
1066 * Scan the exponent one window at a time starting from the most
1071 /* Square the result window-size times */
1072 for (i = 0; i < window; i++)
1073 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &tmp, mont, ctx))
1077 * Get a window's worth of bits from the exponent
1078 * This avoids calling BN_is_bit_set for each bit, which
1079 * is not only slower but also makes each bit vulnerable to
1080 * EM (and likely other) side-channel attacks like One&Done
1081 * (for details see "One&Done: A Single-Decryption EM-Based
1082 * Attack on OpenSSL's Constant-Time Blinded RSA" by M. Alam,
1083 * H. Khan, M. Dey, N. Sinha, R. Callan, A. Zajic, and
1084 * M. Prvulovic, in USENIX Security'18)
1087 wvalue = bn_get_bits(p, bits) & wmask;
1089 * Fetch the appropriate pre-computed value from the pre-buf
1091 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
1095 /* Multiply the result into the intermediate result */
1096 if (!bn_mul_mont_fixed_top(&tmp, &tmp, &am, mont, ctx))
1102 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
1103 * removes padding [if any] and makes return value suitable for public
1106 #if defined(SPARC_T4_MONT)
1107 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
1108 am.d[0] = 1; /* borrow am */
1109 for (i = 1; i < top; i++)
1111 if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
1115 if (!BN_from_montgomery(rr, &tmp, mont, ctx))
1119 if (in_mont == NULL)
1120 BN_MONT_CTX_free(mont);
1121 if (powerbuf != NULL) {
1122 OPENSSL_cleanse(powerbuf, powerbufLen);
1123 OPENSSL_free(powerbufFree);
1129 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1130 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1132 BN_MONT_CTX *mont = NULL;
1133 int b, bits, ret = 0;
1138 #define BN_MOD_MUL_WORD(r, w, m) \
1139 (BN_mul_word(r, (w)) && \
1140 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1141 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1143 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1144 * probably more overhead than always using BN_mod (which uses BN_copy if
1145 * a similar test returns true).
1148 * We can use BN_mod and do not need BN_nnmod because our accumulator is
1149 * never negative (the result of BN_mod does not depend on the sign of
1152 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1153 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1155 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1156 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1157 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1158 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1165 if (!BN_is_odd(m)) {
1166 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
1170 a %= m->d[0]; /* make sure that 'a' is reduced */
1172 bits = BN_num_bits(p);
1174 /* x**0 mod 1, or x**0 mod -1 is still zero. */
1175 if (BN_abs_is_word(m, 1)) {
1190 r = BN_CTX_get(ctx);
1191 t = BN_CTX_get(ctx);
1195 if (in_mont != NULL)
1198 if ((mont = BN_MONT_CTX_new()) == NULL)
1200 if (!BN_MONT_CTX_set(mont, m, ctx))
1204 r_is_one = 1; /* except for Montgomery factor */
1208 /* The result is accumulated in the product r*w. */
1209 w = a; /* bit 'bits-1' of 'p' is always set */
1210 for (b = bits - 2; b >= 0; b--) {
1211 /* First, square r*w. */
1213 if ((next_w / w) != w) { /* overflow */
1215 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1219 if (!BN_MOD_MUL_WORD(r, w, m))
1226 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
1230 /* Second, multiply r*w by 'a' if exponent bit is set. */
1231 if (BN_is_bit_set(p, b)) {
1233 if ((next_w / a) != w) { /* overflow */
1235 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1239 if (!BN_MOD_MUL_WORD(r, w, m))
1248 /* Finally, set r:=r*w. */
1251 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1255 if (!BN_MOD_MUL_WORD(r, w, m))
1260 if (r_is_one) { /* can happen only if a == 1 */
1264 if (!BN_from_montgomery(rr, r, mont, ctx))
1269 if (in_mont == NULL)
1270 BN_MONT_CTX_free(mont);
1276 /* The old fallback, simple version :-) */
1277 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1278 const BIGNUM *m, BN_CTX *ctx)
1280 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
1283 /* Table of variables obtained from 'ctx' */
1284 BIGNUM *val[TABLE_SIZE];
1286 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1287 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
1288 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1289 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1290 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1294 bits = BN_num_bits(p);
1296 /* x**0 mod 1, or x**0 mod -1 is still zero. */
1297 if (BN_abs_is_word(m, 1)) {
1307 d = BN_CTX_get(ctx);
1308 val[0] = BN_CTX_get(ctx);
1312 if (!BN_nnmod(val[0], a, m, ctx))
1314 if (BN_is_zero(val[0])) {
1320 window = BN_window_bits_for_exponent_size(bits);
1322 if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1324 j = 1 << (window - 1);
1325 for (i = 1; i < j; i++) {
1326 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
1327 !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
1332 start = 1; /* This is used to avoid multiplication etc
1333 * when there is only the value '1' in the
1335 wvalue = 0; /* The 'value' of the window */
1336 wstart = bits - 1; /* The top bit of the window */
1337 wend = 0; /* The bottom bit of the window */
1343 if (BN_is_bit_set(p, wstart) == 0) {
1345 if (!BN_mod_mul(r, r, r, m, ctx))
1353 * We now have wstart on a 'set' bit, we now need to work out how bit
1354 * a window to do. To do this we need to scan forward until the last
1355 * set bit before the end of the window
1360 for (i = 1; i < window; i++) {
1363 if (BN_is_bit_set(p, wstart - i)) {
1364 wvalue <<= (i - wend);
1370 /* wend is the size of the current window */
1372 /* add the 'bytes above' */
1374 for (i = 0; i < j; i++) {
1375 if (!BN_mod_mul(r, r, r, m, ctx))
1379 /* wvalue will be an odd number < 2^window */
1380 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1383 /* move the 'window' down further */