2 * Copyright 1995-2018 The OpenSSL Project Authors. All Rights Reserved.
4 * Licensed under the OpenSSL license (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_locl.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 is still zero. */
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 is still zero. */
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_is_zero(aa)) {
364 if (!BN_to_montgomery(val[0], aa, mont, ctx))
367 window = BN_window_bits_for_exponent_size(bits);
369 if (!BN_mod_mul_montgomery(d, val[0], val[0], mont, ctx))
371 j = 1 << (window - 1);
372 for (i = 1; i < j; i++) {
373 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
374 !BN_mod_mul_montgomery(val[i], val[i - 1], d, mont, ctx))
379 start = 1; /* This is used to avoid multiplication etc
380 * when there is only the value '1' in the
382 wvalue = 0; /* The 'value' of the window */
383 wstart = bits - 1; /* The top bit of the window */
384 wend = 0; /* The bottom bit of the window */
386 #if 1 /* by Shay Gueron's suggestion */
387 j = m->top; /* borrow j */
388 if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
389 if (bn_wexpand(r, j) == NULL)
391 /* 2^(top*BN_BITS2) - m */
392 r->d[0] = (0 - m->d[0]) & BN_MASK2;
393 for (i = 1; i < j; i++)
394 r->d[i] = (~m->d[i]) & BN_MASK2;
397 * Upper words will be zero if the corresponding words of 'm' were
398 * 0xfff[...], so decrement r->top accordingly.
403 if (!BN_to_montgomery(r, BN_value_one(), mont, ctx))
406 if (BN_is_bit_set(p, wstart) == 0) {
408 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
417 * We now have wstart on a 'set' bit, we now need to work out how bit
418 * a window to do. To do this we need to scan forward until the last
419 * set bit before the end of the window
424 for (i = 1; i < window; i++) {
427 if (BN_is_bit_set(p, wstart - i)) {
428 wvalue <<= (i - wend);
434 /* wend is the size of the current window */
436 /* add the 'bytes above' */
438 for (i = 0; i < j; i++) {
439 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
443 /* wvalue will be an odd number < 2^window */
444 if (!BN_mod_mul_montgomery(r, r, val[wvalue >> 1], mont, ctx))
447 /* move the 'window' down further */
454 #if defined(SPARC_T4_MONT)
455 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
456 j = mont->N.top; /* borrow j */
457 val[0]->d[0] = 1; /* borrow val[0] */
458 for (i = 1; i < j; i++)
461 if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
465 if (!BN_from_montgomery(rr, r, mont, ctx))
470 BN_MONT_CTX_free(mont);
476 #if defined(SPARC_T4_MONT)
477 static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
482 wordpos = bitpos / BN_BITS2;
484 if (wordpos >= 0 && wordpos < a->top) {
485 ret = a->d[wordpos] & BN_MASK2;
488 if (++wordpos < a->top)
489 ret |= a->d[wordpos] << (BN_BITS2 - bitpos);
493 return ret & BN_MASK2;
498 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
499 * layout so that accessing any of these table values shows the same access
500 * pattern as far as cache lines are concerned. The following functions are
501 * used to transfer a BIGNUM from/to that table.
504 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
505 unsigned char *buf, int idx,
509 int width = 1 << window;
510 BN_ULONG *table = (BN_ULONG *)buf;
513 top = b->top; /* this works because 'buf' is explicitly
515 for (i = 0, j = idx; i < top; i++, j += width) {
522 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
523 unsigned char *buf, int idx,
527 int width = 1 << window;
529 * We declare table 'volatile' in order to discourage compiler
530 * from reordering loads from the table. Concern is that if
531 * reordered in specific manner loads might give away the
532 * information we are trying to conceal. Some would argue that
533 * compiler can reorder them anyway, but it can as well be
534 * argued that doing so would be violation of standard...
536 volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
538 if (bn_wexpand(b, top) == NULL)
542 for (i = 0; i < top; i++, table += width) {
545 for (j = 0; j < width; j++) {
547 ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
553 int xstride = 1 << (window - 2);
554 BN_ULONG y0, y1, y2, y3;
556 i = idx >> (window - 2); /* equivalent of idx / xstride */
557 idx &= xstride - 1; /* equivalent of idx % xstride */
559 y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1);
560 y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1);
561 y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1);
562 y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1);
564 for (i = 0; i < top; i++, table += width) {
567 for (j = 0; j < xstride; j++) {
568 acc |= ( (table[j + 0 * xstride] & y0) |
569 (table[j + 1 * xstride] & y1) |
570 (table[j + 2 * xstride] & y2) |
571 (table[j + 3 * xstride] & y3) )
572 & ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
585 * Given a pointer value, compute the next address that is a cache line
588 #define MOD_EXP_CTIME_ALIGN(x_) \
589 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
592 * This variant of BN_mod_exp_mont() uses fixed windows and the special
593 * precomputation memory layout to limit data-dependency to a minimum to
594 * protect secret exponents (cf. the hyper-threading timing attacks pointed
595 * out by Colin Percival,
596 * http://www.daemonology.net/hyperthreading-considered-harmful/)
598 int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
599 const BIGNUM *m, BN_CTX *ctx,
600 BN_MONT_CTX *in_mont)
602 int i, bits, ret = 0, window, wvalue;
604 BN_MONT_CTX *mont = NULL;
607 unsigned char *powerbufFree = NULL;
609 unsigned char *powerbuf = NULL;
611 #if defined(SPARC_T4_MONT)
620 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
627 * Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak
628 * whether the top bits are zero.
630 bits = p->top * BN_BITS2;
632 /* x**0 mod 1 is still zero. */
645 * Allocate a montgomery context if it was not supplied by the caller. If
646 * this is not done, things will break in the montgomery part.
651 if ((mont = BN_MONT_CTX_new()) == NULL)
653 if (!BN_MONT_CTX_set(mont, m, ctx))
660 * If the size of the operands allow it, perform the optimized
661 * RSAZ exponentiation. For further information see
662 * crypto/bn/rsaz_exp.c and accompanying assembly modules.
664 if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
665 && rsaz_avx2_eligible()) {
666 if (NULL == bn_wexpand(rr, 16))
668 RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
675 } else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
676 if (NULL == bn_wexpand(rr, 8))
678 RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
688 /* Get the window size to use with size of p. */
689 window = BN_window_bits_for_ctime_exponent_size(bits);
690 #if defined(SPARC_T4_MONT)
691 if (window >= 5 && (top & 15) == 0 && top <= 64 &&
692 (OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) ==
693 (CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0]))
697 #if defined(OPENSSL_BN_ASM_MONT5)
699 window = 5; /* ~5% improvement for RSA2048 sign, and even
701 /* reserve space for mont->N.d[] copy */
702 powerbufLen += top * sizeof(mont->N.d[0]);
708 * Allocate a buffer large enough to hold all of the pre-computed powers
709 * of am, am itself and tmp.
711 numPowers = 1 << window;
712 powerbufLen += sizeof(m->d[0]) * (top * numPowers +
714 numPowers ? (2 * top) : numPowers));
716 if (powerbufLen < 3072)
718 alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
722 OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
726 powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
727 memset(powerbuf, 0, powerbufLen);
730 if (powerbufLen < 3072)
734 /* lay down tmp and am right after powers table */
735 tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
737 tmp.top = am.top = 0;
738 tmp.dmax = am.dmax = top;
739 tmp.neg = am.neg = 0;
740 tmp.flags = am.flags = BN_FLG_STATIC_DATA;
742 /* prepare a^0 in Montgomery domain */
743 #if 1 /* by Shay Gueron's suggestion */
744 if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
745 /* 2^(top*BN_BITS2) - m */
746 tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
747 for (i = 1; i < top; i++)
748 tmp.d[i] = (~m->d[i]) & BN_MASK2;
752 if (!BN_to_montgomery(&tmp, BN_value_one(), mont, ctx))
755 /* prepare a^1 in Montgomery domain */
756 if (a->neg || BN_ucmp(a, m) >= 0) {
757 if (!BN_nnmod(&am, a, m, ctx))
759 if (!BN_to_montgomery(&am, &am, mont, ctx))
761 } else if (!BN_to_montgomery(&am, a, mont, ctx))
764 #if defined(SPARC_T4_MONT)
766 typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np,
767 const BN_ULONG *n0, const void *table,
768 int power, int bits);
769 int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np,
770 const BN_ULONG *n0, const void *table,
771 int power, int bits);
772 int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np,
773 const BN_ULONG *n0, const void *table,
774 int power, int bits);
775 int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np,
776 const BN_ULONG *n0, const void *table,
777 int power, int bits);
778 int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np,
779 const BN_ULONG *n0, const void *table,
780 int power, int bits);
781 static const bn_pwr5_mont_f pwr5_funcs[4] = {
782 bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
783 bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
785 bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
787 typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap,
788 const void *bp, const BN_ULONG *np,
790 int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp,
791 const BN_ULONG *np, const BN_ULONG *n0);
792 int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap,
793 const void *bp, const BN_ULONG *np,
795 int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap,
796 const void *bp, const BN_ULONG *np,
798 int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap,
799 const void *bp, const BN_ULONG *np,
801 static const bn_mul_mont_f mul_funcs[4] = {
802 bn_mul_mont_t4_8, bn_mul_mont_t4_16,
803 bn_mul_mont_t4_24, bn_mul_mont_t4_32
805 bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
807 void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap,
808 const void *bp, const BN_ULONG *np,
809 const BN_ULONG *n0, int num);
810 void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap,
811 const void *bp, const BN_ULONG *np,
812 const BN_ULONG *n0, int num);
813 void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap,
814 const void *table, const BN_ULONG *np,
815 const BN_ULONG *n0, int num, int power);
816 void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
817 void *table, size_t power);
818 void bn_gather5_t4(BN_ULONG *out, size_t num,
819 void *table, size_t power);
820 void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num);
822 BN_ULONG *np = mont->N.d, *n0 = mont->n0;
823 int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
827 * BN_to_montgomery can contaminate words above .top [in
828 * BN_DEBUG[_DEBUG] build]...
830 for (i = am.top; i < top; i++)
832 for (i = tmp.top; i < top; i++)
835 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
836 bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
837 if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) &&
838 !(*mul_worker) (tmp.d, am.d, am.d, np, n0))
839 bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
840 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
842 for (i = 3; i < 32; i++) {
843 /* Calculate a^i = a^(i-1) * a */
844 if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) &&
845 !(*mul_worker) (tmp.d, tmp.d, am.d, np, n0))
846 bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
847 bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
850 /* switch to 64-bit domain */
851 np = alloca(top * sizeof(BN_ULONG));
853 bn_flip_t4(np, mont->N.d, top);
856 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
857 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
858 bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
861 * Scan the exponent one window at a time starting from the most
868 wvalue = bn_get_bits(p, bits + 1);
870 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
872 /* retry once and fall back */
873 if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
877 wvalue >>= stride - 5;
879 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
880 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
881 bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
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_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
888 bn_flip_t4(tmp.d, tmp.d, top);
890 /* back to 32-bit domain */
892 bn_correct_top(&tmp);
893 OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
896 #if defined(OPENSSL_BN_ASM_MONT5)
897 if (window == 5 && top > 1) {
899 * This optimization uses ideas from http://eprint.iacr.org/2011/239,
900 * specifically optimization of cache-timing attack countermeasures
901 * and pre-computation optimization.
905 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
906 * 512-bit RSA is hardly relevant, we omit it to spare size...
908 void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
909 const void *table, const BN_ULONG *np,
910 const BN_ULONG *n0, int num, int power);
911 void bn_scatter5(const BN_ULONG *inp, size_t num,
912 void *table, size_t power);
913 void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
914 void bn_power5(BN_ULONG *rp, const BN_ULONG *ap,
915 const void *table, const BN_ULONG *np,
916 const BN_ULONG *n0, int num, int power);
917 int bn_get_bits5(const BN_ULONG *ap, int off);
918 int bn_from_montgomery(BN_ULONG *rp, const BN_ULONG *ap,
919 const BN_ULONG *not_used, const BN_ULONG *np,
920 const BN_ULONG *n0, int num);
922 BN_ULONG *n0 = mont->n0, *np;
925 * BN_to_montgomery can contaminate words above .top [in
926 * BN_DEBUG[_DEBUG] build]...
928 for (i = am.top; i < top; i++)
930 for (i = tmp.top; i < top; i++)
934 * copy mont->N.d[] to improve cache locality
936 for (np = am.d + top, i = 0; i < top; i++)
937 np[i] = mont->N.d[i];
939 bn_scatter5(tmp.d, top, powerbuf, 0);
940 bn_scatter5(am.d, am.top, powerbuf, 1);
941 bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
942 bn_scatter5(tmp.d, top, powerbuf, 2);
945 for (i = 3; i < 32; i++) {
946 /* Calculate a^i = a^(i-1) * a */
947 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
948 bn_scatter5(tmp.d, top, powerbuf, i);
951 /* same as above, but uses squaring for 1/2 of operations */
952 for (i = 4; i < 32; i *= 2) {
953 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
954 bn_scatter5(tmp.d, top, powerbuf, i);
956 for (i = 3; i < 8; i += 2) {
958 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
959 bn_scatter5(tmp.d, top, powerbuf, i);
960 for (j = 2 * i; j < 32; j *= 2) {
961 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
962 bn_scatter5(tmp.d, top, powerbuf, j);
965 for (; i < 16; i += 2) {
966 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
967 bn_scatter5(tmp.d, top, powerbuf, i);
968 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
969 bn_scatter5(tmp.d, top, powerbuf, 2 * i);
971 for (; i < 32; i += 2) {
972 bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
973 bn_scatter5(tmp.d, top, powerbuf, i);
977 for (wvalue = 0, i = bits % 5; i >= 0; i--, bits--)
978 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
979 bn_gather5(tmp.d, top, powerbuf, wvalue);
982 * Scan the exponent one window at a time starting from the most
987 for (wvalue = 0, i = 0; i < 5; i++, bits--)
988 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
990 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
991 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
992 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
993 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
994 bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
995 bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
999 wvalue = bn_get_bits5(p->d, bits - 4);
1001 bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top, wvalue);
1005 ret = bn_from_montgomery(tmp.d, tmp.d, NULL, np, n0, top);
1007 bn_correct_top(&tmp);
1009 if (!BN_copy(rr, &tmp))
1011 goto err; /* non-zero ret means it's not error */
1016 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window))
1018 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window))
1022 * If the window size is greater than 1, then calculate
1023 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1024 * powers could instead be computed as (a^(i/2))^2 to use the slight
1025 * performance advantage of sqr over mul).
1028 if (!BN_mod_mul_montgomery(&tmp, &am, &am, mont, ctx))
1030 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2,
1033 for (i = 3; i < numPowers; i++) {
1034 /* Calculate a^i = a^(i-1) * a */
1035 if (!BN_mod_mul_montgomery(&tmp, &am, &tmp, mont, ctx))
1037 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i,
1044 for (wvalue = 0, i = bits % window; i >= 0; i--, bits--)
1045 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1046 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue,
1051 * Scan the exponent one window at a time starting from the most
1055 wvalue = 0; /* The 'value' of the window */
1057 /* Scan the window, squaring the result as we go */
1058 for (i = 0; i < window; i++, bits--) {
1059 if (!BN_mod_mul_montgomery(&tmp, &tmp, &tmp, mont, ctx))
1061 wvalue = (wvalue << 1) + BN_is_bit_set(p, bits);
1065 * Fetch the appropriate pre-computed value from the pre-buf
1067 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
1071 /* Multiply the result into the intermediate result */
1072 if (!BN_mod_mul_montgomery(&tmp, &tmp, &am, mont, ctx))
1077 /* Convert the final result from montgomery to standard format */
1078 #if defined(SPARC_T4_MONT)
1079 if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
1080 am.d[0] = 1; /* borrow am */
1081 for (i = 1; i < top; i++)
1083 if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
1087 if (!BN_from_montgomery(rr, &tmp, mont, ctx))
1091 if (in_mont == NULL)
1092 BN_MONT_CTX_free(mont);
1093 if (powerbuf != NULL) {
1094 OPENSSL_cleanse(powerbuf, powerbufLen);
1095 OPENSSL_free(powerbufFree);
1101 int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
1102 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
1104 BN_MONT_CTX *mont = NULL;
1105 int b, bits, ret = 0;
1110 #define BN_MOD_MUL_WORD(r, w, m) \
1111 (BN_mul_word(r, (w)) && \
1112 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1113 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1115 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1116 * probably more overhead than always using BN_mod (which uses BN_copy if
1117 * a similar test returns true).
1120 * We can use BN_mod and do not need BN_nnmod because our accumulator is
1121 * never negative (the result of BN_mod does not depend on the sign of
1124 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1125 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1127 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1128 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1129 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1130 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1137 if (!BN_is_odd(m)) {
1138 BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
1142 a %= m->d[0]; /* make sure that 'a' is reduced */
1144 bits = BN_num_bits(p);
1146 /* x**0 mod 1 is still zero. */
1162 r = BN_CTX_get(ctx);
1163 t = BN_CTX_get(ctx);
1167 if (in_mont != NULL)
1170 if ((mont = BN_MONT_CTX_new()) == NULL)
1172 if (!BN_MONT_CTX_set(mont, m, ctx))
1176 r_is_one = 1; /* except for Montgomery factor */
1180 /* The result is accumulated in the product r*w. */
1181 w = a; /* bit 'bits-1' of 'p' is always set */
1182 for (b = bits - 2; b >= 0; b--) {
1183 /* First, square r*w. */
1185 if ((next_w / w) != w) { /* overflow */
1187 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1191 if (!BN_MOD_MUL_WORD(r, w, m))
1198 if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
1202 /* Second, multiply r*w by 'a' if exponent bit is set. */
1203 if (BN_is_bit_set(p, b)) {
1205 if ((next_w / a) != w) { /* overflow */
1207 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1211 if (!BN_MOD_MUL_WORD(r, w, m))
1220 /* Finally, set r:=r*w. */
1223 if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
1227 if (!BN_MOD_MUL_WORD(r, w, m))
1232 if (r_is_one) { /* can happen only if a == 1 */
1236 if (!BN_from_montgomery(rr, r, mont, ctx))
1241 if (in_mont == NULL)
1242 BN_MONT_CTX_free(mont);
1248 /* The old fallback, simple version :-) */
1249 int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
1250 const BIGNUM *m, BN_CTX *ctx)
1252 int i, j, bits, ret = 0, wstart, wend, window, wvalue;
1255 /* Table of variables obtained from 'ctx' */
1256 BIGNUM *val[TABLE_SIZE];
1258 if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
1259 || BN_get_flags(a, BN_FLG_CONSTTIME) != 0
1260 || BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
1261 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1262 BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
1266 bits = BN_num_bits(p);
1268 /* x**0 mod 1 is still zero. */
1279 d = BN_CTX_get(ctx);
1280 val[0] = BN_CTX_get(ctx);
1284 if (!BN_nnmod(val[0], a, m, ctx))
1286 if (BN_is_zero(val[0])) {
1292 window = BN_window_bits_for_exponent_size(bits);
1294 if (!BN_mod_mul(d, val[0], val[0], m, ctx))
1296 j = 1 << (window - 1);
1297 for (i = 1; i < j; i++) {
1298 if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
1299 !BN_mod_mul(val[i], val[i - 1], d, m, ctx))
1304 start = 1; /* This is used to avoid multiplication etc
1305 * when there is only the value '1' in the
1307 wvalue = 0; /* The 'value' of the window */
1308 wstart = bits - 1; /* The top bit of the window */
1309 wend = 0; /* The bottom bit of the window */
1315 if (BN_is_bit_set(p, wstart) == 0) {
1317 if (!BN_mod_mul(r, r, r, m, ctx))
1325 * We now have wstart on a 'set' bit, we now need to work out how bit
1326 * a window to do. To do this we need to scan forward until the last
1327 * set bit before the end of the window
1332 for (i = 1; i < window; i++) {
1335 if (BN_is_bit_set(p, wstart - i)) {
1336 wvalue <<= (i - wend);
1342 /* wend is the size of the current window */
1344 /* add the 'bytes above' */
1346 for (i = 0; i < j; i++) {
1347 if (!BN_mod_mul(r, r, r, m, ctx))
1351 /* wvalue will be an odd number < 2^window */
1352 if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
1355 /* move the 'window' down further */