1 /* crypto/bn/bn_exp.c */
2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
5 * This package is an SSL implementation written
6 * by Eric Young (eay@cryptsoft.com).
7 * The implementation was written so as to conform with Netscapes SSL.
9 * This library is free for commercial and non-commercial use as long as
10 * the following conditions are aheared to. The following conditions
11 * apply to all code found in this distribution, be it the RC4, RSA,
12 * lhash, DES, etc., code; not just the SSL code. The SSL documentation
13 * included with this distribution is covered by the same copyright terms
14 * except that the holder is Tim Hudson (tjh@cryptsoft.com).
16 * Copyright remains Eric Young's, and as such any Copyright notices in
17 * the code are not to be removed.
18 * If this package is used in a product, Eric Young should be given attribution
19 * as the author of the parts of the library used.
20 * This can be in the form of a textual message at program startup or
21 * in documentation (online or textual) provided with the package.
23 * Redistribution and use in source and binary forms, with or without
24 * modification, are permitted provided that the following conditions
26 * 1. Redistributions of source code must retain the copyright
27 * notice, this list of conditions and the following disclaimer.
28 * 2. Redistributions in binary form must reproduce the above copyright
29 * notice, this list of conditions and the following disclaimer in the
30 * documentation and/or other materials provided with the distribution.
31 * 3. All advertising materials mentioning features or use of this software
32 * must display the following acknowledgement:
33 * "This product includes cryptographic software written by
34 * Eric Young (eay@cryptsoft.com)"
35 * The word 'cryptographic' can be left out if the rouines from the library
36 * being used are not cryptographic related :-).
37 * 4. If you include any Windows specific code (or a derivative thereof) from
38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
41 * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
42 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
43 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
44 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
45 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
46 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
47 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
48 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
49 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
50 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
53 * The licence and distribution terms for any publically available version or
54 * derivative of this code cannot be changed. i.e. this code cannot simply be
55 * copied and put under another distribution licence
56 * [including the GNU Public Licence.]
58 /* ====================================================================
59 * Copyright (c) 1998-2005 The OpenSSL Project. All rights reserved.
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
65 * 1. Redistributions of source code must retain the above copyright
66 * notice, this list of conditions and the following disclaimer.
68 * 2. Redistributions in binary form must reproduce the above copyright
69 * notice, this list of conditions and the following disclaimer in
70 * the documentation and/or other materials provided with the
73 * 3. All advertising materials mentioning features or use of this
74 * software must display the following acknowledgment:
75 * "This product includes software developed by the OpenSSL Project
76 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
79 * endorse or promote products derived from this software without
80 * prior written permission. For written permission, please contact
81 * openssl-core@openssl.org.
83 * 5. Products derived from this software may not be called "OpenSSL"
84 * nor may "OpenSSL" appear in their names without prior written
85 * permission of the OpenSSL Project.
87 * 6. Redistributions of any form whatsoever must retain the following
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
95 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
103 * OF THE POSSIBILITY OF SUCH DAMAGE.
104 * ====================================================================
106 * This product includes cryptographic software written by Eric Young
107 * (eay@cryptsoft.com). This product includes software written by Tim
108 * Hudson (tjh@cryptsoft.com).
112 #include "cryptlib.h"
119 # define alloca _alloca
121 #elif defined(__GNUC__)
123 # define alloca(s) __builtin_alloca((s))
130 #if defined(OPENSSL_BN_ASM_MONT) && \
131 (defined(__x86_64) || defined(__x86_64__) || \
132 defined(_M_AMD64) || defined(_M_X64))
133 # include "rsaz_exp.h"
134 # define RSAZ_ENABLED
138 #if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
139 # include "sparc_arch.h"
140 extern unsigned int OPENSSL_sparcv9cap_P
[];
141 # define SPARC_T4_MONT
144 /* maximum precomputation table size for *variable* sliding windows */
145 #define TABLE_SIZE 32
147 /* this one works - simple but works */
148 int BN_exp(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
)
150 int i
, bits
, ret
= 0;
153 if (BN_get_flags(p
, BN_FLG_CONSTTIME
) != 0) {
154 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
155 BNerr(BN_F_BN_EXP
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
160 if ((r
== a
) || (r
== p
))
161 rr
= BN_CTX_get(ctx
);
165 if (rr
== NULL
|| v
== NULL
)
168 if (BN_copy(v
, a
) == NULL
)
170 bits
= BN_num_bits(p
);
173 if (BN_copy(rr
, a
) == NULL
)
180 for (i
= 1; i
< bits
; i
++) {
181 if (!BN_sqr(v
, v
, ctx
))
183 if (BN_is_bit_set(p
, i
)) {
184 if (!BN_mul(rr
, rr
, v
, ctx
))
197 int BN_mod_exp(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, const BIGNUM
*m
,
207 * For even modulus m = 2^k*m_odd, it might make sense to compute
208 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
209 * exponentiation for the odd part), using appropriate exponent
210 * reductions, and combine the results using the CRT.
212 * For now, we use Montgomery only if the modulus is odd; otherwise,
213 * exponentiation using the reciprocal-based quick remaindering
216 * (Timing obtained with expspeed.c [computations a^p mod m
217 * where a, p, m are of the same length: 256, 512, 1024, 2048,
218 * 4096, 8192 bits], compared to the running time of the
219 * standard algorithm:
221 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
222 * 55 .. 77 % [UltraSparc processor, but
223 * debug-solaris-sparcv8-gcc conf.]
225 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
226 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
228 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
229 * at 2048 and more bits, but at 512 and 1024 bits, it was
230 * slower even than the standard algorithm!
232 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
233 * should be obtained when the new Montgomery reduction code
234 * has been integrated into OpenSSL.)
238 #define MONT_EXP_WORD
243 * I have finally been able to take out this pre-condition of the top bit
244 * being set. It was caused by an error in BN_div with negatives. There
245 * was also another problem when for a^b%m a >= m. eay 07-May-97
247 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
250 # ifdef MONT_EXP_WORD
251 if (a
->top
== 1 && !a
->neg
252 && (BN_get_flags(p
, BN_FLG_CONSTTIME
) == 0)) {
253 BN_ULONG A
= a
->d
[0];
254 ret
= BN_mod_exp_mont_word(r
, A
, p
, m
, ctx
, NULL
);
257 ret
= BN_mod_exp_mont(r
, a
, p
, m
, ctx
, NULL
);
262 ret
= BN_mod_exp_recp(r
, a
, p
, m
, ctx
);
266 ret
= BN_mod_exp_simple(r
, a
, p
, m
, ctx
);
274 int BN_mod_exp_recp(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
275 const BIGNUM
*m
, BN_CTX
*ctx
)
277 int i
, j
, bits
, ret
= 0, wstart
, wend
, window
, wvalue
;
280 /* Table of variables obtained from 'ctx' */
281 BIGNUM
*val
[TABLE_SIZE
];
284 if (BN_get_flags(p
, BN_FLG_CONSTTIME
) != 0) {
285 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
286 BNerr(BN_F_BN_MOD_EXP_RECP
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
290 bits
= BN_num_bits(p
);
298 aa
= BN_CTX_get(ctx
);
299 val
[0] = BN_CTX_get(ctx
);
303 BN_RECP_CTX_init(&recp
);
305 /* ignore sign of 'm' */
309 if (BN_RECP_CTX_set(&recp
, aa
, ctx
) <= 0)
312 if (BN_RECP_CTX_set(&recp
, m
, ctx
) <= 0)
316 if (!BN_nnmod(val
[0], a
, m
, ctx
))
318 if (BN_is_zero(val
[0])) {
324 window
= BN_window_bits_for_exponent_size(bits
);
326 if (!BN_mod_mul_reciprocal(aa
, val
[0], val
[0], &recp
, ctx
))
328 j
= 1 << (window
- 1);
329 for (i
= 1; i
< j
; i
++) {
330 if (((val
[i
] = BN_CTX_get(ctx
)) == NULL
) ||
331 !BN_mod_mul_reciprocal(val
[i
], val
[i
- 1], aa
, &recp
, ctx
))
336 start
= 1; /* This is used to avoid multiplication etc
337 * when there is only the value '1' in the
339 wvalue
= 0; /* The 'value' of the window */
340 wstart
= bits
- 1; /* The top bit of the window */
341 wend
= 0; /* The bottom bit of the window */
347 if (BN_is_bit_set(p
, wstart
) == 0) {
349 if (!BN_mod_mul_reciprocal(r
, r
, r
, &recp
, ctx
))
357 * We now have wstart on a 'set' bit, we now need to work out how bit
358 * a window to do. To do this we need to scan forward until the last
359 * set bit before the end of the window
364 for (i
= 1; i
< window
; i
++) {
367 if (BN_is_bit_set(p
, wstart
- i
)) {
368 wvalue
<<= (i
- wend
);
374 /* wend is the size of the current window */
376 /* add the 'bytes above' */
378 for (i
= 0; i
< j
; i
++) {
379 if (!BN_mod_mul_reciprocal(r
, r
, r
, &recp
, ctx
))
383 /* wvalue will be an odd number < 2^window */
384 if (!BN_mod_mul_reciprocal(r
, r
, val
[wvalue
>> 1], &recp
, ctx
))
387 /* move the 'window' down further */
397 BN_RECP_CTX_free(&recp
);
402 int BN_mod_exp_mont(BIGNUM
*rr
, const BIGNUM
*a
, const BIGNUM
*p
,
403 const BIGNUM
*m
, BN_CTX
*ctx
, BN_MONT_CTX
*in_mont
)
405 int i
, j
, bits
, ret
= 0, wstart
, wend
, window
, wvalue
;
409 /* Table of variables obtained from 'ctx' */
410 BIGNUM
*val
[TABLE_SIZE
];
411 BN_MONT_CTX
*mont
= NULL
;
413 if (BN_get_flags(p
, BN_FLG_CONSTTIME
) != 0) {
414 return BN_mod_exp_mont_consttime(rr
, a
, p
, m
, ctx
, in_mont
);
422 BNerr(BN_F_BN_MOD_EXP_MONT
, BN_R_CALLED_WITH_EVEN_MODULUS
);
425 bits
= BN_num_bits(p
);
434 val
[0] = BN_CTX_get(ctx
);
435 if (!d
|| !r
|| !val
[0])
439 * If this is not done, things will break in the montgomery part
445 if ((mont
= BN_MONT_CTX_new()) == NULL
)
447 if (!BN_MONT_CTX_set(mont
, m
, ctx
))
451 if (a
->neg
|| BN_ucmp(a
, m
) >= 0) {
452 if (!BN_nnmod(val
[0], a
, m
, ctx
))
457 if (BN_is_zero(aa
)) {
462 if (!BN_to_montgomery(val
[0], aa
, mont
, ctx
))
465 window
= BN_window_bits_for_exponent_size(bits
);
467 if (!BN_mod_mul_montgomery(d
, val
[0], val
[0], mont
, ctx
))
469 j
= 1 << (window
- 1);
470 for (i
= 1; i
< j
; i
++) {
471 if (((val
[i
] = BN_CTX_get(ctx
)) == NULL
) ||
472 !BN_mod_mul_montgomery(val
[i
], val
[i
- 1], d
, mont
, ctx
))
477 start
= 1; /* This is used to avoid multiplication etc
478 * when there is only the value '1' in the
480 wvalue
= 0; /* The 'value' of the window */
481 wstart
= bits
- 1; /* The top bit of the window */
482 wend
= 0; /* The bottom bit of the window */
484 #if 1 /* by Shay Gueron's suggestion */
485 j
= m
->top
; /* borrow j */
486 if (m
->d
[j
- 1] & (((BN_ULONG
)1) << (BN_BITS2
- 1))) {
487 if (bn_wexpand(r
, j
) == NULL
)
489 /* 2^(top*BN_BITS2) - m */
490 r
->d
[0] = (0 - m
->d
[0]) & BN_MASK2
;
491 for (i
= 1; i
< j
; i
++)
492 r
->d
[i
] = (~m
->d
[i
]) & BN_MASK2
;
495 * Upper words will be zero if the corresponding words of 'm' were
496 * 0xfff[...], so decrement r->top accordingly.
501 if (!BN_to_montgomery(r
, BN_value_one(), mont
, ctx
))
504 if (BN_is_bit_set(p
, wstart
) == 0) {
506 if (!BN_mod_mul_montgomery(r
, r
, r
, mont
, ctx
))
515 * We now have wstart on a 'set' bit, we now need to work out how bit
516 * a window to do. To do this we need to scan forward until the last
517 * set bit before the end of the window
522 for (i
= 1; i
< window
; i
++) {
525 if (BN_is_bit_set(p
, wstart
- i
)) {
526 wvalue
<<= (i
- wend
);
532 /* wend is the size of the current window */
534 /* add the 'bytes above' */
536 for (i
= 0; i
< j
; i
++) {
537 if (!BN_mod_mul_montgomery(r
, r
, r
, mont
, ctx
))
541 /* wvalue will be an odd number < 2^window */
542 if (!BN_mod_mul_montgomery(r
, r
, val
[wvalue
>> 1], mont
, ctx
))
545 /* move the 'window' down further */
552 #if defined(SPARC_T4_MONT)
553 if (OPENSSL_sparcv9cap_P
[0] & (SPARCV9_VIS3
| SPARCV9_PREFER_FPU
)) {
554 j
= mont
->N
.top
; /* borrow j */
555 val
[0]->d
[0] = 1; /* borrow val[0] */
556 for (i
= 1; i
< j
; i
++)
559 if (!BN_mod_mul_montgomery(rr
, r
, val
[0], mont
, ctx
))
563 if (!BN_from_montgomery(rr
, r
, mont
, ctx
))
567 if ((in_mont
== NULL
) && (mont
!= NULL
))
568 BN_MONT_CTX_free(mont
);
574 #if defined(SPARC_T4_MONT)
575 static BN_ULONG
bn_get_bits(const BIGNUM
*a
, int bitpos
)
580 wordpos
= bitpos
/ BN_BITS2
;
582 if (wordpos
>= 0 && wordpos
< a
->top
) {
583 ret
= a
->d
[wordpos
] & BN_MASK2
;
586 if (++wordpos
< a
->top
)
587 ret
|= a
->d
[wordpos
] << (BN_BITS2
- bitpos
);
591 return ret
& BN_MASK2
;
596 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
597 * layout so that accessing any of these table values shows the same access
598 * pattern as far as cache lines are concerned. The following functions are
599 * used to transfer a BIGNUM from/to that table.
602 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM
*b
, int top
,
603 unsigned char *buf
, int idx
,
609 top
= b
->top
; /* this works because 'buf' is explicitly
611 for (i
= 0, j
= idx
; i
< top
* sizeof b
->d
[0]; i
++, j
+= width
) {
612 buf
[j
] = ((unsigned char *)b
->d
)[i
];
618 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM
*b
, int top
,
619 unsigned char *buf
, int idx
,
624 if (bn_wexpand(b
, top
) == NULL
)
627 for (i
= 0, j
= idx
; i
< top
* sizeof b
->d
[0]; i
++, j
+= width
) {
628 ((unsigned char *)b
->d
)[i
] = buf
[j
];
637 * Given a pointer value, compute the next address that is a cache line
640 #define MOD_EXP_CTIME_ALIGN(x_) \
641 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
644 * This variant of BN_mod_exp_mont() uses fixed windows and the special
645 * precomputation memory layout to limit data-dependency to a minimum to
646 * protect secret exponents (cf. the hyper-threading timing attacks pointed
647 * out by Colin Percival,
648 * http://www.daemong-consideredperthreading-considered-harmful/)
650 int BN_mod_exp_mont_consttime(BIGNUM
*rr
, const BIGNUM
*a
, const BIGNUM
*p
,
651 const BIGNUM
*m
, BN_CTX
*ctx
,
652 BN_MONT_CTX
*in_mont
)
654 int i
, bits
, ret
= 0, window
, wvalue
;
656 BN_MONT_CTX
*mont
= NULL
;
659 unsigned char *powerbufFree
= NULL
;
661 unsigned char *powerbuf
= NULL
;
663 #if defined(SPARC_T4_MONT)
673 if (!(m
->d
[0] & 1)) {
674 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME
, BN_R_CALLED_WITH_EVEN_MODULUS
);
677 bits
= BN_num_bits(p
);
686 * Allocate a montgomery context if it was not supplied by the caller. If
687 * this is not done, things will break in the montgomery part.
692 if ((mont
= BN_MONT_CTX_new()) == NULL
)
694 if (!BN_MONT_CTX_set(mont
, m
, ctx
))
700 * If the size of the operands allow it, perform the optimized
701 * RSAZ exponentiation. For further information see
702 * crypto/bn/rsaz_exp.c and accompanying assembly modules.
704 if ((16 == a
->top
) && (16 == p
->top
) && (BN_num_bits(m
) == 1024)
705 && rsaz_avx2_eligible()) {
706 if (NULL
== bn_wexpand(rr
, 16))
708 RSAZ_1024_mod_exp_avx2(rr
->d
, a
->d
, p
->d
, m
->d
, mont
->RR
.d
,
715 } else if ((8 == a
->top
) && (8 == p
->top
) && (BN_num_bits(m
) == 512)) {
716 if (NULL
== bn_wexpand(rr
, 8))
718 RSAZ_512_mod_exp(rr
->d
, a
->d
, p
->d
, m
->d
, mont
->n0
[0], mont
->RR
.d
);
727 /* Get the window size to use with size of p. */
728 window
= BN_window_bits_for_ctime_exponent_size(bits
);
729 #if defined(SPARC_T4_MONT)
730 if (window
>= 5 && (top
& 15) == 0 && top
<= 64 &&
731 (OPENSSL_sparcv9cap_P
[1] & (CFR_MONTMUL
| CFR_MONTSQR
)) ==
732 (CFR_MONTMUL
| CFR_MONTSQR
) && (t4
= OPENSSL_sparcv9cap_P
[0]))
736 #if defined(OPENSSL_BN_ASM_MONT5)
738 window
= 5; /* ~5% improvement for RSA2048 sign, and even
741 powerbufLen
+= 2 * top
* sizeof(m
->d
[0]);
747 * Allocate a buffer large enough to hold all of the pre-computed powers
748 * of am, am itself and tmp.
750 numPowers
= 1 << window
;
751 powerbufLen
+= sizeof(m
->d
[0]) * (top
* numPowers
+
753 numPowers
? (2 * top
) : numPowers
));
755 if (powerbufLen
< 3072)
757 alloca(powerbufLen
+ MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH
);
761 (unsigned char *)OPENSSL_malloc(powerbufLen
+
762 MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH
))
766 powerbuf
= MOD_EXP_CTIME_ALIGN(powerbufFree
);
767 memset(powerbuf
, 0, powerbufLen
);
770 if (powerbufLen
< 3072)
774 /* lay down tmp and am right after powers table */
775 tmp
.d
= (BN_ULONG
*)(powerbuf
+ sizeof(m
->d
[0]) * top
* numPowers
);
777 tmp
.top
= am
.top
= 0;
778 tmp
.dmax
= am
.dmax
= top
;
779 tmp
.neg
= am
.neg
= 0;
780 tmp
.flags
= am
.flags
= BN_FLG_STATIC_DATA
;
782 /* prepare a^0 in Montgomery domain */
783 #if 1 /* by Shay Gueron's suggestion */
784 if (m
->d
[top
- 1] & (((BN_ULONG
)1) << (BN_BITS2
- 1))) {
785 /* 2^(top*BN_BITS2) - m */
786 tmp
.d
[0] = (0 - m
->d
[0]) & BN_MASK2
;
787 for (i
= 1; i
< top
; i
++)
788 tmp
.d
[i
] = (~m
->d
[i
]) & BN_MASK2
;
792 if (!BN_to_montgomery(&tmp
, BN_value_one(), mont
, ctx
))
795 /* prepare a^1 in Montgomery domain */
796 if (a
->neg
|| BN_ucmp(a
, m
) >= 0) {
797 if (!BN_mod(&am
, a
, m
, ctx
))
799 if (!BN_to_montgomery(&am
, &am
, mont
, ctx
))
801 } else if (!BN_to_montgomery(&am
, a
, mont
, ctx
))
804 #if defined(SPARC_T4_MONT)
806 typedef int (*bn_pwr5_mont_f
) (BN_ULONG
*tp
, const BN_ULONG
*np
,
807 const BN_ULONG
*n0
, const void *table
,
808 int power
, int bits
);
809 int bn_pwr5_mont_t4_8(BN_ULONG
*tp
, const BN_ULONG
*np
,
810 const BN_ULONG
*n0
, const void *table
,
811 int power
, int bits
);
812 int bn_pwr5_mont_t4_16(BN_ULONG
*tp
, const BN_ULONG
*np
,
813 const BN_ULONG
*n0
, const void *table
,
814 int power
, int bits
);
815 int bn_pwr5_mont_t4_24(BN_ULONG
*tp
, const BN_ULONG
*np
,
816 const BN_ULONG
*n0
, const void *table
,
817 int power
, int bits
);
818 int bn_pwr5_mont_t4_32(BN_ULONG
*tp
, const BN_ULONG
*np
,
819 const BN_ULONG
*n0
, const void *table
,
820 int power
, int bits
);
821 static const bn_pwr5_mont_f pwr5_funcs
[4] = {
822 bn_pwr5_mont_t4_8
, bn_pwr5_mont_t4_16
,
823 bn_pwr5_mont_t4_24
, bn_pwr5_mont_t4_32
825 bn_pwr5_mont_f pwr5_worker
= pwr5_funcs
[top
/ 16 - 1];
827 typedef int (*bn_mul_mont_f
) (BN_ULONG
*rp
, const BN_ULONG
*ap
,
828 const void *bp
, const BN_ULONG
*np
,
830 int bn_mul_mont_t4_8(BN_ULONG
*rp
, const BN_ULONG
*ap
, const void *bp
,
831 const BN_ULONG
*np
, const BN_ULONG
*n0
);
832 int bn_mul_mont_t4_16(BN_ULONG
*rp
, const BN_ULONG
*ap
,
833 const void *bp
, const BN_ULONG
*np
,
835 int bn_mul_mont_t4_24(BN_ULONG
*rp
, const BN_ULONG
*ap
,
836 const void *bp
, const BN_ULONG
*np
,
838 int bn_mul_mont_t4_32(BN_ULONG
*rp
, const BN_ULONG
*ap
,
839 const void *bp
, const BN_ULONG
*np
,
841 static const bn_mul_mont_f mul_funcs
[4] = {
842 bn_mul_mont_t4_8
, bn_mul_mont_t4_16
,
843 bn_mul_mont_t4_24
, bn_mul_mont_t4_32
845 bn_mul_mont_f mul_worker
= mul_funcs
[top
/ 16 - 1];
847 void bn_mul_mont_vis3(BN_ULONG
*rp
, const BN_ULONG
*ap
,
848 const void *bp
, const BN_ULONG
*np
,
849 const BN_ULONG
*n0
, int num
);
850 void bn_mul_mont_t4(BN_ULONG
*rp
, const BN_ULONG
*ap
,
851 const void *bp
, const BN_ULONG
*np
,
852 const BN_ULONG
*n0
, int num
);
853 void bn_mul_mont_gather5_t4(BN_ULONG
*rp
, const BN_ULONG
*ap
,
854 const void *table
, const BN_ULONG
*np
,
855 const BN_ULONG
*n0
, int num
, int power
);
856 void bn_flip_n_scatter5_t4(const BN_ULONG
*inp
, size_t num
,
857 void *table
, size_t power
);
858 void bn_gather5_t4(BN_ULONG
*out
, size_t num
,
859 void *table
, size_t power
);
860 void bn_flip_t4(BN_ULONG
*dst
, BN_ULONG
*src
, size_t num
);
862 BN_ULONG
*np
= mont
->N
.d
, *n0
= mont
->n0
;
863 int stride
= 5 * (6 - (top
/ 16 - 1)); /* multiple of 5, but less
867 * BN_to_montgomery can contaminate words above .top [in
868 * BN_DEBUG[_DEBUG] build]...
870 for (i
= am
.top
; i
< top
; i
++)
872 for (i
= tmp
.top
; i
< top
; i
++)
875 bn_flip_n_scatter5_t4(tmp
.d
, top
, powerbuf
, 0);
876 bn_flip_n_scatter5_t4(am
.d
, top
, powerbuf
, 1);
877 if (!(*mul_worker
) (tmp
.d
, am
.d
, am
.d
, np
, n0
) &&
878 !(*mul_worker
) (tmp
.d
, am
.d
, am
.d
, np
, n0
))
879 bn_mul_mont_vis3(tmp
.d
, am
.d
, am
.d
, np
, n0
, top
);
880 bn_flip_n_scatter5_t4(tmp
.d
, top
, powerbuf
, 2);
882 for (i
= 3; i
< 32; i
++) {
883 /* Calculate a^i = a^(i-1) * a */
884 if (!(*mul_worker
) (tmp
.d
, tmp
.d
, am
.d
, np
, n0
) &&
885 !(*mul_worker
) (tmp
.d
, tmp
.d
, am
.d
, np
, n0
))
886 bn_mul_mont_vis3(tmp
.d
, tmp
.d
, am
.d
, np
, n0
, top
);
887 bn_flip_n_scatter5_t4(tmp
.d
, top
, powerbuf
, i
);
890 /* switch to 64-bit domain */
891 np
= alloca(top
* sizeof(BN_ULONG
));
893 bn_flip_t4(np
, mont
->N
.d
, top
);
896 for (wvalue
= 0, i
= bits
% 5; i
>= 0; i
--, bits
--)
897 wvalue
= (wvalue
<< 1) + BN_is_bit_set(p
, bits
);
898 bn_gather5_t4(tmp
.d
, top
, powerbuf
, wvalue
);
901 * Scan the exponent one window at a time starting from the most
908 wvalue
= bn_get_bits(p
, bits
+ 1);
910 if ((*pwr5_worker
) (tmp
.d
, np
, n0
, powerbuf
, wvalue
, stride
))
912 /* retry once and fall back */
913 if ((*pwr5_worker
) (tmp
.d
, np
, n0
, powerbuf
, wvalue
, stride
))
917 wvalue
>>= stride
- 5;
919 bn_mul_mont_t4(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
920 bn_mul_mont_t4(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
921 bn_mul_mont_t4(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
922 bn_mul_mont_t4(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
923 bn_mul_mont_t4(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
924 bn_mul_mont_gather5_t4(tmp
.d
, tmp
.d
, powerbuf
, np
, n0
, top
,
928 bn_flip_t4(tmp
.d
, tmp
.d
, top
);
930 /* back to 32-bit domain */
932 bn_correct_top(&tmp
);
933 OPENSSL_cleanse(np
, top
* sizeof(BN_ULONG
));
936 #if defined(OPENSSL_BN_ASM_MONT5)
937 if (window
== 5 && top
> 1) {
939 * This optimization uses ideas from http://eprint.iacr.org/2011/239,
940 * specifically optimization of cache-timing attack countermeasures
941 * and pre-computation optimization.
945 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
946 * 512-bit RSA is hardly relevant, we omit it to spare size...
948 void bn_mul_mont_gather5(BN_ULONG
*rp
, const BN_ULONG
*ap
,
949 const void *table
, const BN_ULONG
*np
,
950 const BN_ULONG
*n0
, int num
, int power
);
951 void bn_scatter5(const BN_ULONG
*inp
, size_t num
,
952 void *table
, size_t power
);
953 void bn_gather5(BN_ULONG
*out
, size_t num
, void *table
, size_t power
);
954 void bn_power5(BN_ULONG
*rp
, const BN_ULONG
*ap
,
955 const void *table
, const BN_ULONG
*np
,
956 const BN_ULONG
*n0
, int num
, int power
);
957 int bn_get_bits5(const BN_ULONG
*ap
, int off
);
958 int bn_from_montgomery(BN_ULONG
*rp
, const BN_ULONG
*ap
,
959 const BN_ULONG
*not_used
, const BN_ULONG
*np
,
960 const BN_ULONG
*n0
, int num
);
962 BN_ULONG
*np
= mont
->N
.d
, *n0
= mont
->n0
, *np2
;
965 * BN_to_montgomery can contaminate words above .top [in
966 * BN_DEBUG[_DEBUG] build]...
968 for (i
= am
.top
; i
< top
; i
++)
970 for (i
= tmp
.top
; i
< top
; i
++)
976 for (np2
= am
.d
+ top
, i
= 0; i
< top
; i
++)
979 bn_scatter5(tmp
.d
, top
, powerbuf
, 0);
980 bn_scatter5(am
.d
, am
.top
, powerbuf
, 1);
981 bn_mul_mont(tmp
.d
, am
.d
, am
.d
, np
, n0
, top
);
982 bn_scatter5(tmp
.d
, top
, powerbuf
, 2);
985 for (i
= 3; i
< 32; i
++) {
986 /* Calculate a^i = a^(i-1) * a */
987 bn_mul_mont_gather5(tmp
.d
, am
.d
, powerbuf
, np2
, n0
, top
, i
- 1);
988 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
991 /* same as above, but uses squaring for 1/2 of operations */
992 for (i
= 4; i
< 32; i
*= 2) {
993 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
994 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
996 for (i
= 3; i
< 8; i
+= 2) {
998 bn_mul_mont_gather5(tmp
.d
, am
.d
, powerbuf
, np2
, n0
, top
, i
- 1);
999 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
1000 for (j
= 2 * i
; j
< 32; j
*= 2) {
1001 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
1002 bn_scatter5(tmp
.d
, top
, powerbuf
, j
);
1005 for (; i
< 16; i
+= 2) {
1006 bn_mul_mont_gather5(tmp
.d
, am
.d
, powerbuf
, np2
, n0
, top
, i
- 1);
1007 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
1008 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
1009 bn_scatter5(tmp
.d
, top
, powerbuf
, 2 * i
);
1011 for (; i
< 32; i
+= 2) {
1012 bn_mul_mont_gather5(tmp
.d
, am
.d
, powerbuf
, np2
, n0
, top
, i
- 1);
1013 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
1017 for (wvalue
= 0, i
= bits
% 5; i
>= 0; i
--, bits
--)
1018 wvalue
= (wvalue
<< 1) + BN_is_bit_set(p
, bits
);
1019 bn_gather5(tmp
.d
, top
, powerbuf
, wvalue
);
1022 * Scan the exponent one window at a time starting from the most
1027 for (wvalue
= 0, i
= 0; i
< 5; i
++, bits
--)
1028 wvalue
= (wvalue
<< 1) + BN_is_bit_set(p
, bits
);
1030 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
1031 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
1032 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
1033 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
1034 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
1035 bn_mul_mont_gather5(tmp
.d
, tmp
.d
, powerbuf
, np
, n0
, top
,
1039 wvalue
= bn_get_bits5(p
->d
, bits
- 4);
1041 bn_power5(tmp
.d
, tmp
.d
, powerbuf
, np2
, n0
, top
, wvalue
);
1045 ret
= bn_from_montgomery(tmp
.d
, tmp
.d
, NULL
, np2
, n0
, top
);
1047 bn_correct_top(&tmp
);
1049 if (!BN_copy(rr
, &tmp
))
1051 goto err
; /* non-zero ret means it's not error */
1056 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp
, top
, powerbuf
, 0, numPowers
))
1058 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am
, top
, powerbuf
, 1, numPowers
))
1062 * If the window size is greater than 1, then calculate
1063 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1064 * powers could instead be computed as (a^(i/2))^2 to use the slight
1065 * performance advantage of sqr over mul).
1068 if (!BN_mod_mul_montgomery(&tmp
, &am
, &am
, mont
, ctx
))
1070 if (!MOD_EXP_CTIME_COPY_TO_PREBUF
1071 (&tmp
, top
, powerbuf
, 2, numPowers
))
1073 for (i
= 3; i
< numPowers
; i
++) {
1074 /* Calculate a^i = a^(i-1) * a */
1075 if (!BN_mod_mul_montgomery(&tmp
, &am
, &tmp
, mont
, ctx
))
1077 if (!MOD_EXP_CTIME_COPY_TO_PREBUF
1078 (&tmp
, top
, powerbuf
, i
, numPowers
))
1084 for (wvalue
= 0, i
= bits
% window
; i
>= 0; i
--, bits
--)
1085 wvalue
= (wvalue
<< 1) + BN_is_bit_set(p
, bits
);
1086 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF
1087 (&tmp
, top
, powerbuf
, wvalue
, numPowers
))
1091 * Scan the exponent one window at a time starting from the most
1095 wvalue
= 0; /* The 'value' of the window */
1097 /* Scan the window, squaring the result as we go */
1098 for (i
= 0; i
< window
; i
++, bits
--) {
1099 if (!BN_mod_mul_montgomery(&tmp
, &tmp
, &tmp
, mont
, ctx
))
1101 wvalue
= (wvalue
<< 1) + BN_is_bit_set(p
, bits
);
1105 * Fetch the appropriate pre-computed value from the pre-buf
1107 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF
1108 (&am
, top
, powerbuf
, wvalue
, numPowers
))
1111 /* Multiply the result into the intermediate result */
1112 if (!BN_mod_mul_montgomery(&tmp
, &tmp
, &am
, mont
, ctx
))
1117 /* Convert the final result from montgomery to standard format */
1118 #if defined(SPARC_T4_MONT)
1119 if (OPENSSL_sparcv9cap_P
[0] & (SPARCV9_VIS3
| SPARCV9_PREFER_FPU
)) {
1120 am
.d
[0] = 1; /* borrow am */
1121 for (i
= 1; i
< top
; i
++)
1123 if (!BN_mod_mul_montgomery(rr
, &tmp
, &am
, mont
, ctx
))
1127 if (!BN_from_montgomery(rr
, &tmp
, mont
, ctx
))
1131 if ((in_mont
== NULL
) && (mont
!= NULL
))
1132 BN_MONT_CTX_free(mont
);
1133 if (powerbuf
!= NULL
) {
1134 OPENSSL_cleanse(powerbuf
, powerbufLen
);
1136 OPENSSL_free(powerbufFree
);
1142 int BN_mod_exp_mont_word(BIGNUM
*rr
, BN_ULONG a
, const BIGNUM
*p
,
1143 const BIGNUM
*m
, BN_CTX
*ctx
, BN_MONT_CTX
*in_mont
)
1145 BN_MONT_CTX
*mont
= NULL
;
1146 int b
, bits
, ret
= 0;
1151 #define BN_MOD_MUL_WORD(r, w, m) \
1152 (BN_mul_word(r, (w)) && \
1153 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1154 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1156 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1157 * probably more overhead than always using BN_mod (which uses BN_copy if
1158 * a similar test returns true).
1161 * We can use BN_mod and do not need BN_nnmod because our accumulator is
1162 * never negative (the result of BN_mod does not depend on the sign of
1165 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1166 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1168 if (BN_get_flags(p
, BN_FLG_CONSTTIME
) != 0) {
1169 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1170 BNerr(BN_F_BN_MOD_EXP_MONT_WORD
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
1177 if (!BN_is_odd(m
)) {
1178 BNerr(BN_F_BN_MOD_EXP_MONT_WORD
, BN_R_CALLED_WITH_EVEN_MODULUS
);
1182 a
%= m
->d
[0]; /* make sure that 'a' is reduced */
1184 bits
= BN_num_bits(p
);
1186 /* x**0 mod 1 is still zero. */
1201 d
= BN_CTX_get(ctx
);
1202 r
= BN_CTX_get(ctx
);
1203 t
= BN_CTX_get(ctx
);
1204 if (d
== NULL
|| r
== NULL
|| t
== NULL
)
1207 if (in_mont
!= NULL
)
1210 if ((mont
= BN_MONT_CTX_new()) == NULL
)
1212 if (!BN_MONT_CTX_set(mont
, m
, ctx
))
1216 r_is_one
= 1; /* except for Montgomery factor */
1220 /* The result is accumulated in the product r*w. */
1221 w
= a
; /* bit 'bits-1' of 'p' is always set */
1222 for (b
= bits
- 2; b
>= 0; b
--) {
1223 /* First, square r*w. */
1225 if ((next_w
/ w
) != w
) { /* overflow */
1227 if (!BN_TO_MONTGOMERY_WORD(r
, w
, mont
))
1231 if (!BN_MOD_MUL_WORD(r
, w
, m
))
1238 if (!BN_mod_mul_montgomery(r
, r
, r
, mont
, ctx
))
1242 /* Second, multiply r*w by 'a' if exponent bit is set. */
1243 if (BN_is_bit_set(p
, b
)) {
1245 if ((next_w
/ a
) != w
) { /* overflow */
1247 if (!BN_TO_MONTGOMERY_WORD(r
, w
, mont
))
1251 if (!BN_MOD_MUL_WORD(r
, w
, m
))
1260 /* Finally, set r:=r*w. */
1263 if (!BN_TO_MONTGOMERY_WORD(r
, w
, mont
))
1267 if (!BN_MOD_MUL_WORD(r
, w
, m
))
1272 if (r_is_one
) { /* can happen only if a == 1 */
1276 if (!BN_from_montgomery(rr
, r
, mont
, ctx
))
1281 if ((in_mont
== NULL
) && (mont
!= NULL
))
1282 BN_MONT_CTX_free(mont
);
1288 /* The old fallback, simple version :-) */
1289 int BN_mod_exp_simple(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
1290 const BIGNUM
*m
, BN_CTX
*ctx
)
1292 int i
, j
, bits
, ret
= 0, wstart
, wend
, window
, wvalue
;
1295 /* Table of variables obtained from 'ctx' */
1296 BIGNUM
*val
[TABLE_SIZE
];
1298 if (BN_get_flags(p
, BN_FLG_CONSTTIME
) != 0) {
1299 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1300 BNerr(BN_F_BN_MOD_EXP_SIMPLE
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
1304 bits
= BN_num_bits(p
);
1312 d
= BN_CTX_get(ctx
);
1313 val
[0] = BN_CTX_get(ctx
);
1317 if (!BN_nnmod(val
[0], a
, m
, ctx
))
1319 if (BN_is_zero(val
[0])) {
1325 window
= BN_window_bits_for_exponent_size(bits
);
1327 if (!BN_mod_mul(d
, val
[0], val
[0], m
, ctx
))
1329 j
= 1 << (window
- 1);
1330 for (i
= 1; i
< j
; i
++) {
1331 if (((val
[i
] = BN_CTX_get(ctx
)) == NULL
) ||
1332 !BN_mod_mul(val
[i
], val
[i
- 1], d
, m
, ctx
))
1337 start
= 1; /* This is used to avoid multiplication etc
1338 * when there is only the value '1' in the
1340 wvalue
= 0; /* The 'value' of the window */
1341 wstart
= bits
- 1; /* The top bit of the window */
1342 wend
= 0; /* The bottom bit of the window */
1348 if (BN_is_bit_set(p
, wstart
) == 0) {
1350 if (!BN_mod_mul(r
, r
, r
, m
, ctx
))
1358 * We now have wstart on a 'set' bit, we now need to work out how bit
1359 * a window to do. To do this we need to scan forward until the last
1360 * set bit before the end of the window
1365 for (i
= 1; i
< window
; i
++) {
1368 if (BN_is_bit_set(p
, wstart
- i
)) {
1369 wvalue
<<= (i
- wend
);
1375 /* wend is the size of the current window */
1377 /* add the 'bytes above' */
1379 for (i
= 0; i
< j
; i
++) {
1380 if (!BN_mod_mul(r
, r
, r
, m
, ctx
))
1384 /* wvalue will be an odd number < 2^window */
1385 if (!BN_mod_mul(r
, r
, val
[wvalue
>> 1], m
, ctx
))
1388 /* move the 'window' down further */