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
);
292 aa
= BN_CTX_get(ctx
);
293 val
[0] = BN_CTX_get(ctx
);
297 BN_RECP_CTX_init(&recp
);
299 /* ignore sign of 'm' */
303 if (BN_RECP_CTX_set(&recp
, aa
, ctx
) <= 0)
306 if (BN_RECP_CTX_set(&recp
, m
, ctx
) <= 0)
310 if (!BN_nnmod(val
[0], a
, m
, ctx
))
312 if (BN_is_zero(val
[0])) {
318 window
= BN_window_bits_for_exponent_size(bits
);
320 if (!BN_mod_mul_reciprocal(aa
, val
[0], val
[0], &recp
, ctx
))
322 j
= 1 << (window
- 1);
323 for (i
= 1; i
< j
; i
++) {
324 if (((val
[i
] = BN_CTX_get(ctx
)) == NULL
) ||
325 !BN_mod_mul_reciprocal(val
[i
], val
[i
- 1], aa
, &recp
, ctx
))
330 start
= 1; /* This is used to avoid multiplication etc
331 * when there is only the value '1' in the
333 wvalue
= 0; /* The 'value' of the window */
334 wstart
= bits
- 1; /* The top bit of the window */
335 wend
= 0; /* The bottom bit of the window */
341 if (BN_is_bit_set(p
, wstart
) == 0) {
343 if (!BN_mod_mul_reciprocal(r
, r
, r
, &recp
, ctx
))
351 * We now have wstart on a 'set' bit, we now need to work out how bit
352 * a window to do. To do this we need to scan forward until the last
353 * set bit before the end of the window
358 for (i
= 1; i
< window
; i
++) {
361 if (BN_is_bit_set(p
, wstart
- i
)) {
362 wvalue
<<= (i
- wend
);
368 /* wend is the size of the current window */
370 /* add the 'bytes above' */
372 for (i
= 0; i
< j
; i
++) {
373 if (!BN_mod_mul_reciprocal(r
, r
, r
, &recp
, ctx
))
377 /* wvalue will be an odd number < 2^window */
378 if (!BN_mod_mul_reciprocal(r
, r
, val
[wvalue
>> 1], &recp
, ctx
))
381 /* move the 'window' down further */
391 BN_RECP_CTX_free(&recp
);
396 int BN_mod_exp_mont(BIGNUM
*rr
, const BIGNUM
*a
, const BIGNUM
*p
,
397 const BIGNUM
*m
, BN_CTX
*ctx
, BN_MONT_CTX
*in_mont
)
399 int i
, j
, bits
, ret
= 0, wstart
, wend
, window
, wvalue
;
403 /* Table of variables obtained from 'ctx' */
404 BIGNUM
*val
[TABLE_SIZE
];
405 BN_MONT_CTX
*mont
= NULL
;
407 if (BN_get_flags(p
, BN_FLG_CONSTTIME
) != 0) {
408 return BN_mod_exp_mont_consttime(rr
, a
, p
, m
, ctx
, in_mont
);
416 BNerr(BN_F_BN_MOD_EXP_MONT
, BN_R_CALLED_WITH_EVEN_MODULUS
);
419 bits
= BN_num_bits(p
);
428 val
[0] = BN_CTX_get(ctx
);
429 if (!d
|| !r
|| !val
[0])
433 * If this is not done, things will break in the montgomery part
439 if ((mont
= BN_MONT_CTX_new()) == NULL
)
441 if (!BN_MONT_CTX_set(mont
, m
, ctx
))
445 if (a
->neg
|| BN_ucmp(a
, m
) >= 0) {
446 if (!BN_nnmod(val
[0], a
, m
, ctx
))
451 if (BN_is_zero(aa
)) {
456 if (!BN_to_montgomery(val
[0], aa
, mont
, ctx
))
459 window
= BN_window_bits_for_exponent_size(bits
);
461 if (!BN_mod_mul_montgomery(d
, val
[0], val
[0], mont
, ctx
))
463 j
= 1 << (window
- 1);
464 for (i
= 1; i
< j
; i
++) {
465 if (((val
[i
] = BN_CTX_get(ctx
)) == NULL
) ||
466 !BN_mod_mul_montgomery(val
[i
], val
[i
- 1], d
, mont
, ctx
))
471 start
= 1; /* This is used to avoid multiplication etc
472 * when there is only the value '1' in the
474 wvalue
= 0; /* The 'value' of the window */
475 wstart
= bits
- 1; /* The top bit of the window */
476 wend
= 0; /* The bottom bit of the window */
478 #if 1 /* by Shay Gueron's suggestion */
479 j
= m
->top
; /* borrow j */
480 if (m
->d
[j
- 1] & (((BN_ULONG
)1) << (BN_BITS2
- 1))) {
481 if (bn_wexpand(r
, j
) == NULL
)
483 /* 2^(top*BN_BITS2) - m */
484 r
->d
[0] = (0 - m
->d
[0]) & BN_MASK2
;
485 for (i
= 1; i
< j
; i
++)
486 r
->d
[i
] = (~m
->d
[i
]) & BN_MASK2
;
489 * Upper words will be zero if the corresponding words of 'm' were
490 * 0xfff[...], so decrement r->top accordingly.
495 if (!BN_to_montgomery(r
, BN_value_one(), mont
, ctx
))
498 if (BN_is_bit_set(p
, wstart
) == 0) {
500 if (!BN_mod_mul_montgomery(r
, r
, r
, mont
, ctx
))
509 * We now have wstart on a 'set' bit, we now need to work out how bit
510 * a window to do. To do this we need to scan forward until the last
511 * set bit before the end of the window
516 for (i
= 1; i
< window
; i
++) {
519 if (BN_is_bit_set(p
, wstart
- i
)) {
520 wvalue
<<= (i
- wend
);
526 /* wend is the size of the current window */
528 /* add the 'bytes above' */
530 for (i
= 0; i
< j
; i
++) {
531 if (!BN_mod_mul_montgomery(r
, r
, r
, mont
, ctx
))
535 /* wvalue will be an odd number < 2^window */
536 if (!BN_mod_mul_montgomery(r
, r
, val
[wvalue
>> 1], mont
, ctx
))
539 /* move the 'window' down further */
546 #if defined(SPARC_T4_MONT)
547 if (OPENSSL_sparcv9cap_P
[0] & (SPARCV9_VIS3
| SPARCV9_PREFER_FPU
)) {
548 j
= mont
->N
.top
; /* borrow j */
549 val
[0]->d
[0] = 1; /* borrow val[0] */
550 for (i
= 1; i
< j
; i
++)
553 if (!BN_mod_mul_montgomery(rr
, r
, val
[0], mont
, ctx
))
557 if (!BN_from_montgomery(rr
, r
, mont
, ctx
))
562 BN_MONT_CTX_free(mont
);
568 #if defined(SPARC_T4_MONT)
569 static BN_ULONG
bn_get_bits(const BIGNUM
*a
, int bitpos
)
574 wordpos
= bitpos
/ BN_BITS2
;
576 if (wordpos
>= 0 && wordpos
< a
->top
) {
577 ret
= a
->d
[wordpos
] & BN_MASK2
;
580 if (++wordpos
< a
->top
)
581 ret
|= a
->d
[wordpos
] << (BN_BITS2
- bitpos
);
585 return ret
& BN_MASK2
;
590 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
591 * layout so that accessing any of these table values shows the same access
592 * pattern as far as cache lines are concerned. The following functions are
593 * used to transfer a BIGNUM from/to that table.
596 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM
*b
, int top
,
597 unsigned char *buf
, int idx
,
603 top
= b
->top
; /* this works because 'buf' is explicitly
605 for (i
= 0, j
= idx
; i
< top
* sizeof b
->d
[0]; i
++, j
+= width
) {
606 buf
[j
] = ((unsigned char *)b
->d
)[i
];
612 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM
*b
, int top
,
613 unsigned char *buf
, int idx
,
618 if (bn_wexpand(b
, top
) == NULL
)
621 for (i
= 0, j
= idx
; i
< top
* sizeof b
->d
[0]; i
++, j
+= width
) {
622 ((unsigned char *)b
->d
)[i
] = buf
[j
];
631 * Given a pointer value, compute the next address that is a cache line
634 #define MOD_EXP_CTIME_ALIGN(x_) \
635 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
638 * This variant of BN_mod_exp_mont() uses fixed windows and the special
639 * precomputation memory layout to limit data-dependency to a minimum to
640 * protect secret exponents (cf. the hyper-threading timing attacks pointed
641 * out by Colin Percival,
642 * http://www.daemong-consideredperthreading-considered-harmful/)
644 int BN_mod_exp_mont_consttime(BIGNUM
*rr
, const BIGNUM
*a
, const BIGNUM
*p
,
645 const BIGNUM
*m
, BN_CTX
*ctx
,
646 BN_MONT_CTX
*in_mont
)
648 int i
, bits
, ret
= 0, window
, wvalue
;
650 BN_MONT_CTX
*mont
= NULL
;
653 unsigned char *powerbufFree
= NULL
;
655 unsigned char *powerbuf
= NULL
;
657 #if defined(SPARC_T4_MONT)
667 if (!(m
->d
[0] & 1)) {
668 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME
, BN_R_CALLED_WITH_EVEN_MODULUS
);
671 bits
= BN_num_bits(p
);
680 * Allocate a montgomery context if it was not supplied by the caller. If
681 * this is not done, things will break in the montgomery part.
686 if ((mont
= BN_MONT_CTX_new()) == NULL
)
688 if (!BN_MONT_CTX_set(mont
, m
, ctx
))
694 * If the size of the operands allow it, perform the optimized
695 * RSAZ exponentiation. For further information see
696 * crypto/bn/rsaz_exp.c and accompanying assembly modules.
698 if ((16 == a
->top
) && (16 == p
->top
) && (BN_num_bits(m
) == 1024)
699 && rsaz_avx2_eligible()) {
700 if (NULL
== bn_wexpand(rr
, 16))
702 RSAZ_1024_mod_exp_avx2(rr
->d
, a
->d
, p
->d
, m
->d
, mont
->RR
.d
,
709 } else if ((8 == a
->top
) && (8 == p
->top
) && (BN_num_bits(m
) == 512)) {
710 if (NULL
== bn_wexpand(rr
, 8))
712 RSAZ_512_mod_exp(rr
->d
, a
->d
, p
->d
, m
->d
, mont
->n0
[0], mont
->RR
.d
);
721 /* Get the window size to use with size of p. */
722 window
= BN_window_bits_for_ctime_exponent_size(bits
);
723 #if defined(SPARC_T4_MONT)
724 if (window
>= 5 && (top
& 15) == 0 && top
<= 64 &&
725 (OPENSSL_sparcv9cap_P
[1] & (CFR_MONTMUL
| CFR_MONTSQR
)) ==
726 (CFR_MONTMUL
| CFR_MONTSQR
) && (t4
= OPENSSL_sparcv9cap_P
[0]))
730 #if defined(OPENSSL_BN_ASM_MONT5)
732 window
= 5; /* ~5% improvement for RSA2048 sign, and even
735 powerbufLen
+= 2 * top
* sizeof(m
->d
[0]);
741 * Allocate a buffer large enough to hold all of the pre-computed powers
742 * of am, am itself and tmp.
744 numPowers
= 1 << window
;
745 powerbufLen
+= sizeof(m
->d
[0]) * (top
* numPowers
+
747 numPowers
? (2 * top
) : numPowers
));
749 if (powerbufLen
< 3072)
751 alloca(powerbufLen
+ MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH
);
755 OPENSSL_malloc(powerbufLen
+ MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH
))
759 powerbuf
= MOD_EXP_CTIME_ALIGN(powerbufFree
);
760 memset(powerbuf
, 0, powerbufLen
);
763 if (powerbufLen
< 3072)
767 /* lay down tmp and am right after powers table */
768 tmp
.d
= (BN_ULONG
*)(powerbuf
+ sizeof(m
->d
[0]) * top
* numPowers
);
770 tmp
.top
= am
.top
= 0;
771 tmp
.dmax
= am
.dmax
= top
;
772 tmp
.neg
= am
.neg
= 0;
773 tmp
.flags
= am
.flags
= BN_FLG_STATIC_DATA
;
775 /* prepare a^0 in Montgomery domain */
776 #if 1 /* by Shay Gueron's suggestion */
777 if (m
->d
[top
- 1] & (((BN_ULONG
)1) << (BN_BITS2
- 1))) {
778 /* 2^(top*BN_BITS2) - m */
779 tmp
.d
[0] = (0 - m
->d
[0]) & BN_MASK2
;
780 for (i
= 1; i
< top
; i
++)
781 tmp
.d
[i
] = (~m
->d
[i
]) & BN_MASK2
;
785 if (!BN_to_montgomery(&tmp
, BN_value_one(), mont
, ctx
))
788 /* prepare a^1 in Montgomery domain */
789 if (a
->neg
|| BN_ucmp(a
, m
) >= 0) {
790 if (!BN_mod(&am
, a
, m
, ctx
))
792 if (!BN_to_montgomery(&am
, &am
, mont
, ctx
))
794 } else if (!BN_to_montgomery(&am
, a
, mont
, ctx
))
797 #if defined(SPARC_T4_MONT)
799 typedef int (*bn_pwr5_mont_f
) (BN_ULONG
*tp
, const BN_ULONG
*np
,
800 const BN_ULONG
*n0
, const void *table
,
801 int power
, int bits
);
802 int bn_pwr5_mont_t4_8(BN_ULONG
*tp
, const BN_ULONG
*np
,
803 const BN_ULONG
*n0
, const void *table
,
804 int power
, int bits
);
805 int bn_pwr5_mont_t4_16(BN_ULONG
*tp
, const BN_ULONG
*np
,
806 const BN_ULONG
*n0
, const void *table
,
807 int power
, int bits
);
808 int bn_pwr5_mont_t4_24(BN_ULONG
*tp
, const BN_ULONG
*np
,
809 const BN_ULONG
*n0
, const void *table
,
810 int power
, int bits
);
811 int bn_pwr5_mont_t4_32(BN_ULONG
*tp
, const BN_ULONG
*np
,
812 const BN_ULONG
*n0
, const void *table
,
813 int power
, int bits
);
814 static const bn_pwr5_mont_f pwr5_funcs
[4] = {
815 bn_pwr5_mont_t4_8
, bn_pwr5_mont_t4_16
,
816 bn_pwr5_mont_t4_24
, bn_pwr5_mont_t4_32
818 bn_pwr5_mont_f pwr5_worker
= pwr5_funcs
[top
/ 16 - 1];
820 typedef int (*bn_mul_mont_f
) (BN_ULONG
*rp
, const BN_ULONG
*ap
,
821 const void *bp
, const BN_ULONG
*np
,
823 int bn_mul_mont_t4_8(BN_ULONG
*rp
, const BN_ULONG
*ap
, const void *bp
,
824 const BN_ULONG
*np
, const BN_ULONG
*n0
);
825 int bn_mul_mont_t4_16(BN_ULONG
*rp
, const BN_ULONG
*ap
,
826 const void *bp
, const BN_ULONG
*np
,
828 int bn_mul_mont_t4_24(BN_ULONG
*rp
, const BN_ULONG
*ap
,
829 const void *bp
, const BN_ULONG
*np
,
831 int bn_mul_mont_t4_32(BN_ULONG
*rp
, const BN_ULONG
*ap
,
832 const void *bp
, const BN_ULONG
*np
,
834 static const bn_mul_mont_f mul_funcs
[4] = {
835 bn_mul_mont_t4_8
, bn_mul_mont_t4_16
,
836 bn_mul_mont_t4_24
, bn_mul_mont_t4_32
838 bn_mul_mont_f mul_worker
= mul_funcs
[top
/ 16 - 1];
840 void bn_mul_mont_vis3(BN_ULONG
*rp
, const BN_ULONG
*ap
,
841 const void *bp
, const BN_ULONG
*np
,
842 const BN_ULONG
*n0
, int num
);
843 void bn_mul_mont_t4(BN_ULONG
*rp
, const BN_ULONG
*ap
,
844 const void *bp
, const BN_ULONG
*np
,
845 const BN_ULONG
*n0
, int num
);
846 void bn_mul_mont_gather5_t4(BN_ULONG
*rp
, const BN_ULONG
*ap
,
847 const void *table
, const BN_ULONG
*np
,
848 const BN_ULONG
*n0
, int num
, int power
);
849 void bn_flip_n_scatter5_t4(const BN_ULONG
*inp
, size_t num
,
850 void *table
, size_t power
);
851 void bn_gather5_t4(BN_ULONG
*out
, size_t num
,
852 void *table
, size_t power
);
853 void bn_flip_t4(BN_ULONG
*dst
, BN_ULONG
*src
, size_t num
);
855 BN_ULONG
*np
= mont
->N
.d
, *n0
= mont
->n0
;
856 int stride
= 5 * (6 - (top
/ 16 - 1)); /* multiple of 5, but less
860 * BN_to_montgomery can contaminate words above .top [in
861 * BN_DEBUG[_DEBUG] build]...
863 for (i
= am
.top
; i
< top
; i
++)
865 for (i
= tmp
.top
; i
< top
; i
++)
868 bn_flip_n_scatter5_t4(tmp
.d
, top
, powerbuf
, 0);
869 bn_flip_n_scatter5_t4(am
.d
, top
, powerbuf
, 1);
870 if (!(*mul_worker
) (tmp
.d
, am
.d
, am
.d
, np
, n0
) &&
871 !(*mul_worker
) (tmp
.d
, am
.d
, am
.d
, np
, n0
))
872 bn_mul_mont_vis3(tmp
.d
, am
.d
, am
.d
, np
, n0
, top
);
873 bn_flip_n_scatter5_t4(tmp
.d
, top
, powerbuf
, 2);
875 for (i
= 3; i
< 32; i
++) {
876 /* Calculate a^i = a^(i-1) * a */
877 if (!(*mul_worker
) (tmp
.d
, tmp
.d
, am
.d
, np
, n0
) &&
878 !(*mul_worker
) (tmp
.d
, tmp
.d
, am
.d
, np
, n0
))
879 bn_mul_mont_vis3(tmp
.d
, tmp
.d
, am
.d
, np
, n0
, top
);
880 bn_flip_n_scatter5_t4(tmp
.d
, top
, powerbuf
, i
);
883 /* switch to 64-bit domain */
884 np
= alloca(top
* sizeof(BN_ULONG
));
886 bn_flip_t4(np
, mont
->N
.d
, top
);
889 for (wvalue
= 0, i
= bits
% 5; i
>= 0; i
--, bits
--)
890 wvalue
= (wvalue
<< 1) + BN_is_bit_set(p
, bits
);
891 bn_gather5_t4(tmp
.d
, top
, powerbuf
, wvalue
);
894 * Scan the exponent one window at a time starting from the most
901 wvalue
= bn_get_bits(p
, bits
+ 1);
903 if ((*pwr5_worker
) (tmp
.d
, np
, n0
, powerbuf
, wvalue
, stride
))
905 /* retry once and fall back */
906 if ((*pwr5_worker
) (tmp
.d
, np
, n0
, powerbuf
, wvalue
, stride
))
910 wvalue
>>= stride
- 5;
912 bn_mul_mont_t4(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
913 bn_mul_mont_t4(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
914 bn_mul_mont_t4(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
915 bn_mul_mont_t4(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
916 bn_mul_mont_t4(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
917 bn_mul_mont_gather5_t4(tmp
.d
, tmp
.d
, powerbuf
, np
, n0
, top
,
921 bn_flip_t4(tmp
.d
, tmp
.d
, top
);
923 /* back to 32-bit domain */
925 bn_correct_top(&tmp
);
926 OPENSSL_cleanse(np
, top
* sizeof(BN_ULONG
));
929 #if defined(OPENSSL_BN_ASM_MONT5)
930 if (window
== 5 && top
> 1) {
932 * This optimization uses ideas from http://eprint.iacr.org/2011/239,
933 * specifically optimization of cache-timing attack countermeasures
934 * and pre-computation optimization.
938 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
939 * 512-bit RSA is hardly relevant, we omit it to spare size...
941 void bn_mul_mont_gather5(BN_ULONG
*rp
, const BN_ULONG
*ap
,
942 const void *table
, const BN_ULONG
*np
,
943 const BN_ULONG
*n0
, int num
, int power
);
944 void bn_scatter5(const BN_ULONG
*inp
, size_t num
,
945 void *table
, size_t power
);
946 void bn_gather5(BN_ULONG
*out
, size_t num
, void *table
, size_t power
);
947 void bn_power5(BN_ULONG
*rp
, const BN_ULONG
*ap
,
948 const void *table
, const BN_ULONG
*np
,
949 const BN_ULONG
*n0
, int num
, int power
);
950 int bn_get_bits5(const BN_ULONG
*ap
, int off
);
951 int bn_from_montgomery(BN_ULONG
*rp
, const BN_ULONG
*ap
,
952 const BN_ULONG
*not_used
, const BN_ULONG
*np
,
953 const BN_ULONG
*n0
, int num
);
955 BN_ULONG
*np
= mont
->N
.d
, *n0
= mont
->n0
, *np2
;
958 * BN_to_montgomery can contaminate words above .top [in
959 * BN_DEBUG[_DEBUG] build]...
961 for (i
= am
.top
; i
< top
; i
++)
963 for (i
= tmp
.top
; i
< top
; i
++)
969 for (np2
= am
.d
+ top
, i
= 0; i
< top
; i
++)
972 bn_scatter5(tmp
.d
, top
, powerbuf
, 0);
973 bn_scatter5(am
.d
, am
.top
, powerbuf
, 1);
974 bn_mul_mont(tmp
.d
, am
.d
, am
.d
, np
, n0
, top
);
975 bn_scatter5(tmp
.d
, top
, powerbuf
, 2);
978 for (i
= 3; i
< 32; i
++) {
979 /* Calculate a^i = a^(i-1) * a */
980 bn_mul_mont_gather5(tmp
.d
, am
.d
, powerbuf
, np2
, n0
, top
, i
- 1);
981 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
984 /* same as above, but uses squaring for 1/2 of operations */
985 for (i
= 4; i
< 32; i
*= 2) {
986 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
987 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
989 for (i
= 3; i
< 8; i
+= 2) {
991 bn_mul_mont_gather5(tmp
.d
, am
.d
, powerbuf
, np2
, n0
, top
, i
- 1);
992 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
993 for (j
= 2 * i
; j
< 32; j
*= 2) {
994 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
995 bn_scatter5(tmp
.d
, top
, powerbuf
, j
);
998 for (; i
< 16; i
+= 2) {
999 bn_mul_mont_gather5(tmp
.d
, am
.d
, powerbuf
, np2
, n0
, top
, i
- 1);
1000 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
1001 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
1002 bn_scatter5(tmp
.d
, top
, powerbuf
, 2 * i
);
1004 for (; i
< 32; i
+= 2) {
1005 bn_mul_mont_gather5(tmp
.d
, am
.d
, powerbuf
, np2
, n0
, top
, i
- 1);
1006 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
1010 for (wvalue
= 0, i
= bits
% 5; i
>= 0; i
--, bits
--)
1011 wvalue
= (wvalue
<< 1) + BN_is_bit_set(p
, bits
);
1012 bn_gather5(tmp
.d
, top
, powerbuf
, wvalue
);
1015 * Scan the exponent one window at a time starting from the most
1020 for (wvalue
= 0, i
= 0; i
< 5; i
++, bits
--)
1021 wvalue
= (wvalue
<< 1) + BN_is_bit_set(p
, bits
);
1023 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
1024 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
1025 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
1026 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
1027 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
1028 bn_mul_mont_gather5(tmp
.d
, tmp
.d
, powerbuf
, np
, n0
, top
,
1032 wvalue
= bn_get_bits5(p
->d
, bits
- 4);
1034 bn_power5(tmp
.d
, tmp
.d
, powerbuf
, np2
, n0
, top
, wvalue
);
1038 ret
= bn_from_montgomery(tmp
.d
, tmp
.d
, NULL
, np2
, n0
, top
);
1040 bn_correct_top(&tmp
);
1042 if (!BN_copy(rr
, &tmp
))
1044 goto err
; /* non-zero ret means it's not error */
1049 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp
, top
, powerbuf
, 0, numPowers
))
1051 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am
, top
, powerbuf
, 1, numPowers
))
1055 * If the window size is greater than 1, then calculate
1056 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1057 * powers could instead be computed as (a^(i/2))^2 to use the slight
1058 * performance advantage of sqr over mul).
1061 if (!BN_mod_mul_montgomery(&tmp
, &am
, &am
, mont
, ctx
))
1063 if (!MOD_EXP_CTIME_COPY_TO_PREBUF
1064 (&tmp
, top
, powerbuf
, 2, numPowers
))
1066 for (i
= 3; i
< numPowers
; i
++) {
1067 /* Calculate a^i = a^(i-1) * a */
1068 if (!BN_mod_mul_montgomery(&tmp
, &am
, &tmp
, mont
, ctx
))
1070 if (!MOD_EXP_CTIME_COPY_TO_PREBUF
1071 (&tmp
, top
, powerbuf
, i
, numPowers
))
1077 for (wvalue
= 0, i
= bits
% window
; i
>= 0; i
--, bits
--)
1078 wvalue
= (wvalue
<< 1) + BN_is_bit_set(p
, bits
);
1079 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF
1080 (&tmp
, top
, powerbuf
, wvalue
, numPowers
))
1084 * Scan the exponent one window at a time starting from the most
1088 wvalue
= 0; /* The 'value' of the window */
1090 /* Scan the window, squaring the result as we go */
1091 for (i
= 0; i
< window
; i
++, bits
--) {
1092 if (!BN_mod_mul_montgomery(&tmp
, &tmp
, &tmp
, mont
, ctx
))
1094 wvalue
= (wvalue
<< 1) + BN_is_bit_set(p
, bits
);
1098 * Fetch the appropriate pre-computed value from the pre-buf
1100 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF
1101 (&am
, top
, powerbuf
, wvalue
, numPowers
))
1104 /* Multiply the result into the intermediate result */
1105 if (!BN_mod_mul_montgomery(&tmp
, &tmp
, &am
, mont
, ctx
))
1110 /* Convert the final result from montgomery to standard format */
1111 #if defined(SPARC_T4_MONT)
1112 if (OPENSSL_sparcv9cap_P
[0] & (SPARCV9_VIS3
| SPARCV9_PREFER_FPU
)) {
1113 am
.d
[0] = 1; /* borrow am */
1114 for (i
= 1; i
< top
; i
++)
1116 if (!BN_mod_mul_montgomery(rr
, &tmp
, &am
, mont
, ctx
))
1120 if (!BN_from_montgomery(rr
, &tmp
, mont
, ctx
))
1124 if (in_mont
== NULL
)
1125 BN_MONT_CTX_free(mont
);
1126 if (powerbuf
!= NULL
) {
1127 OPENSSL_cleanse(powerbuf
, powerbufLen
);
1128 OPENSSL_free(powerbufFree
);
1134 int BN_mod_exp_mont_word(BIGNUM
*rr
, BN_ULONG a
, const BIGNUM
*p
,
1135 const BIGNUM
*m
, BN_CTX
*ctx
, BN_MONT_CTX
*in_mont
)
1137 BN_MONT_CTX
*mont
= NULL
;
1138 int b
, bits
, ret
= 0;
1143 #define BN_MOD_MUL_WORD(r, w, m) \
1144 (BN_mul_word(r, (w)) && \
1145 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1146 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1148 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1149 * probably more overhead than always using BN_mod (which uses BN_copy if
1150 * a similar test returns true).
1153 * We can use BN_mod and do not need BN_nnmod because our accumulator is
1154 * never negative (the result of BN_mod does not depend on the sign of
1157 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1158 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1160 if (BN_get_flags(p
, BN_FLG_CONSTTIME
) != 0) {
1161 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1162 BNerr(BN_F_BN_MOD_EXP_MONT_WORD
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
1169 if (!BN_is_odd(m
)) {
1170 BNerr(BN_F_BN_MOD_EXP_MONT_WORD
, BN_R_CALLED_WITH_EVEN_MODULUS
);
1174 a
%= m
->d
[0]; /* make sure that 'a' is reduced */
1176 bits
= BN_num_bits(p
);
1178 /* x**0 mod 1 is still zero. */
1193 d
= BN_CTX_get(ctx
);
1194 r
= BN_CTX_get(ctx
);
1195 t
= BN_CTX_get(ctx
);
1196 if (d
== NULL
|| r
== NULL
|| t
== NULL
)
1199 if (in_mont
!= NULL
)
1202 if ((mont
= BN_MONT_CTX_new()) == NULL
)
1204 if (!BN_MONT_CTX_set(mont
, m
, ctx
))
1208 r_is_one
= 1; /* except for Montgomery factor */
1212 /* The result is accumulated in the product r*w. */
1213 w
= a
; /* bit 'bits-1' of 'p' is always set */
1214 for (b
= bits
- 2; b
>= 0; b
--) {
1215 /* First, square r*w. */
1217 if ((next_w
/ w
) != w
) { /* overflow */
1219 if (!BN_TO_MONTGOMERY_WORD(r
, w
, mont
))
1223 if (!BN_MOD_MUL_WORD(r
, w
, m
))
1230 if (!BN_mod_mul_montgomery(r
, r
, r
, mont
, ctx
))
1234 /* Second, multiply r*w by 'a' if exponent bit is set. */
1235 if (BN_is_bit_set(p
, b
)) {
1237 if ((next_w
/ a
) != w
) { /* overflow */
1239 if (!BN_TO_MONTGOMERY_WORD(r
, w
, mont
))
1243 if (!BN_MOD_MUL_WORD(r
, w
, m
))
1252 /* Finally, set r:=r*w. */
1255 if (!BN_TO_MONTGOMERY_WORD(r
, w
, mont
))
1259 if (!BN_MOD_MUL_WORD(r
, w
, m
))
1264 if (r_is_one
) { /* can happen only if a == 1 */
1268 if (!BN_from_montgomery(rr
, r
, mont
, ctx
))
1273 if (in_mont
== NULL
)
1274 BN_MONT_CTX_free(mont
);
1280 /* The old fallback, simple version :-) */
1281 int BN_mod_exp_simple(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
1282 const BIGNUM
*m
, BN_CTX
*ctx
)
1284 int i
, j
, bits
, ret
= 0, wstart
, wend
, window
, wvalue
;
1287 /* Table of variables obtained from 'ctx' */
1288 BIGNUM
*val
[TABLE_SIZE
];
1290 if (BN_get_flags(p
, BN_FLG_CONSTTIME
) != 0) {
1291 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1292 BNerr(BN_F_BN_MOD_EXP_SIMPLE
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
1296 bits
= BN_num_bits(p
);
1304 d
= BN_CTX_get(ctx
);
1305 val
[0] = BN_CTX_get(ctx
);
1309 if (!BN_nnmod(val
[0], a
, m
, ctx
))
1311 if (BN_is_zero(val
[0])) {
1317 window
= BN_window_bits_for_exponent_size(bits
);
1319 if (!BN_mod_mul(d
, val
[0], val
[0], m
, ctx
))
1321 j
= 1 << (window
- 1);
1322 for (i
= 1; i
< j
; i
++) {
1323 if (((val
[i
] = BN_CTX_get(ctx
)) == NULL
) ||
1324 !BN_mod_mul(val
[i
], val
[i
- 1], d
, m
, ctx
))
1329 start
= 1; /* This is used to avoid multiplication etc
1330 * when there is only the value '1' in the
1332 wvalue
= 0; /* The 'value' of the window */
1333 wstart
= bits
- 1; /* The top bit of the window */
1334 wend
= 0; /* The bottom bit of the window */
1340 if (BN_is_bit_set(p
, wstart
) == 0) {
1342 if (!BN_mod_mul(r
, r
, r
, m
, ctx
))
1350 * We now have wstart on a 'set' bit, we now need to work out how bit
1351 * a window to do. To do this we need to scan forward until the last
1352 * set bit before the end of the window
1357 for (i
= 1; i
< window
; i
++) {
1360 if (BN_is_bit_set(p
, wstart
- i
)) {
1361 wvalue
<<= (i
- wend
);
1367 /* wend is the size of the current window */
1369 /* add the 'bytes above' */
1371 for (i
= 0; i
< j
; i
++) {
1372 if (!BN_mod_mul(r
, r
, r
, m
, ctx
))
1376 /* wvalue will be an odd number < 2^window */
1377 if (!BN_mod_mul(r
, r
, val
[wvalue
>> 1], m
, ctx
))
1380 /* move the 'window' down further */