2 * Copyright 1995-2016 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_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
48 BNerr(BN_F_BN_EXP
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
53 if ((r
== a
) || (r
== p
))
58 if (rr
== NULL
|| v
== NULL
)
61 if (BN_copy(v
, a
) == NULL
)
63 bits
= BN_num_bits(p
);
66 if (BN_copy(rr
, a
) == NULL
)
73 for (i
= 1; i
< bits
; i
++) {
74 if (!BN_sqr(v
, v
, ctx
))
76 if (BN_is_bit_set(p
, i
)) {
77 if (!BN_mul(rr
, rr
, v
, ctx
))
90 int BN_mod_exp(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, const BIGNUM
*m
,
100 * For even modulus m = 2^k*m_odd, it might make sense to compute
101 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
102 * exponentiation for the odd part), using appropriate exponent
103 * reductions, and combine the results using the CRT.
105 * For now, we use Montgomery only if the modulus is odd; otherwise,
106 * exponentiation using the reciprocal-based quick remaindering
109 * (Timing obtained with expspeed.c [computations a^p mod m
110 * where a, p, m are of the same length: 256, 512, 1024, 2048,
111 * 4096, 8192 bits], compared to the running time of the
112 * standard algorithm:
114 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
115 * 55 .. 77 % [UltraSparc processor, but
116 * debug-solaris-sparcv8-gcc conf.]
118 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
119 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
121 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
122 * at 2048 and more bits, but at 512 and 1024 bits, it was
123 * slower even than the standard algorithm!
125 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
126 * should be obtained when the new Montgomery reduction code
127 * has been integrated into OpenSSL.)
131 #define MONT_EXP_WORD
136 * I have finally been able to take out this pre-condition of the top bit
137 * being set. It was caused by an error in BN_div with negatives. There
138 * was also another problem when for a^b%m a >= m. eay 07-May-97
140 /* if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */
143 # ifdef MONT_EXP_WORD
144 if (a
->top
== 1 && !a
->neg
145 && (BN_get_flags(p
, BN_FLG_CONSTTIME
) == 0)) {
146 BN_ULONG A
= a
->d
[0];
147 ret
= BN_mod_exp_mont_word(r
, A
, p
, m
, ctx
, NULL
);
150 ret
= BN_mod_exp_mont(r
, a
, p
, m
, ctx
, NULL
);
155 ret
= BN_mod_exp_recp(r
, a
, p
, m
, ctx
);
159 ret
= BN_mod_exp_simple(r
, a
, p
, m
, ctx
);
167 int BN_mod_exp_recp(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
168 const BIGNUM
*m
, BN_CTX
*ctx
)
170 int i
, j
, bits
, ret
= 0, wstart
, wend
, window
, wvalue
;
173 /* Table of variables obtained from 'ctx' */
174 BIGNUM
*val
[TABLE_SIZE
];
177 if (BN_get_flags(p
, BN_FLG_CONSTTIME
) != 0) {
178 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
179 BNerr(BN_F_BN_MOD_EXP_RECP
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
183 bits
= BN_num_bits(p
);
185 /* x**0 mod 1 is still zero. */
196 aa
= BN_CTX_get(ctx
);
197 val
[0] = BN_CTX_get(ctx
);
201 BN_RECP_CTX_init(&recp
);
203 /* ignore sign of 'm' */
207 if (BN_RECP_CTX_set(&recp
, aa
, ctx
) <= 0)
210 if (BN_RECP_CTX_set(&recp
, m
, ctx
) <= 0)
214 if (!BN_nnmod(val
[0], a
, m
, ctx
))
216 if (BN_is_zero(val
[0])) {
222 window
= BN_window_bits_for_exponent_size(bits
);
224 if (!BN_mod_mul_reciprocal(aa
, val
[0], val
[0], &recp
, ctx
))
226 j
= 1 << (window
- 1);
227 for (i
= 1; i
< j
; i
++) {
228 if (((val
[i
] = BN_CTX_get(ctx
)) == NULL
) ||
229 !BN_mod_mul_reciprocal(val
[i
], val
[i
- 1], aa
, &recp
, ctx
))
234 start
= 1; /* This is used to avoid multiplication etc
235 * when there is only the value '1' in the
237 wvalue
= 0; /* The 'value' of the window */
238 wstart
= bits
- 1; /* The top bit of the window */
239 wend
= 0; /* The bottom bit of the window */
245 if (BN_is_bit_set(p
, wstart
) == 0) {
247 if (!BN_mod_mul_reciprocal(r
, r
, r
, &recp
, ctx
))
255 * We now have wstart on a 'set' bit, we now need to work out how bit
256 * a window to do. To do this we need to scan forward until the last
257 * set bit before the end of the window
262 for (i
= 1; i
< window
; i
++) {
265 if (BN_is_bit_set(p
, wstart
- i
)) {
266 wvalue
<<= (i
- wend
);
272 /* wend is the size of the current window */
274 /* add the 'bytes above' */
276 for (i
= 0; i
< j
; i
++) {
277 if (!BN_mod_mul_reciprocal(r
, r
, r
, &recp
, ctx
))
281 /* wvalue will be an odd number < 2^window */
282 if (!BN_mod_mul_reciprocal(r
, r
, val
[wvalue
>> 1], &recp
, ctx
))
285 /* move the 'window' down further */
295 BN_RECP_CTX_free(&recp
);
300 int BN_mod_exp_mont(BIGNUM
*rr
, const BIGNUM
*a
, const BIGNUM
*p
,
301 const BIGNUM
*m
, BN_CTX
*ctx
, BN_MONT_CTX
*in_mont
)
303 int i
, j
, bits
, ret
= 0, wstart
, wend
, window
, wvalue
;
307 /* Table of variables obtained from 'ctx' */
308 BIGNUM
*val
[TABLE_SIZE
];
309 BN_MONT_CTX
*mont
= NULL
;
311 if (BN_get_flags(p
, BN_FLG_CONSTTIME
) != 0) {
312 return BN_mod_exp_mont_consttime(rr
, a
, p
, m
, ctx
, in_mont
);
320 BNerr(BN_F_BN_MOD_EXP_MONT
, BN_R_CALLED_WITH_EVEN_MODULUS
);
323 bits
= BN_num_bits(p
);
325 /* x**0 mod 1 is still zero. */
338 val
[0] = BN_CTX_get(ctx
);
339 if (!d
|| !r
|| !val
[0])
343 * If this is not done, things will break in the montgomery part
349 if ((mont
= BN_MONT_CTX_new()) == NULL
)
351 if (!BN_MONT_CTX_set(mont
, m
, ctx
))
355 if (a
->neg
|| BN_ucmp(a
, m
) >= 0) {
356 if (!BN_nnmod(val
[0], a
, m
, ctx
))
361 if (BN_is_zero(aa
)) {
366 if (!BN_to_montgomery(val
[0], aa
, mont
, ctx
))
369 window
= BN_window_bits_for_exponent_size(bits
);
371 if (!BN_mod_mul_montgomery(d
, val
[0], val
[0], mont
, ctx
))
373 j
= 1 << (window
- 1);
374 for (i
= 1; i
< j
; i
++) {
375 if (((val
[i
] = BN_CTX_get(ctx
)) == NULL
) ||
376 !BN_mod_mul_montgomery(val
[i
], val
[i
- 1], d
, mont
, ctx
))
381 start
= 1; /* This is used to avoid multiplication etc
382 * when there is only the value '1' in the
384 wvalue
= 0; /* The 'value' of the window */
385 wstart
= bits
- 1; /* The top bit of the window */
386 wend
= 0; /* The bottom bit of the window */
388 #if 1 /* by Shay Gueron's suggestion */
389 j
= m
->top
; /* borrow j */
390 if (m
->d
[j
- 1] & (((BN_ULONG
)1) << (BN_BITS2
- 1))) {
391 if (bn_wexpand(r
, j
) == NULL
)
393 /* 2^(top*BN_BITS2) - m */
394 r
->d
[0] = (0 - m
->d
[0]) & BN_MASK2
;
395 for (i
= 1; i
< j
; i
++)
396 r
->d
[i
] = (~m
->d
[i
]) & BN_MASK2
;
399 * Upper words will be zero if the corresponding words of 'm' were
400 * 0xfff[...], so decrement r->top accordingly.
405 if (!BN_to_montgomery(r
, BN_value_one(), mont
, ctx
))
408 if (BN_is_bit_set(p
, wstart
) == 0) {
410 if (!BN_mod_mul_montgomery(r
, r
, r
, mont
, ctx
))
419 * We now have wstart on a 'set' bit, we now need to work out how bit
420 * a window to do. To do this we need to scan forward until the last
421 * set bit before the end of the window
426 for (i
= 1; i
< window
; i
++) {
429 if (BN_is_bit_set(p
, wstart
- i
)) {
430 wvalue
<<= (i
- wend
);
436 /* wend is the size of the current window */
438 /* add the 'bytes above' */
440 for (i
= 0; i
< j
; i
++) {
441 if (!BN_mod_mul_montgomery(r
, r
, r
, mont
, ctx
))
445 /* wvalue will be an odd number < 2^window */
446 if (!BN_mod_mul_montgomery(r
, r
, val
[wvalue
>> 1], mont
, ctx
))
449 /* move the 'window' down further */
456 #if defined(SPARC_T4_MONT)
457 if (OPENSSL_sparcv9cap_P
[0] & (SPARCV9_VIS3
| SPARCV9_PREFER_FPU
)) {
458 j
= mont
->N
.top
; /* borrow j */
459 val
[0]->d
[0] = 1; /* borrow val[0] */
460 for (i
= 1; i
< j
; i
++)
463 if (!BN_mod_mul_montgomery(rr
, r
, val
[0], mont
, ctx
))
467 if (!BN_from_montgomery(rr
, r
, mont
, ctx
))
472 BN_MONT_CTX_free(mont
);
478 #if defined(SPARC_T4_MONT)
479 static BN_ULONG
bn_get_bits(const BIGNUM
*a
, int bitpos
)
484 wordpos
= bitpos
/ BN_BITS2
;
486 if (wordpos
>= 0 && wordpos
< a
->top
) {
487 ret
= a
->d
[wordpos
] & BN_MASK2
;
490 if (++wordpos
< a
->top
)
491 ret
|= a
->d
[wordpos
] << (BN_BITS2
- bitpos
);
495 return ret
& BN_MASK2
;
500 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
501 * layout so that accessing any of these table values shows the same access
502 * pattern as far as cache lines are concerned. The following functions are
503 * used to transfer a BIGNUM from/to that table.
506 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM
*b
, int top
,
507 unsigned char *buf
, int idx
,
511 int width
= 1 << window
;
512 BN_ULONG
*table
= (BN_ULONG
*)buf
;
515 top
= b
->top
; /* this works because 'buf' is explicitly
517 for (i
= 0, j
= idx
; i
< top
; i
++, j
+= width
) {
524 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM
*b
, int top
,
525 unsigned char *buf
, int idx
,
529 int width
= 1 << window
;
530 volatile BN_ULONG
*table
= (volatile BN_ULONG
*)buf
;
532 if (bn_wexpand(b
, top
) == NULL
)
536 for (i
= 0; i
< top
; i
++, table
+= width
) {
539 for (j
= 0; j
< width
; j
++) {
541 ((BN_ULONG
)0 - (constant_time_eq_int(j
,idx
)&1));
547 int xstride
= 1 << (window
- 2);
548 BN_ULONG y0
, y1
, y2
, y3
;
550 i
= idx
>> (window
- 2); /* equivalent of idx / xstride */
551 idx
&= xstride
- 1; /* equivalent of idx % xstride */
553 y0
= (BN_ULONG
)0 - (constant_time_eq_int(i
,0)&1);
554 y1
= (BN_ULONG
)0 - (constant_time_eq_int(i
,1)&1);
555 y2
= (BN_ULONG
)0 - (constant_time_eq_int(i
,2)&1);
556 y3
= (BN_ULONG
)0 - (constant_time_eq_int(i
,3)&1);
558 for (i
= 0; i
< top
; i
++, table
+= width
) {
561 for (j
= 0; j
< xstride
; j
++) {
562 acc
|= ( (table
[j
+ 0 * xstride
] & y0
) |
563 (table
[j
+ 1 * xstride
] & y1
) |
564 (table
[j
+ 2 * xstride
] & y2
) |
565 (table
[j
+ 3 * xstride
] & y3
) )
566 & ((BN_ULONG
)0 - (constant_time_eq_int(j
,idx
)&1));
579 * Given a pointer value, compute the next address that is a cache line
582 #define MOD_EXP_CTIME_ALIGN(x_) \
583 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
586 * This variant of BN_mod_exp_mont() uses fixed windows and the special
587 * precomputation memory layout to limit data-dependency to a minimum to
588 * protect secret exponents (cf. the hyper-threading timing attacks pointed
589 * out by Colin Percival,
590 * http://www.daemonology.net/hyperthreading-considered-harmful/)
592 int BN_mod_exp_mont_consttime(BIGNUM
*rr
, const BIGNUM
*a
, const BIGNUM
*p
,
593 const BIGNUM
*m
, BN_CTX
*ctx
,
594 BN_MONT_CTX
*in_mont
)
596 int i
, bits
, ret
= 0, window
, wvalue
;
598 BN_MONT_CTX
*mont
= NULL
;
601 unsigned char *powerbufFree
= NULL
;
603 unsigned char *powerbuf
= NULL
;
605 #if defined(SPARC_T4_MONT)
614 BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME
, BN_R_CALLED_WITH_EVEN_MODULUS
);
620 bits
= BN_num_bits(p
);
622 /* x**0 mod 1 is still zero. */
635 * Allocate a montgomery context if it was not supplied by the caller. If
636 * this is not done, things will break in the montgomery part.
641 if ((mont
= BN_MONT_CTX_new()) == NULL
)
643 if (!BN_MONT_CTX_set(mont
, m
, ctx
))
649 * If the size of the operands allow it, perform the optimized
650 * RSAZ exponentiation. For further information see
651 * crypto/bn/rsaz_exp.c and accompanying assembly modules.
653 if ((16 == a
->top
) && (16 == p
->top
) && (BN_num_bits(m
) == 1024)
654 && rsaz_avx2_eligible()) {
655 if (NULL
== bn_wexpand(rr
, 16))
657 RSAZ_1024_mod_exp_avx2(rr
->d
, a
->d
, p
->d
, m
->d
, mont
->RR
.d
,
664 } else if ((8 == a
->top
) && (8 == p
->top
) && (BN_num_bits(m
) == 512)) {
665 if (NULL
== bn_wexpand(rr
, 8))
667 RSAZ_512_mod_exp(rr
->d
, a
->d
, p
->d
, m
->d
, mont
->n0
[0], mont
->RR
.d
);
676 /* Get the window size to use with size of p. */
677 window
= BN_window_bits_for_ctime_exponent_size(bits
);
678 #if defined(SPARC_T4_MONT)
679 if (window
>= 5 && (top
& 15) == 0 && top
<= 64 &&
680 (OPENSSL_sparcv9cap_P
[1] & (CFR_MONTMUL
| CFR_MONTSQR
)) ==
681 (CFR_MONTMUL
| CFR_MONTSQR
) && (t4
= OPENSSL_sparcv9cap_P
[0]))
685 #if defined(OPENSSL_BN_ASM_MONT5)
687 window
= 5; /* ~5% improvement for RSA2048 sign, and even
689 /* reserve space for mont->N.d[] copy */
690 powerbufLen
+= top
* sizeof(mont
->N
.d
[0]);
696 * Allocate a buffer large enough to hold all of the pre-computed powers
697 * of am, am itself and tmp.
699 numPowers
= 1 << window
;
700 powerbufLen
+= sizeof(m
->d
[0]) * (top
* numPowers
+
702 numPowers
? (2 * top
) : numPowers
));
704 if (powerbufLen
< 3072)
706 alloca(powerbufLen
+ MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH
);
710 OPENSSL_malloc(powerbufLen
+ MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH
))
714 powerbuf
= MOD_EXP_CTIME_ALIGN(powerbufFree
);
715 memset(powerbuf
, 0, powerbufLen
);
718 if (powerbufLen
< 3072)
722 /* lay down tmp and am right after powers table */
723 tmp
.d
= (BN_ULONG
*)(powerbuf
+ sizeof(m
->d
[0]) * top
* numPowers
);
725 tmp
.top
= am
.top
= 0;
726 tmp
.dmax
= am
.dmax
= top
;
727 tmp
.neg
= am
.neg
= 0;
728 tmp
.flags
= am
.flags
= BN_FLG_STATIC_DATA
;
730 /* prepare a^0 in Montgomery domain */
731 #if 1 /* by Shay Gueron's suggestion */
732 if (m
->d
[top
- 1] & (((BN_ULONG
)1) << (BN_BITS2
- 1))) {
733 /* 2^(top*BN_BITS2) - m */
734 tmp
.d
[0] = (0 - m
->d
[0]) & BN_MASK2
;
735 for (i
= 1; i
< top
; i
++)
736 tmp
.d
[i
] = (~m
->d
[i
]) & BN_MASK2
;
740 if (!BN_to_montgomery(&tmp
, BN_value_one(), mont
, ctx
))
743 /* prepare a^1 in Montgomery domain */
744 if (a
->neg
|| BN_ucmp(a
, m
) >= 0) {
745 if (!BN_mod(&am
, a
, m
, ctx
))
747 if (!BN_to_montgomery(&am
, &am
, mont
, ctx
))
749 } else if (!BN_to_montgomery(&am
, a
, mont
, ctx
))
752 #if defined(SPARC_T4_MONT)
754 typedef int (*bn_pwr5_mont_f
) (BN_ULONG
*tp
, const BN_ULONG
*np
,
755 const BN_ULONG
*n0
, const void *table
,
756 int power
, int bits
);
757 int bn_pwr5_mont_t4_8(BN_ULONG
*tp
, const BN_ULONG
*np
,
758 const BN_ULONG
*n0
, const void *table
,
759 int power
, int bits
);
760 int bn_pwr5_mont_t4_16(BN_ULONG
*tp
, const BN_ULONG
*np
,
761 const BN_ULONG
*n0
, const void *table
,
762 int power
, int bits
);
763 int bn_pwr5_mont_t4_24(BN_ULONG
*tp
, const BN_ULONG
*np
,
764 const BN_ULONG
*n0
, const void *table
,
765 int power
, int bits
);
766 int bn_pwr5_mont_t4_32(BN_ULONG
*tp
, const BN_ULONG
*np
,
767 const BN_ULONG
*n0
, const void *table
,
768 int power
, int bits
);
769 static const bn_pwr5_mont_f pwr5_funcs
[4] = {
770 bn_pwr5_mont_t4_8
, bn_pwr5_mont_t4_16
,
771 bn_pwr5_mont_t4_24
, bn_pwr5_mont_t4_32
773 bn_pwr5_mont_f pwr5_worker
= pwr5_funcs
[top
/ 16 - 1];
775 typedef int (*bn_mul_mont_f
) (BN_ULONG
*rp
, const BN_ULONG
*ap
,
776 const void *bp
, const BN_ULONG
*np
,
778 int bn_mul_mont_t4_8(BN_ULONG
*rp
, const BN_ULONG
*ap
, const void *bp
,
779 const BN_ULONG
*np
, const BN_ULONG
*n0
);
780 int bn_mul_mont_t4_16(BN_ULONG
*rp
, const BN_ULONG
*ap
,
781 const void *bp
, const BN_ULONG
*np
,
783 int bn_mul_mont_t4_24(BN_ULONG
*rp
, const BN_ULONG
*ap
,
784 const void *bp
, const BN_ULONG
*np
,
786 int bn_mul_mont_t4_32(BN_ULONG
*rp
, const BN_ULONG
*ap
,
787 const void *bp
, const BN_ULONG
*np
,
789 static const bn_mul_mont_f mul_funcs
[4] = {
790 bn_mul_mont_t4_8
, bn_mul_mont_t4_16
,
791 bn_mul_mont_t4_24
, bn_mul_mont_t4_32
793 bn_mul_mont_f mul_worker
= mul_funcs
[top
/ 16 - 1];
795 void bn_mul_mont_vis3(BN_ULONG
*rp
, const BN_ULONG
*ap
,
796 const void *bp
, const BN_ULONG
*np
,
797 const BN_ULONG
*n0
, int num
);
798 void bn_mul_mont_t4(BN_ULONG
*rp
, const BN_ULONG
*ap
,
799 const void *bp
, const BN_ULONG
*np
,
800 const BN_ULONG
*n0
, int num
);
801 void bn_mul_mont_gather5_t4(BN_ULONG
*rp
, const BN_ULONG
*ap
,
802 const void *table
, const BN_ULONG
*np
,
803 const BN_ULONG
*n0
, int num
, int power
);
804 void bn_flip_n_scatter5_t4(const BN_ULONG
*inp
, size_t num
,
805 void *table
, size_t power
);
806 void bn_gather5_t4(BN_ULONG
*out
, size_t num
,
807 void *table
, size_t power
);
808 void bn_flip_t4(BN_ULONG
*dst
, BN_ULONG
*src
, size_t num
);
810 BN_ULONG
*np
= mont
->N
.d
, *n0
= mont
->n0
;
811 int stride
= 5 * (6 - (top
/ 16 - 1)); /* multiple of 5, but less
815 * BN_to_montgomery can contaminate words above .top [in
816 * BN_DEBUG[_DEBUG] build]...
818 for (i
= am
.top
; i
< top
; i
++)
820 for (i
= tmp
.top
; i
< top
; i
++)
823 bn_flip_n_scatter5_t4(tmp
.d
, top
, powerbuf
, 0);
824 bn_flip_n_scatter5_t4(am
.d
, top
, powerbuf
, 1);
825 if (!(*mul_worker
) (tmp
.d
, am
.d
, am
.d
, np
, n0
) &&
826 !(*mul_worker
) (tmp
.d
, am
.d
, am
.d
, np
, n0
))
827 bn_mul_mont_vis3(tmp
.d
, am
.d
, am
.d
, np
, n0
, top
);
828 bn_flip_n_scatter5_t4(tmp
.d
, top
, powerbuf
, 2);
830 for (i
= 3; i
< 32; i
++) {
831 /* Calculate a^i = a^(i-1) * a */
832 if (!(*mul_worker
) (tmp
.d
, tmp
.d
, am
.d
, np
, n0
) &&
833 !(*mul_worker
) (tmp
.d
, tmp
.d
, am
.d
, np
, n0
))
834 bn_mul_mont_vis3(tmp
.d
, tmp
.d
, am
.d
, np
, n0
, top
);
835 bn_flip_n_scatter5_t4(tmp
.d
, top
, powerbuf
, i
);
838 /* switch to 64-bit domain */
839 np
= alloca(top
* sizeof(BN_ULONG
));
841 bn_flip_t4(np
, mont
->N
.d
, top
);
844 for (wvalue
= 0, i
= bits
% 5; i
>= 0; i
--, bits
--)
845 wvalue
= (wvalue
<< 1) + BN_is_bit_set(p
, bits
);
846 bn_gather5_t4(tmp
.d
, top
, powerbuf
, wvalue
);
849 * Scan the exponent one window at a time starting from the most
856 wvalue
= bn_get_bits(p
, bits
+ 1);
858 if ((*pwr5_worker
) (tmp
.d
, np
, n0
, powerbuf
, wvalue
, stride
))
860 /* retry once and fall back */
861 if ((*pwr5_worker
) (tmp
.d
, np
, n0
, powerbuf
, wvalue
, stride
))
865 wvalue
>>= stride
- 5;
867 bn_mul_mont_t4(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
868 bn_mul_mont_t4(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
869 bn_mul_mont_t4(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
870 bn_mul_mont_t4(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
871 bn_mul_mont_t4(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
872 bn_mul_mont_gather5_t4(tmp
.d
, tmp
.d
, powerbuf
, np
, n0
, top
,
876 bn_flip_t4(tmp
.d
, tmp
.d
, top
);
878 /* back to 32-bit domain */
880 bn_correct_top(&tmp
);
881 OPENSSL_cleanse(np
, top
* sizeof(BN_ULONG
));
884 #if defined(OPENSSL_BN_ASM_MONT5)
885 if (window
== 5 && top
> 1) {
887 * This optimization uses ideas from http://eprint.iacr.org/2011/239,
888 * specifically optimization of cache-timing attack countermeasures
889 * and pre-computation optimization.
893 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
894 * 512-bit RSA is hardly relevant, we omit it to spare size...
896 void bn_mul_mont_gather5(BN_ULONG
*rp
, const BN_ULONG
*ap
,
897 const void *table
, const BN_ULONG
*np
,
898 const BN_ULONG
*n0
, int num
, int power
);
899 void bn_scatter5(const BN_ULONG
*inp
, size_t num
,
900 void *table
, size_t power
);
901 void bn_gather5(BN_ULONG
*out
, size_t num
, void *table
, size_t power
);
902 void bn_power5(BN_ULONG
*rp
, const BN_ULONG
*ap
,
903 const void *table
, const BN_ULONG
*np
,
904 const BN_ULONG
*n0
, int num
, int power
);
905 int bn_get_bits5(const BN_ULONG
*ap
, int off
);
906 int bn_from_montgomery(BN_ULONG
*rp
, const BN_ULONG
*ap
,
907 const BN_ULONG
*not_used
, const BN_ULONG
*np
,
908 const BN_ULONG
*n0
, int num
);
910 BN_ULONG
*n0
= mont
->n0
, *np
;
913 * BN_to_montgomery can contaminate words above .top [in
914 * BN_DEBUG[_DEBUG] build]...
916 for (i
= am
.top
; i
< top
; i
++)
918 for (i
= tmp
.top
; i
< top
; i
++)
922 * copy mont->N.d[] to improve cache locality
924 for (np
= am
.d
+ top
, i
= 0; i
< top
; i
++)
925 np
[i
] = mont
->N
.d
[i
];
927 bn_scatter5(tmp
.d
, top
, powerbuf
, 0);
928 bn_scatter5(am
.d
, am
.top
, powerbuf
, 1);
929 bn_mul_mont(tmp
.d
, am
.d
, am
.d
, np
, n0
, top
);
930 bn_scatter5(tmp
.d
, top
, powerbuf
, 2);
933 for (i
= 3; i
< 32; i
++) {
934 /* Calculate a^i = a^(i-1) * a */
935 bn_mul_mont_gather5(tmp
.d
, am
.d
, powerbuf
, np
, n0
, top
, i
- 1);
936 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
939 /* same as above, but uses squaring for 1/2 of operations */
940 for (i
= 4; i
< 32; i
*= 2) {
941 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
942 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
944 for (i
= 3; i
< 8; i
+= 2) {
946 bn_mul_mont_gather5(tmp
.d
, am
.d
, powerbuf
, np
, n0
, top
, i
- 1);
947 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
948 for (j
= 2 * i
; j
< 32; j
*= 2) {
949 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
950 bn_scatter5(tmp
.d
, top
, powerbuf
, j
);
953 for (; i
< 16; i
+= 2) {
954 bn_mul_mont_gather5(tmp
.d
, am
.d
, powerbuf
, np
, n0
, top
, i
- 1);
955 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
956 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
957 bn_scatter5(tmp
.d
, top
, powerbuf
, 2 * i
);
959 for (; i
< 32; i
+= 2) {
960 bn_mul_mont_gather5(tmp
.d
, am
.d
, powerbuf
, np
, n0
, top
, i
- 1);
961 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
965 for (wvalue
= 0, i
= bits
% 5; i
>= 0; i
--, bits
--)
966 wvalue
= (wvalue
<< 1) + BN_is_bit_set(p
, bits
);
967 bn_gather5(tmp
.d
, top
, powerbuf
, wvalue
);
970 * Scan the exponent one window at a time starting from the most
975 for (wvalue
= 0, i
= 0; i
< 5; i
++, bits
--)
976 wvalue
= (wvalue
<< 1) + BN_is_bit_set(p
, bits
);
978 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
979 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
980 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
981 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
982 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
983 bn_mul_mont_gather5(tmp
.d
, tmp
.d
, powerbuf
, np
, n0
, top
,
987 wvalue
= bn_get_bits5(p
->d
, bits
- 4);
989 bn_power5(tmp
.d
, tmp
.d
, powerbuf
, np
, n0
, top
, wvalue
);
993 ret
= bn_from_montgomery(tmp
.d
, tmp
.d
, NULL
, np
, n0
, top
);
995 bn_correct_top(&tmp
);
997 if (!BN_copy(rr
, &tmp
))
999 goto err
; /* non-zero ret means it's not error */
1004 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp
, top
, powerbuf
, 0, window
))
1006 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am
, top
, powerbuf
, 1, window
))
1010 * If the window size is greater than 1, then calculate
1011 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1012 * powers could instead be computed as (a^(i/2))^2 to use the slight
1013 * performance advantage of sqr over mul).
1016 if (!BN_mod_mul_montgomery(&tmp
, &am
, &am
, mont
, ctx
))
1018 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp
, top
, powerbuf
, 2,
1021 for (i
= 3; i
< numPowers
; i
++) {
1022 /* Calculate a^i = a^(i-1) * a */
1023 if (!BN_mod_mul_montgomery(&tmp
, &am
, &tmp
, mont
, ctx
))
1025 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp
, top
, powerbuf
, i
,
1032 for (wvalue
= 0, i
= bits
% window
; i
>= 0; i
--, bits
--)
1033 wvalue
= (wvalue
<< 1) + BN_is_bit_set(p
, bits
);
1034 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp
, top
, powerbuf
, wvalue
,
1039 * Scan the exponent one window at a time starting from the most
1043 wvalue
= 0; /* The 'value' of the window */
1045 /* Scan the window, squaring the result as we go */
1046 for (i
= 0; i
< window
; i
++, bits
--) {
1047 if (!BN_mod_mul_montgomery(&tmp
, &tmp
, &tmp
, mont
, ctx
))
1049 wvalue
= (wvalue
<< 1) + BN_is_bit_set(p
, bits
);
1053 * Fetch the appropriate pre-computed value from the pre-buf
1055 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am
, top
, powerbuf
, wvalue
,
1059 /* Multiply the result into the intermediate result */
1060 if (!BN_mod_mul_montgomery(&tmp
, &tmp
, &am
, mont
, ctx
))
1065 /* Convert the final result from montgomery to standard format */
1066 #if defined(SPARC_T4_MONT)
1067 if (OPENSSL_sparcv9cap_P
[0] & (SPARCV9_VIS3
| SPARCV9_PREFER_FPU
)) {
1068 am
.d
[0] = 1; /* borrow am */
1069 for (i
= 1; i
< top
; i
++)
1071 if (!BN_mod_mul_montgomery(rr
, &tmp
, &am
, mont
, ctx
))
1075 if (!BN_from_montgomery(rr
, &tmp
, mont
, ctx
))
1079 if (in_mont
== NULL
)
1080 BN_MONT_CTX_free(mont
);
1081 if (powerbuf
!= NULL
) {
1082 OPENSSL_cleanse(powerbuf
, powerbufLen
);
1083 OPENSSL_free(powerbufFree
);
1089 int BN_mod_exp_mont_word(BIGNUM
*rr
, BN_ULONG a
, const BIGNUM
*p
,
1090 const BIGNUM
*m
, BN_CTX
*ctx
, BN_MONT_CTX
*in_mont
)
1092 BN_MONT_CTX
*mont
= NULL
;
1093 int b
, bits
, ret
= 0;
1098 #define BN_MOD_MUL_WORD(r, w, m) \
1099 (BN_mul_word(r, (w)) && \
1100 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1101 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1103 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1104 * probably more overhead than always using BN_mod (which uses BN_copy if
1105 * a similar test returns true).
1108 * We can use BN_mod and do not need BN_nnmod because our accumulator is
1109 * never negative (the result of BN_mod does not depend on the sign of
1112 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1113 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1115 if (BN_get_flags(p
, BN_FLG_CONSTTIME
) != 0) {
1116 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1117 BNerr(BN_F_BN_MOD_EXP_MONT_WORD
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
1124 if (!BN_is_odd(m
)) {
1125 BNerr(BN_F_BN_MOD_EXP_MONT_WORD
, BN_R_CALLED_WITH_EVEN_MODULUS
);
1129 a
%= m
->d
[0]; /* make sure that 'a' is reduced */
1131 bits
= BN_num_bits(p
);
1133 /* x**0 mod 1 is still zero. */
1149 d
= BN_CTX_get(ctx
);
1150 r
= BN_CTX_get(ctx
);
1151 t
= BN_CTX_get(ctx
);
1152 if (d
== NULL
|| r
== NULL
|| t
== NULL
)
1155 if (in_mont
!= NULL
)
1158 if ((mont
= BN_MONT_CTX_new()) == NULL
)
1160 if (!BN_MONT_CTX_set(mont
, m
, ctx
))
1164 r_is_one
= 1; /* except for Montgomery factor */
1168 /* The result is accumulated in the product r*w. */
1169 w
= a
; /* bit 'bits-1' of 'p' is always set */
1170 for (b
= bits
- 2; b
>= 0; b
--) {
1171 /* First, square r*w. */
1173 if ((next_w
/ w
) != w
) { /* overflow */
1175 if (!BN_TO_MONTGOMERY_WORD(r
, w
, mont
))
1179 if (!BN_MOD_MUL_WORD(r
, w
, m
))
1186 if (!BN_mod_mul_montgomery(r
, r
, r
, mont
, ctx
))
1190 /* Second, multiply r*w by 'a' if exponent bit is set. */
1191 if (BN_is_bit_set(p
, b
)) {
1193 if ((next_w
/ a
) != w
) { /* overflow */
1195 if (!BN_TO_MONTGOMERY_WORD(r
, w
, mont
))
1199 if (!BN_MOD_MUL_WORD(r
, w
, m
))
1208 /* Finally, set r:=r*w. */
1211 if (!BN_TO_MONTGOMERY_WORD(r
, w
, mont
))
1215 if (!BN_MOD_MUL_WORD(r
, w
, m
))
1220 if (r_is_one
) { /* can happen only if a == 1 */
1224 if (!BN_from_montgomery(rr
, r
, mont
, ctx
))
1229 if (in_mont
== NULL
)
1230 BN_MONT_CTX_free(mont
);
1236 /* The old fallback, simple version :-) */
1237 int BN_mod_exp_simple(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
1238 const BIGNUM
*m
, BN_CTX
*ctx
)
1240 int i
, j
, bits
, ret
= 0, wstart
, wend
, window
, wvalue
;
1243 /* Table of variables obtained from 'ctx' */
1244 BIGNUM
*val
[TABLE_SIZE
];
1246 if (BN_get_flags(p
, BN_FLG_CONSTTIME
) != 0) {
1247 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1248 BNerr(BN_F_BN_MOD_EXP_SIMPLE
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
1252 bits
= BN_num_bits(p
);
1254 /* x**0 mod 1 is still zero. */
1265 d
= BN_CTX_get(ctx
);
1266 val
[0] = BN_CTX_get(ctx
);
1270 if (!BN_nnmod(val
[0], a
, m
, ctx
))
1272 if (BN_is_zero(val
[0])) {
1278 window
= BN_window_bits_for_exponent_size(bits
);
1280 if (!BN_mod_mul(d
, val
[0], val
[0], m
, ctx
))
1282 j
= 1 << (window
- 1);
1283 for (i
= 1; i
< j
; i
++) {
1284 if (((val
[i
] = BN_CTX_get(ctx
)) == NULL
) ||
1285 !BN_mod_mul(val
[i
], val
[i
- 1], d
, m
, ctx
))
1290 start
= 1; /* This is used to avoid multiplication etc
1291 * when there is only the value '1' in the
1293 wvalue
= 0; /* The 'value' of the window */
1294 wstart
= bits
- 1; /* The top bit of the window */
1295 wend
= 0; /* The bottom bit of the window */
1301 if (BN_is_bit_set(p
, wstart
) == 0) {
1303 if (!BN_mod_mul(r
, r
, r
, m
, ctx
))
1311 * We now have wstart on a 'set' bit, we now need to work out how bit
1312 * a window to do. To do this we need to scan forward until the last
1313 * set bit before the end of the window
1318 for (i
= 1; i
< window
; i
++) {
1321 if (BN_is_bit_set(p
, wstart
- i
)) {
1322 wvalue
<<= (i
- wend
);
1328 /* wend is the size of the current window */
1330 /* add the 'bytes above' */
1332 for (i
= 0; i
< j
; i
++) {
1333 if (!BN_mod_mul(r
, r
, r
, m
, ctx
))
1337 /* wvalue will be an odd number < 2^window */
1338 if (!BN_mod_mul(r
, r
, val
[wvalue
>> 1], m
, ctx
))
1341 /* move the 'window' down further */