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