2 * Copyright 1995-2021 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 "crypto/sparc_arch.h"
33 # define SPARC_T4_MONT
36 /* maximum precomputation table size for *variable* sliding windows */
39 /* this one works - simple but works */
40 int BN_exp(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, BN_CTX
*ctx
)
45 if (BN_get_flags(p
, BN_FLG_CONSTTIME
) != 0
46 || BN_get_flags(a
, BN_FLG_CONSTTIME
) != 0) {
47 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
48 ERR_raise(ERR_LIB_BN
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
53 rr
= ((r
== a
) || (r
== p
)) ? BN_CTX_get(ctx
) : r
;
55 if (rr
== NULL
|| v
== NULL
)
58 if (BN_copy(v
, a
) == NULL
)
60 bits
= BN_num_bits(p
);
63 if (BN_copy(rr
, a
) == NULL
)
70 for (i
= 1; i
< bits
; i
++) {
71 if (!BN_sqr(v
, v
, ctx
))
73 if (BN_is_bit_set(p
, i
)) {
74 if (!BN_mul(rr
, rr
, v
, ctx
))
78 if (r
!= rr
&& BN_copy(r
, rr
) == NULL
)
88 int BN_mod_exp(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
, const BIGNUM
*m
,
98 * For even modulus m = 2^k*m_odd, it might make sense to compute
99 * a^p mod m_odd and a^p mod 2^k separately (with Montgomery
100 * exponentiation for the odd part), using appropriate exponent
101 * reductions, and combine the results using the CRT.
103 * For now, we use Montgomery only if the modulus is odd; otherwise,
104 * exponentiation using the reciprocal-based quick remaindering
107 * (Timing obtained with expspeed.c [computations a^p mod m
108 * where a, p, m are of the same length: 256, 512, 1024, 2048,
109 * 4096, 8192 bits], compared to the running time of the
110 * standard algorithm:
112 * BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
113 * 55 .. 77 % [UltraSparc processor, but
114 * debug-solaris-sparcv8-gcc conf.]
116 * BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
117 * 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
119 * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
120 * at 2048 and more bits, but at 512 and 1024 bits, it was
121 * slower even than the standard algorithm!
123 * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
124 * should be obtained when the new Montgomery reduction code
125 * has been integrated into OpenSSL.)
129 #define MONT_EXP_WORD
134 # ifdef MONT_EXP_WORD
135 if (a
->top
== 1 && !a
->neg
136 && (BN_get_flags(p
, BN_FLG_CONSTTIME
) == 0)
137 && (BN_get_flags(a
, BN_FLG_CONSTTIME
) == 0)
138 && (BN_get_flags(m
, BN_FLG_CONSTTIME
) == 0)) {
139 BN_ULONG A
= a
->d
[0];
140 ret
= BN_mod_exp_mont_word(r
, A
, p
, m
, ctx
, NULL
);
143 ret
= BN_mod_exp_mont(r
, a
, p
, m
, ctx
, NULL
);
148 ret
= BN_mod_exp_recp(r
, a
, p
, m
, ctx
);
152 ret
= BN_mod_exp_simple(r
, a
, p
, m
, ctx
);
160 int BN_mod_exp_recp(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
161 const BIGNUM
*m
, BN_CTX
*ctx
)
163 int i
, j
, bits
, ret
= 0, wstart
, wend
, window
, wvalue
;
166 /* Table of variables obtained from 'ctx' */
167 BIGNUM
*val
[TABLE_SIZE
];
170 if (BN_get_flags(p
, BN_FLG_CONSTTIME
) != 0
171 || BN_get_flags(a
, BN_FLG_CONSTTIME
) != 0
172 || BN_get_flags(m
, BN_FLG_CONSTTIME
) != 0) {
173 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
174 ERR_raise(ERR_LIB_BN
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
178 bits
= BN_num_bits(p
);
180 /* x**0 mod 1, or x**0 mod -1 is still zero. */
181 if (BN_abs_is_word(m
, 1)) {
190 BN_RECP_CTX_init(&recp
);
193 aa
= BN_CTX_get(ctx
);
194 val
[0] = BN_CTX_get(ctx
);
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
257 for (i
= 1; i
< window
; i
++) {
260 if (BN_is_bit_set(p
, wstart
- i
)) {
261 wvalue
<<= (i
- wend
);
267 /* wend is the size of the current window */
269 /* add the 'bytes above' */
271 for (i
= 0; i
< j
; i
++) {
272 if (!BN_mod_mul_reciprocal(r
, r
, r
, &recp
, ctx
))
276 /* wvalue will be an odd number < 2^window */
277 if (!BN_mod_mul_reciprocal(r
, r
, val
[wvalue
>> 1], &recp
, ctx
))
280 /* move the 'window' down further */
290 BN_RECP_CTX_free(&recp
);
295 int BN_mod_exp_mont(BIGNUM
*rr
, const BIGNUM
*a
, const BIGNUM
*p
,
296 const BIGNUM
*m
, BN_CTX
*ctx
, BN_MONT_CTX
*in_mont
)
298 int i
, j
, bits
, ret
= 0, wstart
, wend
, window
, wvalue
;
302 /* Table of variables obtained from 'ctx' */
303 BIGNUM
*val
[TABLE_SIZE
];
304 BN_MONT_CTX
*mont
= NULL
;
306 if (BN_get_flags(p
, BN_FLG_CONSTTIME
) != 0
307 || BN_get_flags(a
, BN_FLG_CONSTTIME
) != 0
308 || BN_get_flags(m
, BN_FLG_CONSTTIME
) != 0) {
309 return BN_mod_exp_mont_consttime(rr
, a
, p
, m
, ctx
, in_mont
);
317 ERR_raise(ERR_LIB_BN
, BN_R_CALLED_WITH_EVEN_MODULUS
);
320 bits
= BN_num_bits(p
);
322 /* x**0 mod 1, or x**0 mod -1 is still zero. */
323 if (BN_abs_is_word(m
, 1)) {
335 val
[0] = BN_CTX_get(ctx
);
340 * If this is not done, things will break in the montgomery part
346 if ((mont
= BN_MONT_CTX_new()) == NULL
)
348 if (!BN_MONT_CTX_set(mont
, m
, ctx
))
352 if (a
->neg
|| BN_ucmp(a
, m
) >= 0) {
353 if (!BN_nnmod(val
[0], a
, m
, ctx
))
358 if (!bn_to_mont_fixed_top(val
[0], aa
, mont
, ctx
))
361 window
= BN_window_bits_for_exponent_size(bits
);
363 if (!bn_mul_mont_fixed_top(d
, val
[0], val
[0], mont
, ctx
))
365 j
= 1 << (window
- 1);
366 for (i
= 1; i
< j
; i
++) {
367 if (((val
[i
] = BN_CTX_get(ctx
)) == NULL
) ||
368 !bn_mul_mont_fixed_top(val
[i
], val
[i
- 1], d
, mont
, ctx
))
373 start
= 1; /* This is used to avoid multiplication etc
374 * when there is only the value '1' in the
376 wvalue
= 0; /* The 'value' of the window */
377 wstart
= bits
- 1; /* The top bit of the window */
378 wend
= 0; /* The bottom bit of the window */
380 #if 1 /* by Shay Gueron's suggestion */
381 j
= m
->top
; /* borrow j */
382 if (m
->d
[j
- 1] & (((BN_ULONG
)1) << (BN_BITS2
- 1))) {
383 if (bn_wexpand(r
, j
) == NULL
)
385 /* 2^(top*BN_BITS2) - m */
386 r
->d
[0] = (0 - m
->d
[0]) & BN_MASK2
;
387 for (i
= 1; i
< j
; i
++)
388 r
->d
[i
] = (~m
->d
[i
]) & BN_MASK2
;
390 r
->flags
|= BN_FLG_FIXED_TOP
;
393 if (!bn_to_mont_fixed_top(r
, BN_value_one(), mont
, ctx
))
396 if (BN_is_bit_set(p
, wstart
) == 0) {
398 if (!bn_mul_mont_fixed_top(r
, r
, r
, mont
, ctx
))
407 * We now have wstart on a 'set' bit, we now need to work out how bit
408 * a window to do. To do this we need to scan forward until the last
409 * set bit before the end of the window
413 for (i
= 1; i
< window
; i
++) {
416 if (BN_is_bit_set(p
, wstart
- i
)) {
417 wvalue
<<= (i
- wend
);
423 /* wend is the size of the current window */
425 /* add the 'bytes above' */
427 for (i
= 0; i
< j
; i
++) {
428 if (!bn_mul_mont_fixed_top(r
, r
, r
, mont
, ctx
))
432 /* wvalue will be an odd number < 2^window */
433 if (!bn_mul_mont_fixed_top(r
, r
, val
[wvalue
>> 1], mont
, ctx
))
436 /* move the 'window' down further */
444 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
445 * removes padding [if any] and makes return value suitable for public
448 #if defined(SPARC_T4_MONT)
449 if (OPENSSL_sparcv9cap_P
[0] & (SPARCV9_VIS3
| SPARCV9_PREFER_FPU
)) {
450 j
= mont
->N
.top
; /* borrow j */
451 val
[0]->d
[0] = 1; /* borrow val[0] */
452 for (i
= 1; i
< j
; i
++)
455 if (!BN_mod_mul_montgomery(rr
, r
, val
[0], mont
, ctx
))
459 if (!BN_from_montgomery(rr
, r
, mont
, ctx
))
464 BN_MONT_CTX_free(mont
);
470 static BN_ULONG
bn_get_bits(const BIGNUM
*a
, int bitpos
)
475 wordpos
= bitpos
/ BN_BITS2
;
477 if (wordpos
>= 0 && wordpos
< a
->top
) {
478 ret
= a
->d
[wordpos
] & BN_MASK2
;
481 if (++wordpos
< a
->top
)
482 ret
|= a
->d
[wordpos
] << (BN_BITS2
- bitpos
);
486 return ret
& BN_MASK2
;
490 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
491 * layout so that accessing any of these table values shows the same access
492 * pattern as far as cache lines are concerned. The following functions are
493 * used to transfer a BIGNUM from/to that table.
496 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM
*b
, int top
,
497 unsigned char *buf
, int idx
,
501 int width
= 1 << window
;
502 BN_ULONG
*table
= (BN_ULONG
*)buf
;
505 top
= b
->top
; /* this works because 'buf' is explicitly
507 for (i
= 0, j
= idx
; i
< top
; i
++, j
+= width
) {
514 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM
*b
, int top
,
515 unsigned char *buf
, int idx
,
519 int width
= 1 << window
;
521 * We declare table 'volatile' in order to discourage compiler
522 * from reordering loads from the table. Concern is that if
523 * reordered in specific manner loads might give away the
524 * information we are trying to conceal. Some would argue that
525 * compiler can reorder them anyway, but it can as well be
526 * argued that doing so would be violation of standard...
528 volatile BN_ULONG
*table
= (volatile BN_ULONG
*)buf
;
530 if (bn_wexpand(b
, top
) == NULL
)
534 for (i
= 0; i
< top
; i
++, table
+= width
) {
537 for (j
= 0; j
< width
; j
++) {
539 ((BN_ULONG
)0 - (constant_time_eq_int(j
,idx
)&1));
545 int xstride
= 1 << (window
- 2);
546 BN_ULONG y0
, y1
, y2
, y3
;
548 i
= idx
>> (window
- 2); /* equivalent of idx / xstride */
549 idx
&= xstride
- 1; /* equivalent of idx % xstride */
551 y0
= (BN_ULONG
)0 - (constant_time_eq_int(i
,0)&1);
552 y1
= (BN_ULONG
)0 - (constant_time_eq_int(i
,1)&1);
553 y2
= (BN_ULONG
)0 - (constant_time_eq_int(i
,2)&1);
554 y3
= (BN_ULONG
)0 - (constant_time_eq_int(i
,3)&1);
556 for (i
= 0; i
< top
; i
++, table
+= width
) {
559 for (j
= 0; j
< xstride
; j
++) {
560 acc
|= ( (table
[j
+ 0 * xstride
] & y0
) |
561 (table
[j
+ 1 * xstride
] & y1
) |
562 (table
[j
+ 2 * xstride
] & y2
) |
563 (table
[j
+ 3 * xstride
] & y3
) )
564 & ((BN_ULONG
)0 - (constant_time_eq_int(j
,idx
)&1));
572 b
->flags
|= BN_FLG_FIXED_TOP
;
577 * Given a pointer value, compute the next address that is a cache line
580 #define MOD_EXP_CTIME_ALIGN(x_) \
581 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
584 * This variant of BN_mod_exp_mont() uses fixed windows and the special
585 * precomputation memory layout to limit data-dependency to a minimum to
586 * protect secret exponents (cf. the hyper-threading timing attacks pointed
587 * out by Colin Percival,
588 * http://www.daemonology.net/hyperthreading-considered-harmful/)
590 int BN_mod_exp_mont_consttime(BIGNUM
*rr
, const BIGNUM
*a
, const BIGNUM
*p
,
591 const BIGNUM
*m
, BN_CTX
*ctx
,
592 BN_MONT_CTX
*in_mont
)
594 int i
, bits
, ret
= 0, window
, wvalue
, wmask
, window0
;
596 BN_MONT_CTX
*mont
= NULL
;
599 unsigned char *powerbufFree
= NULL
;
601 unsigned char *powerbuf
= NULL
;
603 #if defined(SPARC_T4_MONT)
612 ERR_raise(ERR_LIB_BN
, BN_R_CALLED_WITH_EVEN_MODULUS
);
619 * Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak
620 * whether the top bits are zero.
622 bits
= p
->top
* BN_BITS2
;
624 /* x**0 mod 1, or x**0 mod -1 is still zero. */
625 if (BN_abs_is_word(m
, 1)) {
637 * Allocate a montgomery context if it was not supplied by the caller. If
638 * this is not done, things will break in the montgomery part.
643 if ((mont
= BN_MONT_CTX_new()) == NULL
)
645 if (!BN_MONT_CTX_set(mont
, m
, ctx
))
649 if (a
->neg
|| BN_ucmp(a
, m
) >= 0) {
650 BIGNUM
*reduced
= BN_CTX_get(ctx
);
652 || !BN_nnmod(reduced
, a
, m
, ctx
)) {
660 * If the size of the operands allow it, perform the optimized
661 * RSAZ exponentiation. For further information see
662 * crypto/bn/rsaz_exp.c and accompanying assembly modules.
664 if ((16 == a
->top
) && (16 == p
->top
) && (BN_num_bits(m
) == 1024)
665 && rsaz_avx2_eligible()) {
666 if (NULL
== bn_wexpand(rr
, 16))
668 RSAZ_1024_mod_exp_avx2(rr
->d
, a
->d
, p
->d
, m
->d
, mont
->RR
.d
,
675 } else if ((8 == a
->top
) && (8 == p
->top
) && (BN_num_bits(m
) == 512)) {
676 if (NULL
== bn_wexpand(rr
, 8))
678 RSAZ_512_mod_exp(rr
->d
, a
->d
, p
->d
, m
->d
, mont
->n0
[0], mont
->RR
.d
);
687 /* Get the window size to use with size of p. */
688 window
= BN_window_bits_for_ctime_exponent_size(bits
);
689 #if defined(SPARC_T4_MONT)
690 if (window
>= 5 && (top
& 15) == 0 && top
<= 64 &&
691 (OPENSSL_sparcv9cap_P
[1] & (CFR_MONTMUL
| CFR_MONTSQR
)) ==
692 (CFR_MONTMUL
| CFR_MONTSQR
) && (t4
= OPENSSL_sparcv9cap_P
[0]))
696 #if defined(OPENSSL_BN_ASM_MONT5)
698 window
= 5; /* ~5% improvement for RSA2048 sign, and even
700 /* reserve space for mont->N.d[] copy */
701 powerbufLen
+= top
* sizeof(mont
->N
.d
[0]);
707 * Allocate a buffer large enough to hold all of the pre-computed powers
708 * of am, am itself and tmp.
710 numPowers
= 1 << window
;
711 powerbufLen
+= sizeof(m
->d
[0]) * (top
* numPowers
+
713 numPowers
? (2 * top
) : numPowers
));
715 if (powerbufLen
< 3072)
717 alloca(powerbufLen
+ MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH
);
721 OPENSSL_malloc(powerbufLen
+ MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH
))
725 powerbuf
= MOD_EXP_CTIME_ALIGN(powerbufFree
);
726 memset(powerbuf
, 0, powerbufLen
);
729 if (powerbufLen
< 3072)
733 /* lay down tmp and am right after powers table */
734 tmp
.d
= (BN_ULONG
*)(powerbuf
+ sizeof(m
->d
[0]) * top
* numPowers
);
736 tmp
.top
= am
.top
= 0;
737 tmp
.dmax
= am
.dmax
= top
;
738 tmp
.neg
= am
.neg
= 0;
739 tmp
.flags
= am
.flags
= BN_FLG_STATIC_DATA
;
741 /* prepare a^0 in Montgomery domain */
742 #if 1 /* by Shay Gueron's suggestion */
743 if (m
->d
[top
- 1] & (((BN_ULONG
)1) << (BN_BITS2
- 1))) {
744 /* 2^(top*BN_BITS2) - m */
745 tmp
.d
[0] = (0 - m
->d
[0]) & BN_MASK2
;
746 for (i
= 1; i
< top
; i
++)
747 tmp
.d
[i
] = (~m
->d
[i
]) & BN_MASK2
;
751 if (!bn_to_mont_fixed_top(&tmp
, BN_value_one(), mont
, ctx
))
754 /* prepare a^1 in Montgomery domain */
755 if (!bn_to_mont_fixed_top(&am
, a
, mont
, ctx
))
758 #if defined(SPARC_T4_MONT)
760 typedef int (*bn_pwr5_mont_f
) (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_8(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_16(BN_ULONG
*tp
, const BN_ULONG
*np
,
767 const BN_ULONG
*n0
, const void *table
,
768 int power
, int bits
);
769 int bn_pwr5_mont_t4_24(BN_ULONG
*tp
, const BN_ULONG
*np
,
770 const BN_ULONG
*n0
, const void *table
,
771 int power
, int bits
);
772 int bn_pwr5_mont_t4_32(BN_ULONG
*tp
, const BN_ULONG
*np
,
773 const BN_ULONG
*n0
, const void *table
,
774 int power
, int bits
);
775 static const bn_pwr5_mont_f pwr5_funcs
[4] = {
776 bn_pwr5_mont_t4_8
, bn_pwr5_mont_t4_16
,
777 bn_pwr5_mont_t4_24
, bn_pwr5_mont_t4_32
779 bn_pwr5_mont_f pwr5_worker
= pwr5_funcs
[top
/ 16 - 1];
781 typedef int (*bn_mul_mont_f
) (BN_ULONG
*rp
, const BN_ULONG
*ap
,
782 const void *bp
, const BN_ULONG
*np
,
784 int bn_mul_mont_t4_8(BN_ULONG
*rp
, const BN_ULONG
*ap
, const void *bp
,
785 const BN_ULONG
*np
, const BN_ULONG
*n0
);
786 int bn_mul_mont_t4_16(BN_ULONG
*rp
, const BN_ULONG
*ap
,
787 const void *bp
, const BN_ULONG
*np
,
789 int bn_mul_mont_t4_24(BN_ULONG
*rp
, const BN_ULONG
*ap
,
790 const void *bp
, const BN_ULONG
*np
,
792 int bn_mul_mont_t4_32(BN_ULONG
*rp
, const BN_ULONG
*ap
,
793 const void *bp
, const BN_ULONG
*np
,
795 static const bn_mul_mont_f mul_funcs
[4] = {
796 bn_mul_mont_t4_8
, bn_mul_mont_t4_16
,
797 bn_mul_mont_t4_24
, bn_mul_mont_t4_32
799 bn_mul_mont_f mul_worker
= mul_funcs
[top
/ 16 - 1];
801 void bn_mul_mont_vis3(BN_ULONG
*rp
, const BN_ULONG
*ap
,
802 const void *bp
, const BN_ULONG
*np
,
803 const BN_ULONG
*n0
, int num
);
804 void bn_mul_mont_t4(BN_ULONG
*rp
, const BN_ULONG
*ap
,
805 const void *bp
, const BN_ULONG
*np
,
806 const BN_ULONG
*n0
, int num
);
807 void bn_mul_mont_gather5_t4(BN_ULONG
*rp
, const BN_ULONG
*ap
,
808 const void *table
, const BN_ULONG
*np
,
809 const BN_ULONG
*n0
, int num
, int power
);
810 void bn_flip_n_scatter5_t4(const BN_ULONG
*inp
, size_t num
,
811 void *table
, size_t power
);
812 void bn_gather5_t4(BN_ULONG
*out
, size_t num
,
813 void *table
, size_t power
);
814 void bn_flip_t4(BN_ULONG
*dst
, BN_ULONG
*src
, size_t num
);
816 BN_ULONG
*np
= mont
->N
.d
, *n0
= mont
->n0
;
817 int stride
= 5 * (6 - (top
/ 16 - 1)); /* multiple of 5, but less
821 * BN_to_montgomery can contaminate words above .top [in
824 for (i
= am
.top
; i
< top
; i
++)
826 for (i
= tmp
.top
; i
< top
; i
++)
829 bn_flip_n_scatter5_t4(tmp
.d
, top
, powerbuf
, 0);
830 bn_flip_n_scatter5_t4(am
.d
, top
, powerbuf
, 1);
831 if (!(*mul_worker
) (tmp
.d
, am
.d
, am
.d
, np
, n0
) &&
832 !(*mul_worker
) (tmp
.d
, am
.d
, am
.d
, np
, n0
))
833 bn_mul_mont_vis3(tmp
.d
, am
.d
, am
.d
, np
, n0
, top
);
834 bn_flip_n_scatter5_t4(tmp
.d
, top
, powerbuf
, 2);
836 for (i
= 3; i
< 32; i
++) {
837 /* Calculate a^i = a^(i-1) * a */
838 if (!(*mul_worker
) (tmp
.d
, tmp
.d
, am
.d
, np
, n0
) &&
839 !(*mul_worker
) (tmp
.d
, tmp
.d
, am
.d
, np
, n0
))
840 bn_mul_mont_vis3(tmp
.d
, tmp
.d
, am
.d
, np
, n0
, top
);
841 bn_flip_n_scatter5_t4(tmp
.d
, top
, powerbuf
, i
);
844 /* switch to 64-bit domain */
845 np
= alloca(top
* sizeof(BN_ULONG
));
847 bn_flip_t4(np
, mont
->N
.d
, top
);
850 * The exponent may not have a whole number of fixed-size windows.
851 * To simplify the main loop, the initial window has between 1 and
852 * full-window-size bits such that what remains is always a whole
855 window0
= (bits
- 1) % 5 + 1;
856 wmask
= (1 << window0
) - 1;
858 wvalue
= bn_get_bits(p
, bits
) & wmask
;
859 bn_gather5_t4(tmp
.d
, top
, powerbuf
, wvalue
);
862 * Scan the exponent one window at a time starting from the most
869 wvalue
= bn_get_bits(p
, bits
);
871 if ((*pwr5_worker
) (tmp
.d
, np
, n0
, powerbuf
, wvalue
, stride
))
873 /* retry once and fall back */
874 if ((*pwr5_worker
) (tmp
.d
, np
, n0
, powerbuf
, wvalue
, stride
))
878 wvalue
>>= stride
- 5;
880 bn_mul_mont_t4(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
881 bn_mul_mont_t4(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
882 bn_mul_mont_t4(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
883 bn_mul_mont_t4(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
884 bn_mul_mont_t4(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
885 bn_mul_mont_gather5_t4(tmp
.d
, tmp
.d
, powerbuf
, np
, n0
, top
,
889 bn_flip_t4(tmp
.d
, tmp
.d
, top
);
891 /* back to 32-bit domain */
893 bn_correct_top(&tmp
);
894 OPENSSL_cleanse(np
, top
* sizeof(BN_ULONG
));
897 #if defined(OPENSSL_BN_ASM_MONT5)
898 if (window
== 5 && top
> 1) {
900 * This optimization uses ideas from http://eprint.iacr.org/2011/239,
901 * specifically optimization of cache-timing attack countermeasures
902 * and pre-computation optimization.
906 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
907 * 512-bit RSA is hardly relevant, we omit it to spare size...
909 void bn_mul_mont_gather5(BN_ULONG
*rp
, const BN_ULONG
*ap
,
910 const void *table
, const BN_ULONG
*np
,
911 const BN_ULONG
*n0
, int num
, int power
);
912 void bn_scatter5(const BN_ULONG
*inp
, size_t num
,
913 void *table
, size_t power
);
914 void bn_gather5(BN_ULONG
*out
, size_t num
, void *table
, size_t power
);
915 void bn_power5(BN_ULONG
*rp
, const BN_ULONG
*ap
,
916 const void *table
, const BN_ULONG
*np
,
917 const BN_ULONG
*n0
, int num
, int power
);
918 int bn_get_bits5(const BN_ULONG
*ap
, int off
);
919 int bn_from_montgomery(BN_ULONG
*rp
, const BN_ULONG
*ap
,
920 const BN_ULONG
*not_used
, const BN_ULONG
*np
,
921 const BN_ULONG
*n0
, int num
);
923 BN_ULONG
*n0
= mont
->n0
, *np
;
926 * BN_to_montgomery can contaminate words above .top [in
929 for (i
= am
.top
; i
< top
; i
++)
931 for (i
= tmp
.top
; i
< top
; i
++)
935 * copy mont->N.d[] to improve cache locality
937 for (np
= am
.d
+ top
, i
= 0; i
< top
; i
++)
938 np
[i
] = mont
->N
.d
[i
];
940 bn_scatter5(tmp
.d
, top
, powerbuf
, 0);
941 bn_scatter5(am
.d
, am
.top
, powerbuf
, 1);
942 bn_mul_mont(tmp
.d
, am
.d
, am
.d
, np
, n0
, top
);
943 bn_scatter5(tmp
.d
, top
, powerbuf
, 2);
946 for (i
= 3; i
< 32; i
++) {
947 /* Calculate a^i = a^(i-1) * a */
948 bn_mul_mont_gather5(tmp
.d
, am
.d
, powerbuf
, np
, n0
, top
, i
- 1);
949 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
952 /* same as above, but uses squaring for 1/2 of operations */
953 for (i
= 4; i
< 32; i
*= 2) {
954 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
955 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
957 for (i
= 3; i
< 8; i
+= 2) {
959 bn_mul_mont_gather5(tmp
.d
, am
.d
, powerbuf
, np
, n0
, top
, i
- 1);
960 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
961 for (j
= 2 * i
; j
< 32; j
*= 2) {
962 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
963 bn_scatter5(tmp
.d
, top
, powerbuf
, j
);
966 for (; i
< 16; i
+= 2) {
967 bn_mul_mont_gather5(tmp
.d
, am
.d
, powerbuf
, np
, n0
, top
, i
- 1);
968 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
969 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
970 bn_scatter5(tmp
.d
, top
, powerbuf
, 2 * i
);
972 for (; i
< 32; i
+= 2) {
973 bn_mul_mont_gather5(tmp
.d
, am
.d
, powerbuf
, np
, n0
, top
, i
- 1);
974 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
978 * The exponent may not have a whole number of fixed-size windows.
979 * To simplify the main loop, the initial window has between 1 and
980 * full-window-size bits such that what remains is always a whole
983 window0
= (bits
- 1) % 5 + 1;
984 wmask
= (1 << window0
) - 1;
986 wvalue
= bn_get_bits(p
, bits
) & wmask
;
987 bn_gather5(tmp
.d
, top
, powerbuf
, wvalue
);
990 * Scan the exponent one window at a time starting from the most
995 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
996 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
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_gather5(tmp
.d
, tmp
.d
, powerbuf
, np
, n0
, top
,
1001 bn_get_bits5(p
->d
, bits
-= 5));
1005 bn_power5(tmp
.d
, tmp
.d
, powerbuf
, np
, n0
, top
,
1006 bn_get_bits5(p
->d
, bits
-= 5));
1010 ret
= bn_from_montgomery(tmp
.d
, tmp
.d
, NULL
, np
, n0
, top
);
1012 bn_correct_top(&tmp
);
1014 if (!BN_copy(rr
, &tmp
))
1016 goto err
; /* non-zero ret means it's not error */
1021 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp
, top
, powerbuf
, 0, window
))
1023 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am
, top
, powerbuf
, 1, window
))
1027 * If the window size is greater than 1, then calculate
1028 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1029 * powers could instead be computed as (a^(i/2))^2 to use the slight
1030 * performance advantage of sqr over mul).
1033 if (!bn_mul_mont_fixed_top(&tmp
, &am
, &am
, mont
, ctx
))
1035 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp
, top
, powerbuf
, 2,
1038 for (i
= 3; i
< numPowers
; i
++) {
1039 /* Calculate a^i = a^(i-1) * a */
1040 if (!bn_mul_mont_fixed_top(&tmp
, &am
, &tmp
, mont
, ctx
))
1042 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp
, top
, powerbuf
, i
,
1049 * The exponent may not have a whole number of fixed-size windows.
1050 * To simplify the main loop, the initial window has between 1 and
1051 * full-window-size bits such that what remains is always a whole
1054 window0
= (bits
- 1) % window
+ 1;
1055 wmask
= (1 << window0
) - 1;
1057 wvalue
= bn_get_bits(p
, bits
) & wmask
;
1058 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp
, top
, powerbuf
, wvalue
,
1062 wmask
= (1 << window
) - 1;
1064 * Scan the exponent one window at a time starting from the most
1069 /* Square the result window-size times */
1070 for (i
= 0; i
< window
; i
++)
1071 if (!bn_mul_mont_fixed_top(&tmp
, &tmp
, &tmp
, mont
, ctx
))
1075 * Get a window's worth of bits from the exponent
1076 * This avoids calling BN_is_bit_set for each bit, which
1077 * is not only slower but also makes each bit vulnerable to
1078 * EM (and likely other) side-channel attacks like One&Done
1079 * (for details see "One&Done: A Single-Decryption EM-Based
1080 * Attack on OpenSSL's Constant-Time Blinded RSA" by M. Alam,
1081 * H. Khan, M. Dey, N. Sinha, R. Callan, A. Zajic, and
1082 * M. Prvulovic, in USENIX Security'18)
1085 wvalue
= bn_get_bits(p
, bits
) & wmask
;
1087 * Fetch the appropriate pre-computed value from the pre-buf
1089 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am
, top
, powerbuf
, wvalue
,
1093 /* Multiply the result into the intermediate result */
1094 if (!bn_mul_mont_fixed_top(&tmp
, &tmp
, &am
, mont
, ctx
))
1100 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
1101 * removes padding [if any] and makes return value suitable for public
1104 #if defined(SPARC_T4_MONT)
1105 if (OPENSSL_sparcv9cap_P
[0] & (SPARCV9_VIS3
| SPARCV9_PREFER_FPU
)) {
1106 am
.d
[0] = 1; /* borrow am */
1107 for (i
= 1; i
< top
; i
++)
1109 if (!BN_mod_mul_montgomery(rr
, &tmp
, &am
, mont
, ctx
))
1113 if (!BN_from_montgomery(rr
, &tmp
, mont
, ctx
))
1117 if (in_mont
== NULL
)
1118 BN_MONT_CTX_free(mont
);
1119 if (powerbuf
!= NULL
) {
1120 OPENSSL_cleanse(powerbuf
, powerbufLen
);
1121 OPENSSL_free(powerbufFree
);
1127 int BN_mod_exp_mont_word(BIGNUM
*rr
, BN_ULONG a
, const BIGNUM
*p
,
1128 const BIGNUM
*m
, BN_CTX
*ctx
, BN_MONT_CTX
*in_mont
)
1130 BN_MONT_CTX
*mont
= NULL
;
1131 int b
, bits
, ret
= 0;
1136 #define BN_MOD_MUL_WORD(r, w, m) \
1137 (BN_mul_word(r, (w)) && \
1138 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1139 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1141 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1142 * probably more overhead than always using BN_mod (which uses BN_copy if
1143 * a similar test returns true).
1146 * We can use BN_mod and do not need BN_nnmod because our accumulator is
1147 * never negative (the result of BN_mod does not depend on the sign of
1150 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1151 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1153 if (BN_get_flags(p
, BN_FLG_CONSTTIME
) != 0
1154 || BN_get_flags(m
, BN_FLG_CONSTTIME
) != 0) {
1155 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1156 ERR_raise(ERR_LIB_BN
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
1163 if (!BN_is_odd(m
)) {
1164 ERR_raise(ERR_LIB_BN
, BN_R_CALLED_WITH_EVEN_MODULUS
);
1168 a
%= m
->d
[0]; /* make sure that 'a' is reduced */
1170 bits
= BN_num_bits(p
);
1172 /* x**0 mod 1, or x**0 mod -1 is still zero. */
1173 if (BN_abs_is_word(m
, 1)) {
1188 r
= BN_CTX_get(ctx
);
1189 t
= BN_CTX_get(ctx
);
1193 if (in_mont
!= NULL
)
1196 if ((mont
= BN_MONT_CTX_new()) == NULL
)
1198 if (!BN_MONT_CTX_set(mont
, m
, ctx
))
1202 r_is_one
= 1; /* except for Montgomery factor */
1206 /* The result is accumulated in the product r*w. */
1207 w
= a
; /* bit 'bits-1' of 'p' is always set */
1208 for (b
= bits
- 2; b
>= 0; b
--) {
1209 /* First, square r*w. */
1211 if ((next_w
/ w
) != w
) { /* overflow */
1213 if (!BN_TO_MONTGOMERY_WORD(r
, w
, mont
))
1217 if (!BN_MOD_MUL_WORD(r
, w
, m
))
1224 if (!BN_mod_mul_montgomery(r
, r
, r
, mont
, ctx
))
1228 /* Second, multiply r*w by 'a' if exponent bit is set. */
1229 if (BN_is_bit_set(p
, b
)) {
1231 if ((next_w
/ a
) != w
) { /* overflow */
1233 if (!BN_TO_MONTGOMERY_WORD(r
, w
, mont
))
1237 if (!BN_MOD_MUL_WORD(r
, w
, m
))
1246 /* Finally, set r:=r*w. */
1249 if (!BN_TO_MONTGOMERY_WORD(r
, w
, mont
))
1253 if (!BN_MOD_MUL_WORD(r
, w
, m
))
1258 if (r_is_one
) { /* can happen only if a == 1 */
1262 if (!BN_from_montgomery(rr
, r
, mont
, ctx
))
1267 if (in_mont
== NULL
)
1268 BN_MONT_CTX_free(mont
);
1274 /* The old fallback, simple version :-) */
1275 int BN_mod_exp_simple(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
1276 const BIGNUM
*m
, BN_CTX
*ctx
)
1278 int i
, j
, bits
, ret
= 0, wstart
, wend
, window
, wvalue
;
1281 /* Table of variables obtained from 'ctx' */
1282 BIGNUM
*val
[TABLE_SIZE
];
1284 if (BN_get_flags(p
, BN_FLG_CONSTTIME
) != 0
1285 || BN_get_flags(a
, BN_FLG_CONSTTIME
) != 0
1286 || BN_get_flags(m
, BN_FLG_CONSTTIME
) != 0) {
1287 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1288 ERR_raise(ERR_LIB_BN
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
1292 bits
= BN_num_bits(p
);
1294 /* x**0 mod 1, or x**0 mod -1 is still zero. */
1295 if (BN_abs_is_word(m
, 1)) {
1305 d
= BN_CTX_get(ctx
);
1306 val
[0] = BN_CTX_get(ctx
);
1310 if (!BN_nnmod(val
[0], a
, m
, ctx
))
1312 if (BN_is_zero(val
[0])) {
1318 window
= BN_window_bits_for_exponent_size(bits
);
1320 if (!BN_mod_mul(d
, val
[0], val
[0], m
, ctx
))
1322 j
= 1 << (window
- 1);
1323 for (i
= 1; i
< j
; i
++) {
1324 if (((val
[i
] = BN_CTX_get(ctx
)) == NULL
) ||
1325 !BN_mod_mul(val
[i
], val
[i
- 1], d
, m
, ctx
))
1330 start
= 1; /* This is used to avoid multiplication etc
1331 * when there is only the value '1' in the
1333 wvalue
= 0; /* The 'value' of the window */
1334 wstart
= bits
- 1; /* The top bit of the window */
1335 wend
= 0; /* The bottom bit of the window */
1341 if (BN_is_bit_set(p
, wstart
) == 0) {
1343 if (!BN_mod_mul(r
, r
, r
, m
, ctx
))
1351 * We now have wstart on a 'set' bit, we now need to work out how bit
1352 * a window to do. To do this we need to scan forward until the last
1353 * 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 */
1395 * This is a variant of modular exponentiation optimization that does
1396 * parallel 2-primes exponentiation using 256-bit (AVX512VL) AVX512_IFMA ISA
1397 * in 52-bit binary redundant representation.
1398 * If such instructions are not available, or input data size is not supported,
1399 * it falls back to two BN_mod_exp_mont_consttime() calls.
1401 int BN_mod_exp_mont_consttime_x2(BIGNUM
*rr1
, const BIGNUM
*a1
, const BIGNUM
*p1
,
1402 const BIGNUM
*m1
, BN_MONT_CTX
*in_mont1
,
1403 BIGNUM
*rr2
, const BIGNUM
*a2
, const BIGNUM
*p2
,
1404 const BIGNUM
*m2
, BN_MONT_CTX
*in_mont2
,
1410 BN_MONT_CTX
*mont1
= NULL
;
1411 BN_MONT_CTX
*mont2
= NULL
;
1413 if (ossl_rsaz_avx512ifma_eligible() &&
1414 (((a1
->top
== 16) && (p1
->top
== 16) && (BN_num_bits(m1
) == 1024) &&
1415 (a2
->top
== 16) && (p2
->top
== 16) && (BN_num_bits(m2
) == 1024)) ||
1416 ((a1
->top
== 24) && (p1
->top
== 24) && (BN_num_bits(m1
) == 1536) &&
1417 (a2
->top
== 24) && (p2
->top
== 24) && (BN_num_bits(m2
) == 1536)) ||
1418 ((a1
->top
== 32) && (p1
->top
== 32) && (BN_num_bits(m1
) == 2048) &&
1419 (a2
->top
== 32) && (p2
->top
== 32) && (BN_num_bits(m2
) == 2048)))) {
1422 /* Modulus bits of |m1| and |m2| are equal */
1423 int mod_bits
= BN_num_bits(m1
);
1425 if (bn_wexpand(rr1
, topn
) == NULL
)
1427 if (bn_wexpand(rr2
, topn
) == NULL
)
1430 /* Ensure that montgomery contexts are initialized */
1431 if (in_mont1
!= NULL
) {
1434 if ((mont1
= BN_MONT_CTX_new()) == NULL
)
1436 if (!BN_MONT_CTX_set(mont1
, m1
, ctx
))
1439 if (in_mont2
!= NULL
) {
1442 if ((mont2
= BN_MONT_CTX_new()) == NULL
)
1444 if (!BN_MONT_CTX_set(mont2
, m2
, ctx
))
1448 ret
= ossl_rsaz_mod_exp_avx512_x2(rr1
->d
, a1
->d
, p1
->d
, m1
->d
,
1449 mont1
->RR
.d
, mont1
->n0
[0],
1450 rr2
->d
, a2
->d
, p2
->d
, m2
->d
,
1451 mont2
->RR
.d
, mont2
->n0
[0],
1456 bn_correct_top(rr1
);
1461 bn_correct_top(rr2
);
1468 /* rr1 = a1^p1 mod m1 */
1469 ret
= BN_mod_exp_mont_consttime(rr1
, a1
, p1
, m1
, ctx
, in_mont1
);
1470 /* rr2 = a2^p2 mod m2 */
1471 ret
&= BN_mod_exp_mont_consttime(rr2
, a2
, p2
, m2
, ctx
, in_mont2
);
1475 if (in_mont2
== NULL
)
1476 BN_MONT_CTX_free(mont2
);
1477 if (in_mont1
== NULL
)
1478 BN_MONT_CTX_free(mont1
);