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)) {
191 aa
= BN_CTX_get(ctx
);
192 val
[0] = BN_CTX_get(ctx
);
196 BN_RECP_CTX_init(&recp
);
198 /* ignore sign of 'm' */
202 if (BN_RECP_CTX_set(&recp
, aa
, ctx
) <= 0)
205 if (BN_RECP_CTX_set(&recp
, m
, ctx
) <= 0)
209 if (!BN_nnmod(val
[0], a
, m
, ctx
))
211 if (BN_is_zero(val
[0])) {
217 window
= BN_window_bits_for_exponent_size(bits
);
219 if (!BN_mod_mul_reciprocal(aa
, val
[0], val
[0], &recp
, ctx
))
221 j
= 1 << (window
- 1);
222 for (i
= 1; i
< j
; i
++) {
223 if (((val
[i
] = BN_CTX_get(ctx
)) == NULL
) ||
224 !BN_mod_mul_reciprocal(val
[i
], val
[i
- 1], aa
, &recp
, ctx
))
229 start
= 1; /* This is used to avoid multiplication etc
230 * when there is only the value '1' in the
232 wvalue
= 0; /* The 'value' of the window */
233 wstart
= bits
- 1; /* The top bit of the window */
234 wend
= 0; /* The bottom bit of the window */
240 if (BN_is_bit_set(p
, wstart
) == 0) {
242 if (!BN_mod_mul_reciprocal(r
, r
, r
, &recp
, ctx
))
250 * We now have wstart on a 'set' bit, we now need to work out how bit
251 * a window to do. To do this we need to scan forward until the last
252 * set bit before the end of the window
256 for (i
= 1; i
< window
; i
++) {
259 if (BN_is_bit_set(p
, wstart
- i
)) {
260 wvalue
<<= (i
- wend
);
266 /* wend is the size of the current window */
268 /* add the 'bytes above' */
270 for (i
= 0; i
< j
; i
++) {
271 if (!BN_mod_mul_reciprocal(r
, r
, r
, &recp
, ctx
))
275 /* wvalue will be an odd number < 2^window */
276 if (!BN_mod_mul_reciprocal(r
, r
, val
[wvalue
>> 1], &recp
, ctx
))
279 /* move the 'window' down further */
289 BN_RECP_CTX_free(&recp
);
294 int BN_mod_exp_mont(BIGNUM
*rr
, const BIGNUM
*a
, const BIGNUM
*p
,
295 const BIGNUM
*m
, BN_CTX
*ctx
, BN_MONT_CTX
*in_mont
)
297 int i
, j
, bits
, ret
= 0, wstart
, wend
, window
, wvalue
;
301 /* Table of variables obtained from 'ctx' */
302 BIGNUM
*val
[TABLE_SIZE
];
303 BN_MONT_CTX
*mont
= NULL
;
305 if (BN_get_flags(p
, BN_FLG_CONSTTIME
) != 0
306 || BN_get_flags(a
, BN_FLG_CONSTTIME
) != 0
307 || BN_get_flags(m
, BN_FLG_CONSTTIME
) != 0) {
308 return BN_mod_exp_mont_consttime(rr
, a
, p
, m
, ctx
, in_mont
);
316 ERR_raise(ERR_LIB_BN
, BN_R_CALLED_WITH_EVEN_MODULUS
);
319 bits
= BN_num_bits(p
);
321 /* x**0 mod 1, or x**0 mod -1 is still zero. */
322 if (BN_abs_is_word(m
, 1)) {
334 val
[0] = BN_CTX_get(ctx
);
339 * If this is not done, things will break in the montgomery part
345 if ((mont
= BN_MONT_CTX_new()) == NULL
)
347 if (!BN_MONT_CTX_set(mont
, m
, ctx
))
351 if (a
->neg
|| BN_ucmp(a
, m
) >= 0) {
352 if (!BN_nnmod(val
[0], a
, m
, ctx
))
357 if (!bn_to_mont_fixed_top(val
[0], aa
, mont
, ctx
))
360 window
= BN_window_bits_for_exponent_size(bits
);
362 if (!bn_mul_mont_fixed_top(d
, val
[0], val
[0], mont
, ctx
))
364 j
= 1 << (window
- 1);
365 for (i
= 1; i
< j
; i
++) {
366 if (((val
[i
] = BN_CTX_get(ctx
)) == NULL
) ||
367 !bn_mul_mont_fixed_top(val
[i
], val
[i
- 1], d
, mont
, ctx
))
372 start
= 1; /* This is used to avoid multiplication etc
373 * when there is only the value '1' in the
375 wvalue
= 0; /* The 'value' of the window */
376 wstart
= bits
- 1; /* The top bit of the window */
377 wend
= 0; /* The bottom bit of the window */
379 #if 1 /* by Shay Gueron's suggestion */
380 j
= m
->top
; /* borrow j */
381 if (m
->d
[j
- 1] & (((BN_ULONG
)1) << (BN_BITS2
- 1))) {
382 if (bn_wexpand(r
, j
) == NULL
)
384 /* 2^(top*BN_BITS2) - m */
385 r
->d
[0] = (0 - m
->d
[0]) & BN_MASK2
;
386 for (i
= 1; i
< j
; i
++)
387 r
->d
[i
] = (~m
->d
[i
]) & BN_MASK2
;
389 r
->flags
|= BN_FLG_FIXED_TOP
;
392 if (!bn_to_mont_fixed_top(r
, BN_value_one(), mont
, ctx
))
395 if (BN_is_bit_set(p
, wstart
) == 0) {
397 if (!bn_mul_mont_fixed_top(r
, r
, r
, mont
, ctx
))
406 * We now have wstart on a 'set' bit, we now need to work out how bit
407 * a window to do. To do this we need to scan forward until the last
408 * set bit before the end of the window
412 for (i
= 1; i
< window
; i
++) {
415 if (BN_is_bit_set(p
, wstart
- i
)) {
416 wvalue
<<= (i
- wend
);
422 /* wend is the size of the current window */
424 /* add the 'bytes above' */
426 for (i
= 0; i
< j
; i
++) {
427 if (!bn_mul_mont_fixed_top(r
, r
, r
, mont
, ctx
))
431 /* wvalue will be an odd number < 2^window */
432 if (!bn_mul_mont_fixed_top(r
, r
, val
[wvalue
>> 1], mont
, ctx
))
435 /* move the 'window' down further */
443 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
444 * removes padding [if any] and makes return value suitable for public
447 #if defined(SPARC_T4_MONT)
448 if (OPENSSL_sparcv9cap_P
[0] & (SPARCV9_VIS3
| SPARCV9_PREFER_FPU
)) {
449 j
= mont
->N
.top
; /* borrow j */
450 val
[0]->d
[0] = 1; /* borrow val[0] */
451 for (i
= 1; i
< j
; i
++)
454 if (!BN_mod_mul_montgomery(rr
, r
, val
[0], mont
, ctx
))
458 if (!BN_from_montgomery(rr
, r
, mont
, ctx
))
463 BN_MONT_CTX_free(mont
);
469 static BN_ULONG
bn_get_bits(const BIGNUM
*a
, int bitpos
)
474 wordpos
= bitpos
/ BN_BITS2
;
476 if (wordpos
>= 0 && wordpos
< a
->top
) {
477 ret
= a
->d
[wordpos
] & BN_MASK2
;
480 if (++wordpos
< a
->top
)
481 ret
|= a
->d
[wordpos
] << (BN_BITS2
- bitpos
);
485 return ret
& BN_MASK2
;
489 * BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
490 * layout so that accessing any of these table values shows the same access
491 * pattern as far as cache lines are concerned. The following functions are
492 * used to transfer a BIGNUM from/to that table.
495 static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM
*b
, int top
,
496 unsigned char *buf
, int idx
,
500 int width
= 1 << window
;
501 BN_ULONG
*table
= (BN_ULONG
*)buf
;
504 top
= b
->top
; /* this works because 'buf' is explicitly
506 for (i
= 0, j
= idx
; i
< top
; i
++, j
+= width
) {
513 static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM
*b
, int top
,
514 unsigned char *buf
, int idx
,
518 int width
= 1 << window
;
520 * We declare table 'volatile' in order to discourage compiler
521 * from reordering loads from the table. Concern is that if
522 * reordered in specific manner loads might give away the
523 * information we are trying to conceal. Some would argue that
524 * compiler can reorder them anyway, but it can as well be
525 * argued that doing so would be violation of standard...
527 volatile BN_ULONG
*table
= (volatile BN_ULONG
*)buf
;
529 if (bn_wexpand(b
, top
) == NULL
)
533 for (i
= 0; i
< top
; i
++, table
+= width
) {
536 for (j
= 0; j
< width
; j
++) {
538 ((BN_ULONG
)0 - (constant_time_eq_int(j
,idx
)&1));
544 int xstride
= 1 << (window
- 2);
545 BN_ULONG y0
, y1
, y2
, y3
;
547 i
= idx
>> (window
- 2); /* equivalent of idx / xstride */
548 idx
&= xstride
- 1; /* equivalent of idx % xstride */
550 y0
= (BN_ULONG
)0 - (constant_time_eq_int(i
,0)&1);
551 y1
= (BN_ULONG
)0 - (constant_time_eq_int(i
,1)&1);
552 y2
= (BN_ULONG
)0 - (constant_time_eq_int(i
,2)&1);
553 y3
= (BN_ULONG
)0 - (constant_time_eq_int(i
,3)&1);
555 for (i
= 0; i
< top
; i
++, table
+= width
) {
558 for (j
= 0; j
< xstride
; j
++) {
559 acc
|= ( (table
[j
+ 0 * xstride
] & y0
) |
560 (table
[j
+ 1 * xstride
] & y1
) |
561 (table
[j
+ 2 * xstride
] & y2
) |
562 (table
[j
+ 3 * xstride
] & y3
) )
563 & ((BN_ULONG
)0 - (constant_time_eq_int(j
,idx
)&1));
571 b
->flags
|= BN_FLG_FIXED_TOP
;
576 * Given a pointer value, compute the next address that is a cache line
579 #define MOD_EXP_CTIME_ALIGN(x_) \
580 ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
583 * This variant of BN_mod_exp_mont() uses fixed windows and the special
584 * precomputation memory layout to limit data-dependency to a minimum to
585 * protect secret exponents (cf. the hyper-threading timing attacks pointed
586 * out by Colin Percival,
587 * http://www.daemonology.net/hyperthreading-considered-harmful/)
589 int BN_mod_exp_mont_consttime(BIGNUM
*rr
, const BIGNUM
*a
, const BIGNUM
*p
,
590 const BIGNUM
*m
, BN_CTX
*ctx
,
591 BN_MONT_CTX
*in_mont
)
593 int i
, bits
, ret
= 0, window
, wvalue
, wmask
, window0
;
595 BN_MONT_CTX
*mont
= NULL
;
598 unsigned char *powerbufFree
= NULL
;
600 unsigned char *powerbuf
= NULL
;
602 #if defined(SPARC_T4_MONT)
611 ERR_raise(ERR_LIB_BN
, BN_R_CALLED_WITH_EVEN_MODULUS
);
618 * Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak
619 * whether the top bits are zero.
621 bits
= p
->top
* BN_BITS2
;
623 /* x**0 mod 1, or x**0 mod -1 is still zero. */
624 if (BN_abs_is_word(m
, 1)) {
636 * Allocate a montgomery context if it was not supplied by the caller. If
637 * this is not done, things will break in the montgomery part.
642 if ((mont
= BN_MONT_CTX_new()) == NULL
)
644 if (!BN_MONT_CTX_set(mont
, m
, ctx
))
648 if (a
->neg
|| BN_ucmp(a
, m
) >= 0) {
649 BIGNUM
*reduced
= BN_CTX_get(ctx
);
651 || !BN_nnmod(reduced
, a
, m
, ctx
)) {
659 * If the size of the operands allow it, perform the optimized
660 * RSAZ exponentiation. For further information see
661 * crypto/bn/rsaz_exp.c and accompanying assembly modules.
663 if ((16 == a
->top
) && (16 == p
->top
) && (BN_num_bits(m
) == 1024)
664 && rsaz_avx2_eligible()) {
665 if (NULL
== bn_wexpand(rr
, 16))
667 RSAZ_1024_mod_exp_avx2(rr
->d
, a
->d
, p
->d
, m
->d
, mont
->RR
.d
,
674 } else if ((8 == a
->top
) && (8 == p
->top
) && (BN_num_bits(m
) == 512)) {
675 if (NULL
== bn_wexpand(rr
, 8))
677 RSAZ_512_mod_exp(rr
->d
, a
->d
, p
->d
, m
->d
, mont
->n0
[0], mont
->RR
.d
);
686 /* Get the window size to use with size of p. */
687 window
= BN_window_bits_for_ctime_exponent_size(bits
);
688 #if defined(SPARC_T4_MONT)
689 if (window
>= 5 && (top
& 15) == 0 && top
<= 64 &&
690 (OPENSSL_sparcv9cap_P
[1] & (CFR_MONTMUL
| CFR_MONTSQR
)) ==
691 (CFR_MONTMUL
| CFR_MONTSQR
) && (t4
= OPENSSL_sparcv9cap_P
[0]))
695 #if defined(OPENSSL_BN_ASM_MONT5)
697 window
= 5; /* ~5% improvement for RSA2048 sign, and even
699 /* reserve space for mont->N.d[] copy */
700 powerbufLen
+= top
* sizeof(mont
->N
.d
[0]);
706 * Allocate a buffer large enough to hold all of the pre-computed powers
707 * of am, am itself and tmp.
709 numPowers
= 1 << window
;
710 powerbufLen
+= sizeof(m
->d
[0]) * (top
* numPowers
+
712 numPowers
? (2 * top
) : numPowers
));
714 if (powerbufLen
< 3072)
716 alloca(powerbufLen
+ MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH
);
720 OPENSSL_malloc(powerbufLen
+ MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH
))
724 powerbuf
= MOD_EXP_CTIME_ALIGN(powerbufFree
);
725 memset(powerbuf
, 0, powerbufLen
);
728 if (powerbufLen
< 3072)
732 /* lay down tmp and am right after powers table */
733 tmp
.d
= (BN_ULONG
*)(powerbuf
+ sizeof(m
->d
[0]) * top
* numPowers
);
735 tmp
.top
= am
.top
= 0;
736 tmp
.dmax
= am
.dmax
= top
;
737 tmp
.neg
= am
.neg
= 0;
738 tmp
.flags
= am
.flags
= BN_FLG_STATIC_DATA
;
740 /* prepare a^0 in Montgomery domain */
741 #if 1 /* by Shay Gueron's suggestion */
742 if (m
->d
[top
- 1] & (((BN_ULONG
)1) << (BN_BITS2
- 1))) {
743 /* 2^(top*BN_BITS2) - m */
744 tmp
.d
[0] = (0 - m
->d
[0]) & BN_MASK2
;
745 for (i
= 1; i
< top
; i
++)
746 tmp
.d
[i
] = (~m
->d
[i
]) & BN_MASK2
;
750 if (!bn_to_mont_fixed_top(&tmp
, BN_value_one(), mont
, ctx
))
753 /* prepare a^1 in Montgomery domain */
754 if (!bn_to_mont_fixed_top(&am
, a
, mont
, ctx
))
757 #if defined(SPARC_T4_MONT)
759 typedef int (*bn_pwr5_mont_f
) (BN_ULONG
*tp
, const BN_ULONG
*np
,
760 const BN_ULONG
*n0
, const void *table
,
761 int power
, int bits
);
762 int bn_pwr5_mont_t4_8(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_16(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_24(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_32(BN_ULONG
*tp
, const BN_ULONG
*np
,
772 const BN_ULONG
*n0
, const void *table
,
773 int power
, int bits
);
774 static const bn_pwr5_mont_f pwr5_funcs
[4] = {
775 bn_pwr5_mont_t4_8
, bn_pwr5_mont_t4_16
,
776 bn_pwr5_mont_t4_24
, bn_pwr5_mont_t4_32
778 bn_pwr5_mont_f pwr5_worker
= pwr5_funcs
[top
/ 16 - 1];
780 typedef int (*bn_mul_mont_f
) (BN_ULONG
*rp
, const BN_ULONG
*ap
,
781 const void *bp
, const BN_ULONG
*np
,
783 int bn_mul_mont_t4_8(BN_ULONG
*rp
, const BN_ULONG
*ap
, const void *bp
,
784 const BN_ULONG
*np
, const BN_ULONG
*n0
);
785 int bn_mul_mont_t4_16(BN_ULONG
*rp
, const BN_ULONG
*ap
,
786 const void *bp
, const BN_ULONG
*np
,
788 int bn_mul_mont_t4_24(BN_ULONG
*rp
, const BN_ULONG
*ap
,
789 const void *bp
, const BN_ULONG
*np
,
791 int bn_mul_mont_t4_32(BN_ULONG
*rp
, const BN_ULONG
*ap
,
792 const void *bp
, const BN_ULONG
*np
,
794 static const bn_mul_mont_f mul_funcs
[4] = {
795 bn_mul_mont_t4_8
, bn_mul_mont_t4_16
,
796 bn_mul_mont_t4_24
, bn_mul_mont_t4_32
798 bn_mul_mont_f mul_worker
= mul_funcs
[top
/ 16 - 1];
800 void bn_mul_mont_vis3(BN_ULONG
*rp
, const BN_ULONG
*ap
,
801 const void *bp
, const BN_ULONG
*np
,
802 const BN_ULONG
*n0
, int num
);
803 void bn_mul_mont_t4(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_gather5_t4(BN_ULONG
*rp
, const BN_ULONG
*ap
,
807 const void *table
, const BN_ULONG
*np
,
808 const BN_ULONG
*n0
, int num
, int power
);
809 void bn_flip_n_scatter5_t4(const BN_ULONG
*inp
, size_t num
,
810 void *table
, size_t power
);
811 void bn_gather5_t4(BN_ULONG
*out
, size_t num
,
812 void *table
, size_t power
);
813 void bn_flip_t4(BN_ULONG
*dst
, BN_ULONG
*src
, size_t num
);
815 BN_ULONG
*np
= mont
->N
.d
, *n0
= mont
->n0
;
816 int stride
= 5 * (6 - (top
/ 16 - 1)); /* multiple of 5, but less
820 * BN_to_montgomery can contaminate words above .top [in
823 for (i
= am
.top
; i
< top
; i
++)
825 for (i
= tmp
.top
; i
< top
; i
++)
828 bn_flip_n_scatter5_t4(tmp
.d
, top
, powerbuf
, 0);
829 bn_flip_n_scatter5_t4(am
.d
, top
, powerbuf
, 1);
830 if (!(*mul_worker
) (tmp
.d
, am
.d
, am
.d
, np
, n0
) &&
831 !(*mul_worker
) (tmp
.d
, am
.d
, am
.d
, np
, n0
))
832 bn_mul_mont_vis3(tmp
.d
, am
.d
, am
.d
, np
, n0
, top
);
833 bn_flip_n_scatter5_t4(tmp
.d
, top
, powerbuf
, 2);
835 for (i
= 3; i
< 32; i
++) {
836 /* Calculate a^i = a^(i-1) * a */
837 if (!(*mul_worker
) (tmp
.d
, tmp
.d
, am
.d
, np
, n0
) &&
838 !(*mul_worker
) (tmp
.d
, tmp
.d
, am
.d
, np
, n0
))
839 bn_mul_mont_vis3(tmp
.d
, tmp
.d
, am
.d
, np
, n0
, top
);
840 bn_flip_n_scatter5_t4(tmp
.d
, top
, powerbuf
, i
);
843 /* switch to 64-bit domain */
844 np
= alloca(top
* sizeof(BN_ULONG
));
846 bn_flip_t4(np
, mont
->N
.d
, top
);
849 * The exponent may not have a whole number of fixed-size windows.
850 * To simplify the main loop, the initial window has between 1 and
851 * full-window-size bits such that what remains is always a whole
854 window0
= (bits
- 1) % 5 + 1;
855 wmask
= (1 << window0
) - 1;
857 wvalue
= bn_get_bits(p
, bits
) & wmask
;
858 bn_gather5_t4(tmp
.d
, top
, powerbuf
, wvalue
);
861 * Scan the exponent one window at a time starting from the most
868 wvalue
= bn_get_bits(p
, bits
);
870 if ((*pwr5_worker
) (tmp
.d
, np
, n0
, powerbuf
, wvalue
, stride
))
872 /* retry once and fall back */
873 if ((*pwr5_worker
) (tmp
.d
, np
, n0
, powerbuf
, wvalue
, stride
))
877 wvalue
>>= stride
- 5;
879 bn_mul_mont_t4(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
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_gather5_t4(tmp
.d
, tmp
.d
, powerbuf
, np
, n0
, top
,
888 bn_flip_t4(tmp
.d
, tmp
.d
, top
);
890 /* back to 32-bit domain */
892 bn_correct_top(&tmp
);
893 OPENSSL_cleanse(np
, top
* sizeof(BN_ULONG
));
896 #if defined(OPENSSL_BN_ASM_MONT5)
897 if (window
== 5 && top
> 1) {
899 * This optimization uses ideas from http://eprint.iacr.org/2011/239,
900 * specifically optimization of cache-timing attack countermeasures
901 * and pre-computation optimization.
905 * Dedicated window==4 case improves 512-bit RSA sign by ~15%, but as
906 * 512-bit RSA is hardly relevant, we omit it to spare size...
908 void bn_mul_mont_gather5(BN_ULONG
*rp
, const BN_ULONG
*ap
,
909 const void *table
, const BN_ULONG
*np
,
910 const BN_ULONG
*n0
, int num
, int power
);
911 void bn_scatter5(const BN_ULONG
*inp
, size_t num
,
912 void *table
, size_t power
);
913 void bn_gather5(BN_ULONG
*out
, size_t num
, void *table
, size_t power
);
914 void bn_power5(BN_ULONG
*rp
, const BN_ULONG
*ap
,
915 const void *table
, const BN_ULONG
*np
,
916 const BN_ULONG
*n0
, int num
, int power
);
917 int bn_get_bits5(const BN_ULONG
*ap
, int off
);
918 int bn_from_montgomery(BN_ULONG
*rp
, const BN_ULONG
*ap
,
919 const BN_ULONG
*not_used
, const BN_ULONG
*np
,
920 const BN_ULONG
*n0
, int num
);
922 BN_ULONG
*n0
= mont
->n0
, *np
;
925 * BN_to_montgomery can contaminate words above .top [in
928 for (i
= am
.top
; i
< top
; i
++)
930 for (i
= tmp
.top
; i
< top
; i
++)
934 * copy mont->N.d[] to improve cache locality
936 for (np
= am
.d
+ top
, i
= 0; i
< top
; i
++)
937 np
[i
] = mont
->N
.d
[i
];
939 bn_scatter5(tmp
.d
, top
, powerbuf
, 0);
940 bn_scatter5(am
.d
, am
.top
, powerbuf
, 1);
941 bn_mul_mont(tmp
.d
, am
.d
, am
.d
, np
, n0
, top
);
942 bn_scatter5(tmp
.d
, top
, powerbuf
, 2);
945 for (i
= 3; i
< 32; i
++) {
946 /* Calculate a^i = a^(i-1) * a */
947 bn_mul_mont_gather5(tmp
.d
, am
.d
, powerbuf
, np
, n0
, top
, i
- 1);
948 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
951 /* same as above, but uses squaring for 1/2 of operations */
952 for (i
= 4; i
< 32; i
*= 2) {
953 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
954 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
956 for (i
= 3; i
< 8; i
+= 2) {
958 bn_mul_mont_gather5(tmp
.d
, am
.d
, powerbuf
, np
, n0
, top
, i
- 1);
959 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
960 for (j
= 2 * i
; j
< 32; j
*= 2) {
961 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
962 bn_scatter5(tmp
.d
, top
, powerbuf
, j
);
965 for (; i
< 16; i
+= 2) {
966 bn_mul_mont_gather5(tmp
.d
, am
.d
, powerbuf
, np
, n0
, top
, i
- 1);
967 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
968 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
969 bn_scatter5(tmp
.d
, top
, powerbuf
, 2 * i
);
971 for (; i
< 32; i
+= 2) {
972 bn_mul_mont_gather5(tmp
.d
, am
.d
, powerbuf
, np
, n0
, top
, i
- 1);
973 bn_scatter5(tmp
.d
, top
, powerbuf
, i
);
977 * The exponent may not have a whole number of fixed-size windows.
978 * To simplify the main loop, the initial window has between 1 and
979 * full-window-size bits such that what remains is always a whole
982 window0
= (bits
- 1) % 5 + 1;
983 wmask
= (1 << window0
) - 1;
985 wvalue
= bn_get_bits(p
, bits
) & wmask
;
986 bn_gather5(tmp
.d
, top
, powerbuf
, wvalue
);
989 * Scan the exponent one window at a time starting from the most
994 bn_mul_mont(tmp
.d
, tmp
.d
, tmp
.d
, np
, n0
, top
);
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_gather5(tmp
.d
, tmp
.d
, powerbuf
, np
, n0
, top
,
1000 bn_get_bits5(p
->d
, bits
-= 5));
1004 bn_power5(tmp
.d
, tmp
.d
, powerbuf
, np
, n0
, top
,
1005 bn_get_bits5(p
->d
, bits
-= 5));
1009 ret
= bn_from_montgomery(tmp
.d
, tmp
.d
, NULL
, np
, n0
, top
);
1011 bn_correct_top(&tmp
);
1013 if (!BN_copy(rr
, &tmp
))
1015 goto err
; /* non-zero ret means it's not error */
1020 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp
, top
, powerbuf
, 0, window
))
1022 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am
, top
, powerbuf
, 1, window
))
1026 * If the window size is greater than 1, then calculate
1027 * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
1028 * powers could instead be computed as (a^(i/2))^2 to use the slight
1029 * performance advantage of sqr over mul).
1032 if (!bn_mul_mont_fixed_top(&tmp
, &am
, &am
, mont
, ctx
))
1034 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp
, top
, powerbuf
, 2,
1037 for (i
= 3; i
< numPowers
; i
++) {
1038 /* Calculate a^i = a^(i-1) * a */
1039 if (!bn_mul_mont_fixed_top(&tmp
, &am
, &tmp
, mont
, ctx
))
1041 if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp
, top
, powerbuf
, i
,
1048 * The exponent may not have a whole number of fixed-size windows.
1049 * To simplify the main loop, the initial window has between 1 and
1050 * full-window-size bits such that what remains is always a whole
1053 window0
= (bits
- 1) % window
+ 1;
1054 wmask
= (1 << window0
) - 1;
1056 wvalue
= bn_get_bits(p
, bits
) & wmask
;
1057 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp
, top
, powerbuf
, wvalue
,
1061 wmask
= (1 << window
) - 1;
1063 * Scan the exponent one window at a time starting from the most
1068 /* Square the result window-size times */
1069 for (i
= 0; i
< window
; i
++)
1070 if (!bn_mul_mont_fixed_top(&tmp
, &tmp
, &tmp
, mont
, ctx
))
1074 * Get a window's worth of bits from the exponent
1075 * This avoids calling BN_is_bit_set for each bit, which
1076 * is not only slower but also makes each bit vulnerable to
1077 * EM (and likely other) side-channel attacks like One&Done
1078 * (for details see "One&Done: A Single-Decryption EM-Based
1079 * Attack on OpenSSL's Constant-Time Blinded RSA" by M. Alam,
1080 * H. Khan, M. Dey, N. Sinha, R. Callan, A. Zajic, and
1081 * M. Prvulovic, in USENIX Security'18)
1084 wvalue
= bn_get_bits(p
, bits
) & wmask
;
1086 * Fetch the appropriate pre-computed value from the pre-buf
1088 if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am
, top
, powerbuf
, wvalue
,
1092 /* Multiply the result into the intermediate result */
1093 if (!bn_mul_mont_fixed_top(&tmp
, &tmp
, &am
, mont
, ctx
))
1099 * Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
1100 * removes padding [if any] and makes return value suitable for public
1103 #if defined(SPARC_T4_MONT)
1104 if (OPENSSL_sparcv9cap_P
[0] & (SPARCV9_VIS3
| SPARCV9_PREFER_FPU
)) {
1105 am
.d
[0] = 1; /* borrow am */
1106 for (i
= 1; i
< top
; i
++)
1108 if (!BN_mod_mul_montgomery(rr
, &tmp
, &am
, mont
, ctx
))
1112 if (!BN_from_montgomery(rr
, &tmp
, mont
, ctx
))
1116 if (in_mont
== NULL
)
1117 BN_MONT_CTX_free(mont
);
1118 if (powerbuf
!= NULL
) {
1119 OPENSSL_cleanse(powerbuf
, powerbufLen
);
1120 OPENSSL_free(powerbufFree
);
1126 int BN_mod_exp_mont_word(BIGNUM
*rr
, BN_ULONG a
, const BIGNUM
*p
,
1127 const BIGNUM
*m
, BN_CTX
*ctx
, BN_MONT_CTX
*in_mont
)
1129 BN_MONT_CTX
*mont
= NULL
;
1130 int b
, bits
, ret
= 0;
1135 #define BN_MOD_MUL_WORD(r, w, m) \
1136 (BN_mul_word(r, (w)) && \
1137 (/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
1138 (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
1140 * BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
1141 * probably more overhead than always using BN_mod (which uses BN_copy if
1142 * a similar test returns true).
1145 * We can use BN_mod and do not need BN_nnmod because our accumulator is
1146 * never negative (the result of BN_mod does not depend on the sign of
1149 #define BN_TO_MONTGOMERY_WORD(r, w, mont) \
1150 (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
1152 if (BN_get_flags(p
, BN_FLG_CONSTTIME
) != 0
1153 || BN_get_flags(m
, BN_FLG_CONSTTIME
) != 0) {
1154 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1155 ERR_raise(ERR_LIB_BN
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
1162 if (!BN_is_odd(m
)) {
1163 ERR_raise(ERR_LIB_BN
, BN_R_CALLED_WITH_EVEN_MODULUS
);
1167 a
%= m
->d
[0]; /* make sure that 'a' is reduced */
1169 bits
= BN_num_bits(p
);
1171 /* x**0 mod 1, or x**0 mod -1 is still zero. */
1172 if (BN_abs_is_word(m
, 1)) {
1187 r
= BN_CTX_get(ctx
);
1188 t
= BN_CTX_get(ctx
);
1192 if (in_mont
!= NULL
)
1195 if ((mont
= BN_MONT_CTX_new()) == NULL
)
1197 if (!BN_MONT_CTX_set(mont
, m
, ctx
))
1201 r_is_one
= 1; /* except for Montgomery factor */
1205 /* The result is accumulated in the product r*w. */
1206 w
= a
; /* bit 'bits-1' of 'p' is always set */
1207 for (b
= bits
- 2; b
>= 0; b
--) {
1208 /* First, square r*w. */
1210 if ((next_w
/ w
) != w
) { /* overflow */
1212 if (!BN_TO_MONTGOMERY_WORD(r
, w
, mont
))
1216 if (!BN_MOD_MUL_WORD(r
, w
, m
))
1223 if (!BN_mod_mul_montgomery(r
, r
, r
, mont
, ctx
))
1227 /* Second, multiply r*w by 'a' if exponent bit is set. */
1228 if (BN_is_bit_set(p
, b
)) {
1230 if ((next_w
/ a
) != w
) { /* overflow */
1232 if (!BN_TO_MONTGOMERY_WORD(r
, w
, mont
))
1236 if (!BN_MOD_MUL_WORD(r
, w
, m
))
1245 /* Finally, set r:=r*w. */
1248 if (!BN_TO_MONTGOMERY_WORD(r
, w
, mont
))
1252 if (!BN_MOD_MUL_WORD(r
, w
, m
))
1257 if (r_is_one
) { /* can happen only if a == 1 */
1261 if (!BN_from_montgomery(rr
, r
, mont
, ctx
))
1266 if (in_mont
== NULL
)
1267 BN_MONT_CTX_free(mont
);
1273 /* The old fallback, simple version :-) */
1274 int BN_mod_exp_simple(BIGNUM
*r
, const BIGNUM
*a
, const BIGNUM
*p
,
1275 const BIGNUM
*m
, BN_CTX
*ctx
)
1277 int i
, j
, bits
, ret
= 0, wstart
, wend
, window
, wvalue
;
1280 /* Table of variables obtained from 'ctx' */
1281 BIGNUM
*val
[TABLE_SIZE
];
1283 if (BN_get_flags(p
, BN_FLG_CONSTTIME
) != 0
1284 || BN_get_flags(a
, BN_FLG_CONSTTIME
) != 0
1285 || BN_get_flags(m
, BN_FLG_CONSTTIME
) != 0) {
1286 /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
1287 ERR_raise(ERR_LIB_BN
, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED
);
1291 bits
= BN_num_bits(p
);
1293 /* x**0 mod 1, or x**0 mod -1 is still zero. */
1294 if (BN_abs_is_word(m
, 1)) {
1304 d
= BN_CTX_get(ctx
);
1305 val
[0] = BN_CTX_get(ctx
);
1309 if (!BN_nnmod(val
[0], a
, m
, ctx
))
1311 if (BN_is_zero(val
[0])) {
1317 window
= BN_window_bits_for_exponent_size(bits
);
1319 if (!BN_mod_mul(d
, val
[0], val
[0], m
, ctx
))
1321 j
= 1 << (window
- 1);
1322 for (i
= 1; i
< j
; i
++) {
1323 if (((val
[i
] = BN_CTX_get(ctx
)) == NULL
) ||
1324 !BN_mod_mul(val
[i
], val
[i
- 1], d
, m
, ctx
))
1329 start
= 1; /* This is used to avoid multiplication etc
1330 * when there is only the value '1' in the
1332 wvalue
= 0; /* The 'value' of the window */
1333 wstart
= bits
- 1; /* The top bit of the window */
1334 wend
= 0; /* The bottom bit of the window */
1340 if (BN_is_bit_set(p
, wstart
) == 0) {
1342 if (!BN_mod_mul(r
, r
, r
, m
, ctx
))
1350 * We now have wstart on a 'set' bit, we now need to work out how bit
1351 * a window to do. To do this we need to scan forward until the last
1352 * set bit before the end of the window
1356 for (i
= 1; i
< window
; i
++) {
1359 if (BN_is_bit_set(p
, wstart
- i
)) {
1360 wvalue
<<= (i
- wend
);
1366 /* wend is the size of the current window */
1368 /* add the 'bytes above' */
1370 for (i
= 0; i
< j
; i
++) {
1371 if (!BN_mod_mul(r
, r
, r
, m
, ctx
))
1375 /* wvalue will be an odd number < 2^window */
1376 if (!BN_mod_mul(r
, r
, val
[wvalue
>> 1], m
, ctx
))
1379 /* move the 'window' down further */
1394 * This is a variant of modular exponentiation optimization that does
1395 * parallel 2-primes exponentiation using 256-bit (AVX512VL) AVX512_IFMA ISA
1396 * in 52-bit binary redundant representation.
1397 * If such instructions are not available, or input data size is not supported,
1398 * it falls back to two BN_mod_exp_mont_consttime() calls.
1400 int BN_mod_exp_mont_consttime_x2(BIGNUM
*rr1
, const BIGNUM
*a1
, const BIGNUM
*p1
,
1401 const BIGNUM
*m1
, BN_MONT_CTX
*in_mont1
,
1402 BIGNUM
*rr2
, const BIGNUM
*a2
, const BIGNUM
*p2
,
1403 const BIGNUM
*m2
, BN_MONT_CTX
*in_mont2
,
1409 BN_MONT_CTX
*mont1
= NULL
;
1410 BN_MONT_CTX
*mont2
= NULL
;
1412 if (ossl_rsaz_avx512ifma_eligible() &&
1413 ((a1
->top
== 16) && (p1
->top
== 16) && (BN_num_bits(m1
) == 1024) &&
1414 (a2
->top
== 16) && (p2
->top
== 16) && (BN_num_bits(m2
) == 1024))) {
1416 if (bn_wexpand(rr1
, 16) == NULL
)
1418 if (bn_wexpand(rr2
, 16) == NULL
)
1421 /* Ensure that montgomery contexts are initialized */
1422 if (in_mont1
!= NULL
) {
1425 if ((mont1
= BN_MONT_CTX_new()) == NULL
)
1427 if (!BN_MONT_CTX_set(mont1
, m1
, ctx
))
1430 if (in_mont2
!= NULL
) {
1433 if ((mont2
= BN_MONT_CTX_new()) == NULL
)
1435 if (!BN_MONT_CTX_set(mont2
, m2
, ctx
))
1439 ret
= ossl_rsaz_mod_exp_avx512_x2(rr1
->d
, a1
->d
, p1
->d
, m1
->d
,
1440 mont1
->RR
.d
, mont1
->n0
[0],
1441 rr2
->d
, a2
->d
, p2
->d
, m2
->d
,
1442 mont2
->RR
.d
, mont2
->n0
[0],
1443 1024 /* factor bit size */);
1447 bn_correct_top(rr1
);
1452 bn_correct_top(rr2
);
1459 /* rr1 = a1^p1 mod m1 */
1460 ret
= BN_mod_exp_mont_consttime(rr1
, a1
, p1
, m1
, ctx
, in_mont1
);
1461 /* rr2 = a2^p2 mod m2 */
1462 ret
&= BN_mod_exp_mont_consttime(rr2
, a2
, p2
, m2
, ctx
, in_mont2
);
1466 if (in_mont2
== NULL
)
1467 BN_MONT_CTX_free(mont2
);
1468 if (in_mont1
== NULL
)
1469 BN_MONT_CTX_free(mont1
);