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openssl/crypto/bn/bn_exp.c

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v1.1.1t
2023-05-09 22:08:48 +00:00
/*
* Copyright 1995-2023 The OpenSSL Project Authors. All Rights Reserved.
*
* Licensed under the OpenSSL license (the "License"). You may not use
* this file except in compliance with the License. You can obtain a copy
* in the file LICENSE in the source distribution or at
* https://www.openssl.org/source/license.html
*/
#include "internal/cryptlib.h"
#include "internal/constant_time.h"
#include "bn_local.h"
#include <stdlib.h>
#ifdef _WIN32
# include <malloc.h>
# ifndef alloca
# define alloca _alloca
# endif
#elif defined(__GNUC__)
# ifndef alloca
# define alloca(s) __builtin_alloca((s))
# endif
#elif defined(__sun)
# include <alloca.h>
#endif
#include "rsaz_exp.h"
#undef SPARC_T4_MONT
#if defined(OPENSSL_BN_ASM_MONT) && (defined(__sparc__) || defined(__sparc))
# include "sparc_arch.h"
extern unsigned int OPENSSL_sparcv9cap_P[];
# define SPARC_T4_MONT
#endif
/* maximum precomputation table size for *variable* sliding windows */
#define TABLE_SIZE 32
/*
* Beyond this limit the constant time code is disabled due to
* the possible overflow in the computation of powerbufLen in
* BN_mod_exp_mont_consttime.
* When this limit is exceeded, the computation will be done using
* non-constant time code, but it will take very long.
*/
#define BN_CONSTTIME_SIZE_LIMIT (INT_MAX / BN_BYTES / 256)
/* this one works - simple but works */
int BN_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
{
int i, bits, ret = 0;
BIGNUM *v, *rr;
if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
|| BN_get_flags(a, BN_FLG_CONSTTIME) != 0) {
/* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
BNerr(BN_F_BN_EXP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
return 0;
}
BN_CTX_start(ctx);
rr = ((r == a) || (r == p)) ? BN_CTX_get(ctx) : r;
v = BN_CTX_get(ctx);
if (rr == NULL || v == NULL)
goto err;
if (BN_copy(v, a) == NULL)
goto err;
bits = BN_num_bits(p);
if (BN_is_odd(p)) {
if (BN_copy(rr, a) == NULL)
goto err;
} else {
if (!BN_one(rr))
goto err;
}
for (i = 1; i < bits; i++) {
if (!BN_sqr(v, v, ctx))
goto err;
if (BN_is_bit_set(p, i)) {
if (!BN_mul(rr, rr, v, ctx))
goto err;
}
}
if (r != rr && BN_copy(r, rr) == NULL)
goto err;
ret = 1;
err:
BN_CTX_end(ctx);
bn_check_top(r);
return ret;
}
int BN_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
BN_CTX *ctx)
{
int ret;
bn_check_top(a);
bn_check_top(p);
bn_check_top(m);
/*-
* For even modulus m = 2^k*m_odd, it might make sense to compute
* a^p mod m_odd and a^p mod 2^k separately (with Montgomery
* exponentiation for the odd part), using appropriate exponent
* reductions, and combine the results using the CRT.
*
* For now, we use Montgomery only if the modulus is odd; otherwise,
* exponentiation using the reciprocal-based quick remaindering
* algorithm is used.
*
* (Timing obtained with expspeed.c [computations a^p mod m
* where a, p, m are of the same length: 256, 512, 1024, 2048,
* 4096, 8192 bits], compared to the running time of the
* standard algorithm:
*
* BN_mod_exp_mont 33 .. 40 % [AMD K6-2, Linux, debug configuration]
* 55 .. 77 % [UltraSparc processor, but
* debug-solaris-sparcv8-gcc conf.]
*
* BN_mod_exp_recp 50 .. 70 % [AMD K6-2, Linux, debug configuration]
* 62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
*
* On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
* at 2048 and more bits, but at 512 and 1024 bits, it was
* slower even than the standard algorithm!
*
* "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
* should be obtained when the new Montgomery reduction code
* has been integrated into OpenSSL.)
*/
#define MONT_MUL_MOD
#define MONT_EXP_WORD
#define RECP_MUL_MOD
#ifdef MONT_MUL_MOD
if (BN_is_odd(m)) {
# ifdef MONT_EXP_WORD
if (a->top == 1 && !a->neg
&& (BN_get_flags(p, BN_FLG_CONSTTIME) == 0)
&& (BN_get_flags(a, BN_FLG_CONSTTIME) == 0)
&& (BN_get_flags(m, BN_FLG_CONSTTIME) == 0)) {
BN_ULONG A = a->d[0];
ret = BN_mod_exp_mont_word(r, A, p, m, ctx, NULL);
} else
# endif
ret = BN_mod_exp_mont(r, a, p, m, ctx, NULL);
} else
#endif
#ifdef RECP_MUL_MOD
{
ret = BN_mod_exp_recp(r, a, p, m, ctx);
}
#else
{
ret = BN_mod_exp_simple(r, a, p, m, ctx);
}
#endif
bn_check_top(r);
return ret;
}
int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
const BIGNUM *m, BN_CTX *ctx)
{
int i, j, bits, ret = 0, wstart, wend, window, wvalue;
int start = 1;
BIGNUM *aa;
/* Table of variables obtained from 'ctx' */
BIGNUM *val[TABLE_SIZE];
BN_RECP_CTX recp;
if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
|| BN_get_flags(a, BN_FLG_CONSTTIME) != 0
|| BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
/* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
BNerr(BN_F_BN_MOD_EXP_RECP, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
return 0;
}
bits = BN_num_bits(p);
if (bits == 0) {
/* x**0 mod 1, or x**0 mod -1 is still zero. */
if (BN_abs_is_word(m, 1)) {
ret = 1;
BN_zero(r);
} else {
ret = BN_one(r);
}
return ret;
}
BN_RECP_CTX_init(&recp);
BN_CTX_start(ctx);
aa = BN_CTX_get(ctx);
val[0] = BN_CTX_get(ctx);
if (val[0] == NULL)
goto err;
if (m->neg) {
/* ignore sign of 'm' */
if (!BN_copy(aa, m))
goto err;
aa->neg = 0;
if (BN_RECP_CTX_set(&recp, aa, ctx) <= 0)
goto err;
} else {
if (BN_RECP_CTX_set(&recp, m, ctx) <= 0)
goto err;
}
if (!BN_nnmod(val[0], a, m, ctx))
goto err; /* 1 */
if (BN_is_zero(val[0])) {
BN_zero(r);
ret = 1;
goto err;
}
window = BN_window_bits_for_exponent_size(bits);
if (window > 1) {
if (!BN_mod_mul_reciprocal(aa, val[0], val[0], &recp, ctx))
goto err; /* 2 */
j = 1 << (window - 1);
for (i = 1; i < j; i++) {
if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
!BN_mod_mul_reciprocal(val[i], val[i - 1], aa, &recp, ctx))
goto err;
}
}
start = 1; /* This is used to avoid multiplication etc
* when there is only the value '1' in the
* buffer. */
wvalue = 0; /* The 'value' of the window */
wstart = bits - 1; /* The top bit of the window */
wend = 0; /* The bottom bit of the window */
if (!BN_one(r))
goto err;
for (;;) {
if (BN_is_bit_set(p, wstart) == 0) {
if (!start)
if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
goto err;
if (wstart == 0)
break;
wstart--;
continue;
}
/*
* We now have wstart on a 'set' bit, we now need to work out how bit
* a window to do. To do this we need to scan forward until the last
* set bit before the end of the window
*/
j = wstart;
wvalue = 1;
wend = 0;
for (i = 1; i < window; i++) {
if (wstart - i < 0)
break;
if (BN_is_bit_set(p, wstart - i)) {
wvalue <<= (i - wend);
wvalue |= 1;
wend = i;
}
}
/* wend is the size of the current window */
j = wend + 1;
/* add the 'bytes above' */
if (!start)
for (i = 0; i < j; i++) {
if (!BN_mod_mul_reciprocal(r, r, r, &recp, ctx))
goto err;
}
/* wvalue will be an odd number < 2^window */
if (!BN_mod_mul_reciprocal(r, r, val[wvalue >> 1], &recp, ctx))
goto err;
/* move the 'window' down further */
wstart -= wend + 1;
wvalue = 0;
start = 0;
if (wstart < 0)
break;
}
ret = 1;
err:
BN_CTX_end(ctx);
BN_RECP_CTX_free(&recp);
bn_check_top(r);
return ret;
}
int BN_mod_exp_mont(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
{
int i, j, bits, ret = 0, wstart, wend, window, wvalue;
int start = 1;
BIGNUM *d, *r;
const BIGNUM *aa;
/* Table of variables obtained from 'ctx' */
BIGNUM *val[TABLE_SIZE];
BN_MONT_CTX *mont = NULL;
bn_check_top(a);
bn_check_top(p);
bn_check_top(m);
if (!BN_is_odd(m)) {
BNerr(BN_F_BN_MOD_EXP_MONT, BN_R_CALLED_WITH_EVEN_MODULUS);
return 0;
}
if (m->top <= BN_CONSTTIME_SIZE_LIMIT
&& (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
|| BN_get_flags(a, BN_FLG_CONSTTIME) != 0
|| BN_get_flags(m, BN_FLG_CONSTTIME) != 0)) {
return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
}
bits = BN_num_bits(p);
if (bits == 0) {
/* x**0 mod 1, or x**0 mod -1 is still zero. */
if (BN_abs_is_word(m, 1)) {
ret = 1;
BN_zero(rr);
} else {
ret = BN_one(rr);
}
return ret;
}
BN_CTX_start(ctx);
d = BN_CTX_get(ctx);
r = BN_CTX_get(ctx);
val[0] = BN_CTX_get(ctx);
if (val[0] == NULL)
goto err;
/*
* If this is not done, things will break in the montgomery part
*/
if (in_mont != NULL)
mont = in_mont;
else {
if ((mont = BN_MONT_CTX_new()) == NULL)
goto err;
if (!BN_MONT_CTX_set(mont, m, ctx))
goto err;
}
if (a->neg || BN_ucmp(a, m) >= 0) {
if (!BN_nnmod(val[0], a, m, ctx))
goto err;
aa = val[0];
} else
aa = a;
if (!bn_to_mont_fixed_top(val[0], aa, mont, ctx))
goto err; /* 1 */
window = BN_window_bits_for_exponent_size(bits);
if (window > 1) {
if (!bn_mul_mont_fixed_top(d, val[0], val[0], mont, ctx))
goto err; /* 2 */
j = 1 << (window - 1);
for (i = 1; i < j; i++) {
if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
!bn_mul_mont_fixed_top(val[i], val[i - 1], d, mont, ctx))
goto err;
}
}
start = 1; /* This is used to avoid multiplication etc
* when there is only the value '1' in the
* buffer. */
wvalue = 0; /* The 'value' of the window */
wstart = bits - 1; /* The top bit of the window */
wend = 0; /* The bottom bit of the window */
#if 1 /* by Shay Gueron's suggestion */
j = m->top; /* borrow j */
if (m->d[j - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
if (bn_wexpand(r, j) == NULL)
goto err;
/* 2^(top*BN_BITS2) - m */
r->d[0] = (0 - m->d[0]) & BN_MASK2;
for (i = 1; i < j; i++)
r->d[i] = (~m->d[i]) & BN_MASK2;
r->top = j;
r->flags |= BN_FLG_FIXED_TOP;
} else
#endif
if (!bn_to_mont_fixed_top(r, BN_value_one(), mont, ctx))
goto err;
for (;;) {
if (BN_is_bit_set(p, wstart) == 0) {
if (!start) {
if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx))
goto err;
}
if (wstart == 0)
break;
wstart--;
continue;
}
/*
* We now have wstart on a 'set' bit, we now need to work out how bit
* a window to do. To do this we need to scan forward until the last
* set bit before the end of the window
*/
j = wstart;
wvalue = 1;
wend = 0;
for (i = 1; i < window; i++) {
if (wstart - i < 0)
break;
if (BN_is_bit_set(p, wstart - i)) {
wvalue <<= (i - wend);
wvalue |= 1;
wend = i;
}
}
/* wend is the size of the current window */
j = wend + 1;
/* add the 'bytes above' */
if (!start)
for (i = 0; i < j; i++) {
if (!bn_mul_mont_fixed_top(r, r, r, mont, ctx))
goto err;
}
/* wvalue will be an odd number < 2^window */
if (!bn_mul_mont_fixed_top(r, r, val[wvalue >> 1], mont, ctx))
goto err;
/* move the 'window' down further */
wstart -= wend + 1;
wvalue = 0;
start = 0;
if (wstart < 0)
break;
}
/*
* Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
* removes padding [if any] and makes return value suitable for public
* API consumer.
*/
#if defined(SPARC_T4_MONT)
if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
j = mont->N.top; /* borrow j */
val[0]->d[0] = 1; /* borrow val[0] */
for (i = 1; i < j; i++)
val[0]->d[i] = 0;
val[0]->top = j;
if (!BN_mod_mul_montgomery(rr, r, val[0], mont, ctx))
goto err;
} else
#endif
if (!BN_from_montgomery(rr, r, mont, ctx))
goto err;
ret = 1;
err:
if (in_mont == NULL)
BN_MONT_CTX_free(mont);
BN_CTX_end(ctx);
bn_check_top(rr);
return ret;
}
static BN_ULONG bn_get_bits(const BIGNUM *a, int bitpos)
{
BN_ULONG ret = 0;
int wordpos;
wordpos = bitpos / BN_BITS2;
bitpos %= BN_BITS2;
if (wordpos >= 0 && wordpos < a->top) {
ret = a->d[wordpos] & BN_MASK2;
if (bitpos) {
ret >>= bitpos;
if (++wordpos < a->top)
ret |= a->d[wordpos] << (BN_BITS2 - bitpos);
}
}
return ret & BN_MASK2;
}
/*
* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific
* layout so that accessing any of these table values shows the same access
* pattern as far as cache lines are concerned. The following functions are
* used to transfer a BIGNUM from/to that table.
*/
static int MOD_EXP_CTIME_COPY_TO_PREBUF(const BIGNUM *b, int top,
unsigned char *buf, int idx,
int window)
{
int i, j;
int width = 1 << window;
BN_ULONG *table = (BN_ULONG *)buf;
if (top > b->top)
top = b->top; /* this works because 'buf' is explicitly
* zeroed */
for (i = 0, j = idx; i < top; i++, j += width) {
table[j] = b->d[i];
}
return 1;
}
static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top,
unsigned char *buf, int idx,
int window)
{
int i, j;
int width = 1 << window;
/*
* We declare table 'volatile' in order to discourage compiler
* from reordering loads from the table. Concern is that if
* reordered in specific manner loads might give away the
* information we are trying to conceal. Some would argue that
* compiler can reorder them anyway, but it can as well be
* argued that doing so would be violation of standard...
*/
volatile BN_ULONG *table = (volatile BN_ULONG *)buf;
if (bn_wexpand(b, top) == NULL)
return 0;
if (window <= 3) {
for (i = 0; i < top; i++, table += width) {
BN_ULONG acc = 0;
for (j = 0; j < width; j++) {
acc |= table[j] &
((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
}
b->d[i] = acc;
}
} else {
int xstride = 1 << (window - 2);
BN_ULONG y0, y1, y2, y3;
i = idx >> (window - 2); /* equivalent of idx / xstride */
idx &= xstride - 1; /* equivalent of idx % xstride */
y0 = (BN_ULONG)0 - (constant_time_eq_int(i,0)&1);
y1 = (BN_ULONG)0 - (constant_time_eq_int(i,1)&1);
y2 = (BN_ULONG)0 - (constant_time_eq_int(i,2)&1);
y3 = (BN_ULONG)0 - (constant_time_eq_int(i,3)&1);
for (i = 0; i < top; i++, table += width) {
BN_ULONG acc = 0;
for (j = 0; j < xstride; j++) {
acc |= ( (table[j + 0 * xstride] & y0) |
(table[j + 1 * xstride] & y1) |
(table[j + 2 * xstride] & y2) |
(table[j + 3 * xstride] & y3) )
& ((BN_ULONG)0 - (constant_time_eq_int(j,idx)&1));
}
b->d[i] = acc;
}
}
b->top = top;
b->flags |= BN_FLG_FIXED_TOP;
return 1;
}
/*
* Given a pointer value, compute the next address that is a cache line
* multiple.
*/
#define MOD_EXP_CTIME_ALIGN(x_) \
((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((size_t)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))
/*
* This variant of BN_mod_exp_mont() uses fixed windows and the special
* precomputation memory layout to limit data-dependency to a minimum to
* protect secret exponents (cf. the hyper-threading timing attacks pointed
* out by Colin Percival,
* http://www.daemonology.net/hyperthreading-considered-harmful/)
*/
int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
const BIGNUM *m, BN_CTX *ctx,
BN_MONT_CTX *in_mont)
{
int i, bits, ret = 0, window, wvalue, wmask, window0;
int top;
BN_MONT_CTX *mont = NULL;
int numPowers;
unsigned char *powerbufFree = NULL;
int powerbufLen = 0;
unsigned char *powerbuf = NULL;
BIGNUM tmp, am;
#if defined(SPARC_T4_MONT)
unsigned int t4 = 0;
#endif
bn_check_top(a);
bn_check_top(p);
bn_check_top(m);
if (!BN_is_odd(m)) {
BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME, BN_R_CALLED_WITH_EVEN_MODULUS);
return 0;
}
top = m->top;
if (top > BN_CONSTTIME_SIZE_LIMIT) {
/* Prevent overflowing the powerbufLen computation below */
return BN_mod_exp_mont(rr, a, p, m, ctx, in_mont);
}
/*
* Use all bits stored in |p|, rather than |BN_num_bits|, so we do not leak
* whether the top bits are zero.
*/
bits = p->top * BN_BITS2;
if (bits == 0) {
/* x**0 mod 1, or x**0 mod -1 is still zero. */
if (BN_abs_is_word(m, 1)) {
ret = 1;
BN_zero(rr);
} else {
ret = BN_one(rr);
}
return ret;
}
BN_CTX_start(ctx);
/*
* Allocate a montgomery context if it was not supplied by the caller. If
* this is not done, things will break in the montgomery part.
*/
if (in_mont != NULL)
mont = in_mont;
else {
if ((mont = BN_MONT_CTX_new()) == NULL)
goto err;
if (!BN_MONT_CTX_set(mont, m, ctx))
goto err;
}
if (a->neg || BN_ucmp(a, m) >= 0) {
BIGNUM *reduced = BN_CTX_get(ctx);
if (reduced == NULL
|| !BN_nnmod(reduced, a, m, ctx)) {
goto err;
}
a = reduced;
}
#ifdef RSAZ_ENABLED
/*
* If the size of the operands allow it, perform the optimized
* RSAZ exponentiation. For further information see
* crypto/bn/rsaz_exp.c and accompanying assembly modules.
*/
if ((16 == a->top) && (16 == p->top) && (BN_num_bits(m) == 1024)
&& rsaz_avx2_eligible()) {
if (NULL == bn_wexpand(rr, 16))
goto err;
RSAZ_1024_mod_exp_avx2(rr->d, a->d, p->d, m->d, mont->RR.d,
mont->n0[0]);
rr->top = 16;
rr->neg = 0;
bn_correct_top(rr);
ret = 1;
goto err;
} else if ((8 == a->top) && (8 == p->top) && (BN_num_bits(m) == 512)) {
if (NULL == bn_wexpand(rr, 8))
goto err;
RSAZ_512_mod_exp(rr->d, a->d, p->d, m->d, mont->n0[0], mont->RR.d);
rr->top = 8;
rr->neg = 0;
bn_correct_top(rr);
ret = 1;
goto err;
}
#endif
/* Get the window size to use with size of p. */
window = BN_window_bits_for_ctime_exponent_size(bits);
#if defined(SPARC_T4_MONT)
if (window >= 5 && (top & 15) == 0 && top <= 64 &&
(OPENSSL_sparcv9cap_P[1] & (CFR_MONTMUL | CFR_MONTSQR)) ==
(CFR_MONTMUL | CFR_MONTSQR) && (t4 = OPENSSL_sparcv9cap_P[0]))
window = 5;
else
#endif
#if defined(OPENSSL_BN_ASM_MONT5)
if (window >= 5 && top <= BN_SOFT_LIMIT) {
window = 5; /* ~5% improvement for RSA2048 sign, and even
* for RSA4096 */
/* reserve space for mont->N.d[] copy */
powerbufLen += top * sizeof(mont->N.d[0]);
}
#endif
(void)0;
/*
* Allocate a buffer large enough to hold all of the pre-computed powers
* of am, am itself and tmp.
*/
numPowers = 1 << window;
powerbufLen += sizeof(m->d[0]) * (top * numPowers +
((2 * top) >
numPowers ? (2 * top) : numPowers));
#ifdef alloca
if (powerbufLen < 3072)
powerbufFree =
alloca(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH);
else
#endif
if ((powerbufFree =
OPENSSL_malloc(powerbufLen + MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH))
== NULL)
goto err;
powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
memset(powerbuf, 0, powerbufLen);
#ifdef alloca
if (powerbufLen < 3072)
powerbufFree = NULL;
#endif
/* lay down tmp and am right after powers table */
tmp.d = (BN_ULONG *)(powerbuf + sizeof(m->d[0]) * top * numPowers);
am.d = tmp.d + top;
tmp.top = am.top = 0;
tmp.dmax = am.dmax = top;
tmp.neg = am.neg = 0;
tmp.flags = am.flags = BN_FLG_STATIC_DATA;
/* prepare a^0 in Montgomery domain */
#if 1 /* by Shay Gueron's suggestion */
if (m->d[top - 1] & (((BN_ULONG)1) << (BN_BITS2 - 1))) {
/* 2^(top*BN_BITS2) - m */
tmp.d[0] = (0 - m->d[0]) & BN_MASK2;
for (i = 1; i < top; i++)
tmp.d[i] = (~m->d[i]) & BN_MASK2;
tmp.top = top;
} else
#endif
if (!bn_to_mont_fixed_top(&tmp, BN_value_one(), mont, ctx))
goto err;
/* prepare a^1 in Montgomery domain */
if (!bn_to_mont_fixed_top(&am, a, mont, ctx))
goto err;
if (top > BN_SOFT_LIMIT)
goto fallback;
#if defined(SPARC_T4_MONT)
if (t4) {
typedef int (*bn_pwr5_mont_f) (BN_ULONG *tp, const BN_ULONG *np,
const BN_ULONG *n0, const void *table,
int power, int bits);
int bn_pwr5_mont_t4_8(BN_ULONG *tp, const BN_ULONG *np,
const BN_ULONG *n0, const void *table,
int power, int bits);
int bn_pwr5_mont_t4_16(BN_ULONG *tp, const BN_ULONG *np,
const BN_ULONG *n0, const void *table,
int power, int bits);
int bn_pwr5_mont_t4_24(BN_ULONG *tp, const BN_ULONG *np,
const BN_ULONG *n0, const void *table,
int power, int bits);
int bn_pwr5_mont_t4_32(BN_ULONG *tp, const BN_ULONG *np,
const BN_ULONG *n0, const void *table,
int power, int bits);
static const bn_pwr5_mont_f pwr5_funcs[4] = {
bn_pwr5_mont_t4_8, bn_pwr5_mont_t4_16,
bn_pwr5_mont_t4_24, bn_pwr5_mont_t4_32
};
bn_pwr5_mont_f pwr5_worker = pwr5_funcs[top / 16 - 1];
typedef int (*bn_mul_mont_f) (BN_ULONG *rp, const BN_ULONG *ap,
const void *bp, const BN_ULONG *np,
const BN_ULONG *n0);
int bn_mul_mont_t4_8(BN_ULONG *rp, const BN_ULONG *ap, const void *bp,
const BN_ULONG *np, const BN_ULONG *n0);
int bn_mul_mont_t4_16(BN_ULONG *rp, const BN_ULONG *ap,
const void *bp, const BN_ULONG *np,
const BN_ULONG *n0);
int bn_mul_mont_t4_24(BN_ULONG *rp, const BN_ULONG *ap,
const void *bp, const BN_ULONG *np,
const BN_ULONG *n0);
int bn_mul_mont_t4_32(BN_ULONG *rp, const BN_ULONG *ap,
const void *bp, const BN_ULONG *np,
const BN_ULONG *n0);
static const bn_mul_mont_f mul_funcs[4] = {
bn_mul_mont_t4_8, bn_mul_mont_t4_16,
bn_mul_mont_t4_24, bn_mul_mont_t4_32
};
bn_mul_mont_f mul_worker = mul_funcs[top / 16 - 1];
void bn_mul_mont_vis3(BN_ULONG *rp, const BN_ULONG *ap,
const void *bp, const BN_ULONG *np,
const BN_ULONG *n0, int num);
void bn_mul_mont_t4(BN_ULONG *rp, const BN_ULONG *ap,
const void *bp, const BN_ULONG *np,
const BN_ULONG *n0, int num);
void bn_mul_mont_gather5_t4(BN_ULONG *rp, const BN_ULONG *ap,
const void *table, const BN_ULONG *np,
const BN_ULONG *n0, int num, int power);
void bn_flip_n_scatter5_t4(const BN_ULONG *inp, size_t num,
void *table, size_t power);
void bn_gather5_t4(BN_ULONG *out, size_t num,
void *table, size_t power);
void bn_flip_t4(BN_ULONG *dst, BN_ULONG *src, size_t num);
BN_ULONG *np = mont->N.d, *n0 = mont->n0;
int stride = 5 * (6 - (top / 16 - 1)); /* multiple of 5, but less
* than 32 */
/*
* BN_to_montgomery can contaminate words above .top [in
* BN_DEBUG[_DEBUG] build]...
*/
for (i = am.top; i < top; i++)
am.d[i] = 0;
for (i = tmp.top; i < top; i++)
tmp.d[i] = 0;
bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 0);
bn_flip_n_scatter5_t4(am.d, top, powerbuf, 1);
if (!(*mul_worker) (tmp.d, am.d, am.d, np, n0) &&
!(*mul_worker) (tmp.d, am.d, am.d, np, n0))
bn_mul_mont_vis3(tmp.d, am.d, am.d, np, n0, top);
bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, 2);
for (i = 3; i < 32; i++) {
/* Calculate a^i = a^(i-1) * a */
if (!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0) &&
!(*mul_worker) (tmp.d, tmp.d, am.d, np, n0))
bn_mul_mont_vis3(tmp.d, tmp.d, am.d, np, n0, top);
bn_flip_n_scatter5_t4(tmp.d, top, powerbuf, i);
}
/* switch to 64-bit domain */
np = alloca(top * sizeof(BN_ULONG));
top /= 2;
bn_flip_t4(np, mont->N.d, top);
/*
* The exponent may not have a whole number of fixed-size windows.
* To simplify the main loop, the initial window has between 1 and
* full-window-size bits such that what remains is always a whole
* number of windows
*/
window0 = (bits - 1) % 5 + 1;
wmask = (1 << window0) - 1;
bits -= window0;
wvalue = bn_get_bits(p, bits) & wmask;
bn_gather5_t4(tmp.d, top, powerbuf, wvalue);
/*
* Scan the exponent one window at a time starting from the most
* significant bits.
*/
while (bits > 0) {
if (bits < stride)
stride = bits;
bits -= stride;
wvalue = bn_get_bits(p, bits);
if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
continue;
/* retry once and fall back */
if ((*pwr5_worker) (tmp.d, np, n0, powerbuf, wvalue, stride))
continue;
bits += stride - 5;
wvalue >>= stride - 5;
wvalue &= 31;
bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
bn_mul_mont_t4(tmp.d, tmp.d, tmp.d, np, n0, top);
bn_mul_mont_gather5_t4(tmp.d, tmp.d, powerbuf, np, n0, top,
wvalue);
}
bn_flip_t4(tmp.d, tmp.d, top);
top *= 2;
/* back to 32-bit domain */
tmp.top = top;
bn_correct_top(&tmp);
OPENSSL_cleanse(np, top * sizeof(BN_ULONG));
} else
#endif
#if defined(OPENSSL_BN_ASM_MONT5)
if (window == 5 && top > 1) {
/*
* This optimization uses ideas from https://eprint.iacr.org/2011/239,
* specifically optimization of cache-timing attack countermeasures,
* pre-computation optimization, and Almost Montgomery Multiplication.
*
* The paper discusses a 4-bit window to optimize 512-bit modular
* exponentiation, used in RSA-1024 with CRT, but RSA-1024 is no longer
* important.
*
* |bn_mul_mont_gather5| and |bn_power5| implement the "almost"
* reduction variant, so the values here may not be fully reduced.
* They are bounded by R (i.e. they fit in |top| words), not |m|.
* Additionally, we pass these "almost" reduced inputs into
* |bn_mul_mont|, which implements the normal reduction variant.
* Given those inputs, |bn_mul_mont| may not give reduced
* output, but it will still produce "almost" reduced output.
*/
void bn_mul_mont_gather5(BN_ULONG *rp, const BN_ULONG *ap,
const void *table, const BN_ULONG *np,
const BN_ULONG *n0, int num, int power);
void bn_scatter5(const BN_ULONG *inp, size_t num,
void *table, size_t power);
void bn_gather5(BN_ULONG *out, size_t num, void *table, size_t power);
void bn_power5(BN_ULONG *rp, const BN_ULONG *ap,
const void *table, const BN_ULONG *np,
const BN_ULONG *n0, int num, int power);
int bn_get_bits5(const BN_ULONG *ap, int off);
BN_ULONG *n0 = mont->n0, *np;
/*
* BN_to_montgomery can contaminate words above .top [in
* BN_DEBUG[_DEBUG] build]...
*/
for (i = am.top; i < top; i++)
am.d[i] = 0;
for (i = tmp.top; i < top; i++)
tmp.d[i] = 0;
/*
* copy mont->N.d[] to improve cache locality
*/
for (np = am.d + top, i = 0; i < top; i++)
np[i] = mont->N.d[i];
bn_scatter5(tmp.d, top, powerbuf, 0);
bn_scatter5(am.d, am.top, powerbuf, 1);
bn_mul_mont(tmp.d, am.d, am.d, np, n0, top);
bn_scatter5(tmp.d, top, powerbuf, 2);
# if 0
for (i = 3; i < 32; i++) {
/* Calculate a^i = a^(i-1) * a */
bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
bn_scatter5(tmp.d, top, powerbuf, i);
}
# else
/* same as above, but uses squaring for 1/2 of operations */
for (i = 4; i < 32; i *= 2) {
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
bn_scatter5(tmp.d, top, powerbuf, i);
}
for (i = 3; i < 8; i += 2) {
int j;
bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
bn_scatter5(tmp.d, top, powerbuf, i);
for (j = 2 * i; j < 32; j *= 2) {
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
bn_scatter5(tmp.d, top, powerbuf, j);
}
}
for (; i < 16; i += 2) {
bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
bn_scatter5(tmp.d, top, powerbuf, i);
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
bn_scatter5(tmp.d, top, powerbuf, 2 * i);
}
for (; i < 32; i += 2) {
bn_mul_mont_gather5(tmp.d, am.d, powerbuf, np, n0, top, i - 1);
bn_scatter5(tmp.d, top, powerbuf, i);
}
# endif
/*
* The exponent may not have a whole number of fixed-size windows.
* To simplify the main loop, the initial window has between 1 and
* full-window-size bits such that what remains is always a whole
* number of windows
*/
window0 = (bits - 1) % 5 + 1;
wmask = (1 << window0) - 1;
bits -= window0;
wvalue = bn_get_bits(p, bits) & wmask;
bn_gather5(tmp.d, top, powerbuf, wvalue);
/*
* Scan the exponent one window at a time starting from the most
* significant bits.
*/
if (top & 7) {
while (bits > 0) {
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
bn_mul_mont(tmp.d, tmp.d, tmp.d, np, n0, top);
bn_mul_mont_gather5(tmp.d, tmp.d, powerbuf, np, n0, top,
bn_get_bits5(p->d, bits -= 5));
}
} else {
while (bits > 0) {
bn_power5(tmp.d, tmp.d, powerbuf, np, n0, top,
bn_get_bits5(p->d, bits -= 5));
}
}
tmp.top = top;
/*
* The result is now in |tmp| in Montgomery form, but it may not be
* fully reduced. This is within bounds for |BN_from_montgomery|
* (tmp < R <= m*R) so it will, when converting from Montgomery form,
* produce a fully reduced result.
*
* This differs from Figure 2 of the paper, which uses AMM(h, 1) to
* convert from Montgomery form with unreduced output, followed by an
* extra reduction step. In the paper's terminology, we replace
* steps 9 and 10 with MM(h, 1).
*/
} else
#endif
{
fallback:
if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 0, window))
goto err;
if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&am, top, powerbuf, 1, window))
goto err;
/*
* If the window size is greater than 1, then calculate
* val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1) (even
* powers could instead be computed as (a^(i/2))^2 to use the slight
* performance advantage of sqr over mul).
*/
if (window > 1) {
if (!bn_mul_mont_fixed_top(&tmp, &am, &am, mont, ctx))
goto err;
if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, 2,
window))
goto err;
for (i = 3; i < numPowers; i++) {
/* Calculate a^i = a^(i-1) * a */
if (!bn_mul_mont_fixed_top(&tmp, &am, &tmp, mont, ctx))
goto err;
if (!MOD_EXP_CTIME_COPY_TO_PREBUF(&tmp, top, powerbuf, i,
window))
goto err;
}
}
/*
* The exponent may not have a whole number of fixed-size windows.
* To simplify the main loop, the initial window has between 1 and
* full-window-size bits such that what remains is always a whole
* number of windows
*/
window0 = (bits - 1) % window + 1;
wmask = (1 << window0) - 1;
bits -= window0;
wvalue = bn_get_bits(p, bits) & wmask;
if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&tmp, top, powerbuf, wvalue,
window))
goto err;
wmask = (1 << window) - 1;
/*
* Scan the exponent one window at a time starting from the most
* significant bits.
*/
while (bits > 0) {
/* Square the result window-size times */
for (i = 0; i < window; i++)
if (!bn_mul_mont_fixed_top(&tmp, &tmp, &tmp, mont, ctx))
goto err;
/*
* Get a window's worth of bits from the exponent
* This avoids calling BN_is_bit_set for each bit, which
* is not only slower but also makes each bit vulnerable to
* EM (and likely other) side-channel attacks like One&Done
* (for details see "One&Done: A Single-Decryption EM-Based
* Attack on OpenSSL's Constant-Time Blinded RSA" by M. Alam,
* H. Khan, M. Dey, N. Sinha, R. Callan, A. Zajic, and
* M. Prvulovic, in USENIX Security'18)
*/
bits -= window;
wvalue = bn_get_bits(p, bits) & wmask;
/*
* Fetch the appropriate pre-computed value from the pre-buf
*/
if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(&am, top, powerbuf, wvalue,
window))
goto err;
/* Multiply the result into the intermediate result */
if (!bn_mul_mont_fixed_top(&tmp, &tmp, &am, mont, ctx))
goto err;
}
}
/*
* Done with zero-padded intermediate BIGNUMs. Final BN_from_montgomery
* removes padding [if any] and makes return value suitable for public
* API consumer.
*/
#if defined(SPARC_T4_MONT)
if (OPENSSL_sparcv9cap_P[0] & (SPARCV9_VIS3 | SPARCV9_PREFER_FPU)) {
am.d[0] = 1; /* borrow am */
for (i = 1; i < top; i++)
am.d[i] = 0;
if (!BN_mod_mul_montgomery(rr, &tmp, &am, mont, ctx))
goto err;
} else
#endif
if (!BN_from_montgomery(rr, &tmp, mont, ctx))
goto err;
ret = 1;
err:
if (in_mont == NULL)
BN_MONT_CTX_free(mont);
if (powerbuf != NULL) {
OPENSSL_cleanse(powerbuf, powerbufLen);
OPENSSL_free(powerbufFree);
}
BN_CTX_end(ctx);
return ret;
}
int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
{
BN_MONT_CTX *mont = NULL;
int b, bits, ret = 0;
int r_is_one;
BN_ULONG w, next_w;
BIGNUM *r, *t;
BIGNUM *swap_tmp;
#define BN_MOD_MUL_WORD(r, w, m) \
(BN_mul_word(r, (w)) && \
(/* BN_ucmp(r, (m)) < 0 ? 1 :*/ \
(BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
/*
* BN_MOD_MUL_WORD is only used with 'w' large, so the BN_ucmp test is
* probably more overhead than always using BN_mod (which uses BN_copy if
* a similar test returns true).
*/
/*
* We can use BN_mod and do not need BN_nnmod because our accumulator is
* never negative (the result of BN_mod does not depend on the sign of
* the modulus).
*/
#define BN_TO_MONTGOMERY_WORD(r, w, mont) \
(BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))
if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
|| BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
/* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
BNerr(BN_F_BN_MOD_EXP_MONT_WORD, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
return 0;
}
bn_check_top(p);
bn_check_top(m);
if (!BN_is_odd(m)) {
BNerr(BN_F_BN_MOD_EXP_MONT_WORD, BN_R_CALLED_WITH_EVEN_MODULUS);
return 0;
}
if (m->top == 1)
a %= m->d[0]; /* make sure that 'a' is reduced */
bits = BN_num_bits(p);
if (bits == 0) {
/* x**0 mod 1, or x**0 mod -1 is still zero. */
if (BN_abs_is_word(m, 1)) {
ret = 1;
BN_zero(rr);
} else {
ret = BN_one(rr);
}
return ret;
}
if (a == 0) {
BN_zero(rr);
ret = 1;
return ret;
}
BN_CTX_start(ctx);
r = BN_CTX_get(ctx);
t = BN_CTX_get(ctx);
if (t == NULL)
goto err;
if (in_mont != NULL)
mont = in_mont;
else {
if ((mont = BN_MONT_CTX_new()) == NULL)
goto err;
if (!BN_MONT_CTX_set(mont, m, ctx))
goto err;
}
r_is_one = 1; /* except for Montgomery factor */
/* bits-1 >= 0 */
/* The result is accumulated in the product r*w. */
w = a; /* bit 'bits-1' of 'p' is always set */
for (b = bits - 2; b >= 0; b--) {
/* First, square r*w. */
next_w = w * w;
if ((next_w / w) != w) { /* overflow */
if (r_is_one) {
if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
goto err;
r_is_one = 0;
} else {
if (!BN_MOD_MUL_WORD(r, w, m))
goto err;
}
next_w = 1;
}
w = next_w;
if (!r_is_one) {
if (!BN_mod_mul_montgomery(r, r, r, mont, ctx))
goto err;
}
/* Second, multiply r*w by 'a' if exponent bit is set. */
if (BN_is_bit_set(p, b)) {
next_w = w * a;
if ((next_w / a) != w) { /* overflow */
if (r_is_one) {
if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
goto err;
r_is_one = 0;
} else {
if (!BN_MOD_MUL_WORD(r, w, m))
goto err;
}
next_w = a;
}
w = next_w;
}
}
/* Finally, set r:=r*w. */
if (w != 1) {
if (r_is_one) {
if (!BN_TO_MONTGOMERY_WORD(r, w, mont))
goto err;
r_is_one = 0;
} else {
if (!BN_MOD_MUL_WORD(r, w, m))
goto err;
}
}
if (r_is_one) { /* can happen only if a == 1 */
if (!BN_one(rr))
goto err;
} else {
if (!BN_from_montgomery(rr, r, mont, ctx))
goto err;
}
ret = 1;
err:
if (in_mont == NULL)
BN_MONT_CTX_free(mont);
BN_CTX_end(ctx);
bn_check_top(rr);
return ret;
}
/* The old fallback, simple version :-) */
int BN_mod_exp_simple(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
const BIGNUM *m, BN_CTX *ctx)
{
int i, j, bits, ret = 0, wstart, wend, window, wvalue;
int start = 1;
BIGNUM *d;
/* Table of variables obtained from 'ctx' */
BIGNUM *val[TABLE_SIZE];
if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0
|| BN_get_flags(a, BN_FLG_CONSTTIME) != 0
|| BN_get_flags(m, BN_FLG_CONSTTIME) != 0) {
/* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
BNerr(BN_F_BN_MOD_EXP_SIMPLE, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
return 0;
}
bits = BN_num_bits(p);
if (bits == 0) {
/* x**0 mod 1, or x**0 mod -1 is still zero. */
if (BN_abs_is_word(m, 1)) {
ret = 1;
BN_zero(r);
} else {
ret = BN_one(r);
}
return ret;
}
BN_CTX_start(ctx);
d = BN_CTX_get(ctx);
val[0] = BN_CTX_get(ctx);
if (val[0] == NULL)
goto err;
if (!BN_nnmod(val[0], a, m, ctx))
goto err; /* 1 */
if (BN_is_zero(val[0])) {
BN_zero(r);
ret = 1;
goto err;
}
window = BN_window_bits_for_exponent_size(bits);
if (window > 1) {
if (!BN_mod_mul(d, val[0], val[0], m, ctx))
goto err; /* 2 */
j = 1 << (window - 1);
for (i = 1; i < j; i++) {
if (((val[i] = BN_CTX_get(ctx)) == NULL) ||
!BN_mod_mul(val[i], val[i - 1], d, m, ctx))
goto err;
}
}
start = 1; /* This is used to avoid multiplication etc
* when there is only the value '1' in the
* buffer. */
wvalue = 0; /* The 'value' of the window */
wstart = bits - 1; /* The top bit of the window */
wend = 0; /* The bottom bit of the window */
if (!BN_one(r))
goto err;
for (;;) {
if (BN_is_bit_set(p, wstart) == 0) {
if (!start)
if (!BN_mod_mul(r, r, r, m, ctx))
goto err;
if (wstart == 0)
break;
wstart--;
continue;
}
/*
* We now have wstart on a 'set' bit, we now need to work out how bit
* a window to do. To do this we need to scan forward until the last
* set bit before the end of the window
*/
j = wstart;
wvalue = 1;
wend = 0;
for (i = 1; i < window; i++) {
if (wstart - i < 0)
break;
if (BN_is_bit_set(p, wstart - i)) {
wvalue <<= (i - wend);
wvalue |= 1;
wend = i;
}
}
/* wend is the size of the current window */
j = wend + 1;
/* add the 'bytes above' */
if (!start)
for (i = 0; i < j; i++) {
if (!BN_mod_mul(r, r, r, m, ctx))
goto err;
}
/* wvalue will be an odd number < 2^window */
if (!BN_mod_mul(r, r, val[wvalue >> 1], m, ctx))
goto err;
/* move the 'window' down further */
wstart -= wend + 1;
wvalue = 0;
start = 0;
if (wstart < 0)
break;
}
ret = 1;
err:
BN_CTX_end(ctx);
bn_check_top(r);
return ret;
}