ref: 009439541d2c6e8af2596f8fb1b4df85861fd212
dir: /third_party/boringssl/src/crypto/fipsmodule/bn/div.c.inc/
/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
* All rights reserved.
*
* This package is an SSL implementation written
* by Eric Young (eay@cryptsoft.com).
* The implementation was written so as to conform with Netscapes SSL.
*
* This library is free for commercial and non-commercial use as long as
* the following conditions are aheared to. The following conditions
* apply to all code found in this distribution, be it the RC4, RSA,
* lhash, DES, etc., code; not just the SSL code. The SSL documentation
* included with this distribution is covered by the same copyright terms
* except that the holder is Tim Hudson (tjh@cryptsoft.com).
*
* Copyright remains Eric Young's, and as such any Copyright notices in
* the code are not to be removed.
* If this package is used in a product, Eric Young should be given attribution
* as the author of the parts of the library used.
* This can be in the form of a textual message at program startup or
* in documentation (online or textual) provided with the package.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. All advertising materials mentioning features or use of this software
* must display the following acknowledgement:
* "This product includes cryptographic software written by
* Eric Young (eay@cryptsoft.com)"
* The word 'cryptographic' can be left out if the rouines from the library
* being used are not cryptographic related :-).
* 4. If you include any Windows specific code (or a derivative thereof) from
* the apps directory (application code) you must include an acknowledgement:
* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
*
* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* The licence and distribution terms for any publically available version or
* derivative of this code cannot be changed. i.e. this code cannot simply be
* copied and put under another distribution licence
* [including the GNU Public Licence.] */
#include <openssl/bn.h>
#include <assert.h>
#include <limits.h>
#include <openssl/err.h>
#include "internal.h"
// bn_div_words divides a double-width |h|,|l| by |d| and returns the result,
// which must fit in a |BN_ULONG|.
OPENSSL_UNUSED static BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l,
BN_ULONG d) {
BN_ULONG dh, dl, q, ret = 0, th, tl, t;
int i, count = 2;
if (d == 0) {
return BN_MASK2;
}
i = BN_num_bits_word(d);
assert((i == BN_BITS2) || (h <= (BN_ULONG)1 << i));
i = BN_BITS2 - i;
if (h >= d) {
h -= d;
}
if (i) {
d <<= i;
h = (h << i) | (l >> (BN_BITS2 - i));
l <<= i;
}
dh = (d & BN_MASK2h) >> BN_BITS4;
dl = (d & BN_MASK2l);
for (;;) {
if ((h >> BN_BITS4) == dh) {
q = BN_MASK2l;
} else {
q = h / dh;
}
th = q * dh;
tl = dl * q;
for (;;) {
t = h - th;
if ((t & BN_MASK2h) ||
((tl) <= ((t << BN_BITS4) | ((l & BN_MASK2h) >> BN_BITS4)))) {
break;
}
q--;
th -= dh;
tl -= dl;
}
t = (tl >> BN_BITS4);
tl = (tl << BN_BITS4) & BN_MASK2h;
th += t;
if (l < tl) {
th++;
}
l -= tl;
if (h < th) {
h += d;
q--;
}
h -= th;
if (--count == 0) {
break;
}
ret = q << BN_BITS4;
h = (h << BN_BITS4) | (l >> BN_BITS4);
l = (l & BN_MASK2l) << BN_BITS4;
}
ret |= q;
return ret;
}
static inline void bn_div_rem_words(BN_ULONG *quotient_out, BN_ULONG *rem_out,
BN_ULONG n0, BN_ULONG n1, BN_ULONG d0) {
// GCC and Clang generate function calls to |__udivdi3| and |__umoddi3| when
// the |BN_ULLONG|-based C code is used.
//
// GCC bugs:
// * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=14224
// * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=43721
// * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=54183
// * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=58897
// * https://gcc.gnu.org/bugzilla/show_bug.cgi?id=65668
//
// Clang bugs:
// * https://github.com/llvm/llvm-project/issues/6769
// * https://github.com/llvm/llvm-project/issues/12790
//
// These is specific to x86 and x86_64; Arm and RISC-V do not have double-wide
// division instructions.
#if defined(BN_CAN_USE_INLINE_ASM) && defined(OPENSSL_X86)
__asm__ volatile("divl %4"
: "=a"(*quotient_out), "=d"(*rem_out)
: "a"(n1), "d"(n0), "rm"(d0)
: "cc");
#elif defined(BN_CAN_USE_INLINE_ASM) && defined(OPENSSL_X86_64)
__asm__ volatile("divq %4"
: "=a"(*quotient_out), "=d"(*rem_out)
: "a"(n1), "d"(n0), "rm"(d0)
: "cc");
#else
#if defined(BN_CAN_DIVIDE_ULLONG)
BN_ULLONG n = (((BN_ULLONG)n0) << BN_BITS2) | n1;
*quotient_out = (BN_ULONG)(n / d0);
#else
*quotient_out = bn_div_words(n0, n1, d0);
#endif
*rem_out = n1 - (*quotient_out * d0);
#endif
}
int BN_div(BIGNUM *quotient, BIGNUM *rem, const BIGNUM *numerator,
const BIGNUM *divisor, BN_CTX *ctx) {
// This function implements long division, per Knuth, The Art of Computer
// Programming, Volume 2, Chapter 4.3.1, Algorithm D. This algorithm only
// divides non-negative integers, but we round towards zero, so we divide
// absolute values and adjust the signs separately.
//
// Inputs to this function are assumed public and may be leaked by timing and
// cache side channels. Division with secret inputs should use other
// implementation strategies such as Montgomery reduction.
if (BN_is_zero(divisor)) {
OPENSSL_PUT_ERROR(BN, BN_R_DIV_BY_ZERO);
return 0;
}
BN_CTX_start(ctx);
BIGNUM *tmp = BN_CTX_get(ctx);
BIGNUM *snum = BN_CTX_get(ctx);
BIGNUM *sdiv = BN_CTX_get(ctx);
BIGNUM *res = quotient == NULL ? BN_CTX_get(ctx) : quotient;
if (tmp == NULL || snum == NULL || sdiv == NULL || res == NULL) {
goto err;
}
// Knuth step D1: Normalise the numbers such that the divisor's MSB is set.
// This ensures, in Knuth's terminology, that v1 >= b/2, needed for the
// quotient estimation step.
int norm_shift = BN_BITS2 - (BN_num_bits(divisor) % BN_BITS2);
if (!BN_lshift(sdiv, divisor, norm_shift) ||
!BN_lshift(snum, numerator, norm_shift)) {
goto err;
}
// This algorithm relies on |sdiv| being minimal width. We do not use this
// function on secret inputs, so leaking this is fine. Also minimize |snum| to
// avoid looping on leading zeros, as we're not trying to be leak-free.
bn_set_minimal_width(sdiv);
bn_set_minimal_width(snum);
int div_n = sdiv->width;
const BN_ULONG d0 = sdiv->d[div_n - 1];
const BN_ULONG d1 = (div_n == 1) ? 0 : sdiv->d[div_n - 2];
assert(d0 & (((BN_ULONG)1) << (BN_BITS2 - 1)));
// Extend |snum| with zeros to satisfy the long division invariants:
// - |snum| must have at least |div_n| + 1 words.
// - |snum|'s most significant word must be zero to guarantee the first loop
// iteration works with a prefix greater than |sdiv|. (This is the extra u0
// digit in Knuth step D1.)
int num_n = snum->width <= div_n ? div_n + 1 : snum->width + 1;
if (!bn_resize_words(snum, num_n)) {
goto err;
}
// Knuth step D2: The quotient's width is the difference between numerator and
// denominator. Also set up its sign and size a temporary for the loop.
int loop = num_n - div_n;
res->neg = snum->neg ^ sdiv->neg;
if (!bn_wexpand(res, loop) || //
!bn_wexpand(tmp, div_n + 1)) {
goto err;
}
res->width = loop;
// Knuth steps D2 through D7: Compute the quotient with a word-by-word long
// division. Note that Knuth indexes words from most to least significant, so
// our index is reversed. Each loop iteration computes res->d[i] of the
// quotient and updates snum with the running remainder. Before each loop
// iteration, the div_n words beginning at snum->d[i+1] must be less than
// snum.
for (int i = loop - 1; i >= 0; i--) {
// The next word of the quotient, q, is floor(wnum / sdiv), where wnum is
// the div_n + 1 words beginning at snum->d[i]. i starts at
// num_n - div_n - 1, so there are at least div_n + 1 words available.
//
// Knuth step D3: Compute q', an estimate of q by looking at the top words
// of wnum and sdiv. We must estimate such that q' = q or q' = q + 1.
BN_ULONG q, rm = 0;
BN_ULONG *wnum = snum->d + i;
BN_ULONG n0 = wnum[div_n];
BN_ULONG n1 = wnum[div_n - 1];
if (n0 == d0) {
// Estimate q' = b - 1, where b is the base.
q = BN_MASK2;
// Knuth also runs the fixup routine in this case, but this would require
// computing rm and is unnecessary. q' is already close enough. That is,
// the true quotient, q is either b - 1 or b - 2.
//
// By the loop invariant, q <= b - 1, so we must show that q >= b - 2. We
// do this by showing wnum / sdiv >= b - 2. Suppose wnum / sdiv < b - 2.
// wnum and sdiv have the same most significant word, so:
//
// wnum >= n0 * b^div_n
// sdiv < (n0 + 1) * b^(d_div - 1)
//
// Thus:
//
// b - 2 > wnum / sdiv
// > (n0 * b^div_n) / (n0 + 1) * b^(div_n - 1)
// = (n0 * b) / (n0 + 1)
//
// (n0 + 1) * (b - 2) > n0 * b
// n0 * b + b - 2 * n0 - 2 > n0 * b
// b - 2 > 2 * n0
// b/2 - 1 > n0
//
// This contradicts the normalization condition, so q >= b - 2 and our
// estimate is close enough.
} else {
// Estimate q' = floor(n0n1 / d0). Per Theorem B, q' - 2 <= q <= q', which
// is slightly outside of our bounds.
assert(n0 < d0);
bn_div_rem_words(&q, &rm, n0, n1, d0);
// Fix the estimate by examining one more word and adjusting q' as needed.
// This is the second half of step D3 and is sufficient per exercises 19,
// 20, and 21. Although only one iteration is needed to correct q + 2 to
// q + 1, Knuth uses a loop. A loop will often also correct q + 1 to q,
// saving the slightly more expensive underflow handling below.
if (div_n > 1) {
BN_ULONG n2 = wnum[div_n - 2];
#ifdef BN_ULLONG
BN_ULLONG t2 = (BN_ULLONG)d1 * q;
for (;;) {
if (t2 <= ((((BN_ULLONG)rm) << BN_BITS2) | n2)) {
break;
}
q--;
rm += d0;
if (rm < d0) {
// If rm overflows, the true value exceeds BN_ULONG and the next
// t2 comparison should exit the loop.
break;
}
t2 -= d1;
}
#else // !BN_ULLONG
BN_ULONG t2l, t2h;
BN_UMULT_LOHI(t2l, t2h, d1, q);
for (;;) {
if (t2h < rm || (t2h == rm && t2l <= n2)) {
break;
}
q--;
rm += d0;
if (rm < d0) {
// If rm overflows, the true value exceeds BN_ULONG and the next
// t2 comparison should exit the loop.
break;
}
if (t2l < d1) {
t2h--;
}
t2l -= d1;
}
#endif // !BN_ULLONG
}
}
// Knuth step D4 through D6: Now q' = q or q' = q + 1, and
// -sdiv < wnum - sdiv * q < sdiv. If q' = q + 1, the subtraction will
// underflow, and we fix it up below.
tmp->d[div_n] = bn_mul_words(tmp->d, sdiv->d, div_n, q);
if (bn_sub_words(wnum, wnum, tmp->d, div_n + 1)) {
q--;
// The final addition is expected to overflow, canceling the underflow.
wnum[div_n] += bn_add_words(wnum, wnum, sdiv->d, div_n);
}
// q is now correct, and wnum has been updated to the running remainder.
res->d[i] = q;
}
// Trim leading zeros and correct any negative zeros.
bn_set_minimal_width(snum);
bn_set_minimal_width(res);
// Knuth step D8: Unnormalize. snum now contains the remainder.
if (rem != NULL && !BN_rshift(rem, snum, norm_shift)) {
goto err;
}
BN_CTX_end(ctx);
return 1;
err:
BN_CTX_end(ctx);
return 0;
}
int BN_nnmod(BIGNUM *r, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx) {
if (!(BN_mod(r, m, d, ctx))) {
return 0;
}
if (!r->neg) {
return 1;
}
// now -d < r < 0, so we have to set r := r + d. Ignoring the sign bits, this
// is r = d - r.
return BN_usub(r, d, r);
}
BN_ULONG bn_reduce_once(BN_ULONG *r, const BN_ULONG *a, BN_ULONG carry,
const BN_ULONG *m, size_t num) {
assert(r != a);
// |r| = |a| - |m|. |bn_sub_words| performs the bulk of the subtraction, and
// then we apply the borrow to |carry|.
carry -= bn_sub_words(r, a, m, num);
// We know 0 <= |a| < 2*|m|, so -|m| <= |r| < |m|.
//
// If 0 <= |r| < |m|, |r| fits in |num| words and |carry| is zero. We then
// wish to select |r| as the answer. Otherwise -m <= r < 0 and we wish to
// return |r| + |m|, or |a|. |carry| must then be -1 or all ones. In both
// cases, |carry| is a suitable input to |bn_select_words|.
//
// Although |carry| may be one if it was one on input and |bn_sub_words|
// returns zero, this would give |r| > |m|, violating our input assumptions.
declassify_assert(carry + 1 <= 1);
bn_select_words(r, carry, a /* r < 0 */, r /* r >= 0 */, num);
return carry;
}
BN_ULONG bn_reduce_once_in_place(BN_ULONG *r, BN_ULONG carry, const BN_ULONG *m,
BN_ULONG *tmp, size_t num) {
// See |bn_reduce_once| for why this logic works.
carry -= bn_sub_words(tmp, r, m, num);
declassify_assert(carry + 1 <= 1);
bn_select_words(r, carry, r /* tmp < 0 */, tmp /* tmp >= 0 */, num);
return carry;
}
void bn_mod_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
const BN_ULONG *m, BN_ULONG *tmp, size_t num) {
// r = a - b
BN_ULONG borrow = bn_sub_words(r, a, b, num);
// tmp = a - b + m
bn_add_words(tmp, r, m, num);
bn_select_words(r, 0 - borrow, tmp /* r < 0 */, r /* r >= 0 */, num);
}
void bn_mod_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
const BN_ULONG *m, BN_ULONG *tmp, size_t num) {
BN_ULONG carry = bn_add_words(r, a, b, num);
bn_reduce_once_in_place(r, carry, m, tmp, num);
}
int bn_div_consttime(BIGNUM *quotient, BIGNUM *remainder,
const BIGNUM *numerator, const BIGNUM *divisor,
unsigned divisor_min_bits, BN_CTX *ctx) {
if (BN_is_negative(numerator) || BN_is_negative(divisor)) {
OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);
return 0;
}
if (BN_is_zero(divisor)) {
OPENSSL_PUT_ERROR(BN, BN_R_DIV_BY_ZERO);
return 0;
}
// This function implements long division in binary. It is not very efficient,
// but it is simple, easy to make constant-time, and performant enough for RSA
// key generation.
int ret = 0;
BN_CTX_start(ctx);
BIGNUM *q = quotient, *r = remainder;
if (quotient == NULL || quotient == numerator || quotient == divisor) {
q = BN_CTX_get(ctx);
}
if (remainder == NULL || remainder == numerator || remainder == divisor) {
r = BN_CTX_get(ctx);
}
BIGNUM *tmp = BN_CTX_get(ctx);
if (q == NULL || r == NULL || tmp == NULL ||
!bn_wexpand(q, numerator->width) ||
!bn_wexpand(r, divisor->width) ||
!bn_wexpand(tmp, divisor->width)) {
goto err;
}
OPENSSL_memset(q->d, 0, numerator->width * sizeof(BN_ULONG));
q->width = numerator->width;
q->neg = 0;
OPENSSL_memset(r->d, 0, divisor->width * sizeof(BN_ULONG));
r->width = divisor->width;
r->neg = 0;
// Incorporate |numerator| into |r|, one bit at a time, reducing after each
// step. We maintain the invariant that |0 <= r < divisor| and
// |q * divisor + r = n| where |n| is the portion of |numerator| incorporated
// so far.
//
// First, we short-circuit the loop: if we know |divisor| has at least
// |divisor_min_bits| bits, the top |divisor_min_bits - 1| can be incorporated
// without reductions. This significantly speeds up |RSA_check_key|. For
// simplicity, we round down to a whole number of words.
declassify_assert(divisor_min_bits <= BN_num_bits(divisor));
int initial_words = 0;
if (divisor_min_bits > 0) {
initial_words = (divisor_min_bits - 1) / BN_BITS2;
if (initial_words > numerator->width) {
initial_words = numerator->width;
}
OPENSSL_memcpy(r->d, numerator->d + numerator->width - initial_words,
initial_words * sizeof(BN_ULONG));
}
for (int i = numerator->width - initial_words - 1; i >= 0; i--) {
for (int bit = BN_BITS2 - 1; bit >= 0; bit--) {
// Incorporate the next bit of the numerator, by computing
// r = 2*r or 2*r + 1. Note the result fits in one more word. We store the
// extra word in |carry|.
BN_ULONG carry = bn_add_words(r->d, r->d, r->d, divisor->width);
r->d[0] |= (numerator->d[i] >> bit) & 1;
// |r| was previously fully-reduced, so we know:
// 2*0 <= r <= 2*(divisor-1) + 1
// 0 <= r <= 2*divisor - 1 < 2*divisor.
// Thus |r| satisfies the preconditions for |bn_reduce_once_in_place|.
BN_ULONG subtracted = bn_reduce_once_in_place(r->d, carry, divisor->d,
tmp->d, divisor->width);
// The corresponding bit of the quotient is set iff we needed to subtract.
q->d[i] |= (~subtracted & 1) << bit;
}
}
if ((quotient != NULL && !BN_copy(quotient, q)) ||
(remainder != NULL && !BN_copy(remainder, r))) {
goto err;
}
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
static BIGNUM *bn_scratch_space_from_ctx(size_t width, BN_CTX *ctx) {
BIGNUM *ret = BN_CTX_get(ctx);
if (ret == NULL ||
!bn_wexpand(ret, width)) {
return NULL;
}
ret->neg = 0;
ret->width = (int)width;
return ret;
}
// bn_resized_from_ctx returns |bn| with width at least |width| or NULL on
// error. This is so it may be used with low-level "words" functions. If
// necessary, it allocates a new |BIGNUM| with a lifetime of the current scope
// in |ctx|, so the caller does not need to explicitly free it. |bn| must fit in
// |width| words.
static const BIGNUM *bn_resized_from_ctx(const BIGNUM *bn, size_t width,
BN_CTX *ctx) {
if ((size_t)bn->width >= width) {
// Any excess words must be zero.
assert(bn_fits_in_words(bn, width));
return bn;
}
BIGNUM *ret = bn_scratch_space_from_ctx(width, ctx);
if (ret == NULL ||
!BN_copy(ret, bn) ||
!bn_resize_words(ret, width)) {
return NULL;
}
return ret;
}
int BN_mod_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
BN_CTX *ctx) {
if (!BN_add(r, a, b)) {
return 0;
}
return BN_nnmod(r, r, m, ctx);
}
int BN_mod_add_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
const BIGNUM *m) {
BN_CTX *ctx = BN_CTX_new();
int ok = ctx != NULL &&
bn_mod_add_consttime(r, a, b, m, ctx);
BN_CTX_free(ctx);
return ok;
}
int bn_mod_add_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
const BIGNUM *m, BN_CTX *ctx) {
BN_CTX_start(ctx);
a = bn_resized_from_ctx(a, m->width, ctx);
b = bn_resized_from_ctx(b, m->width, ctx);
BIGNUM *tmp = bn_scratch_space_from_ctx(m->width, ctx);
int ok = a != NULL && b != NULL && tmp != NULL &&
bn_wexpand(r, m->width);
if (ok) {
bn_mod_add_words(r->d, a->d, b->d, m->d, tmp->d, m->width);
r->width = m->width;
r->neg = 0;
}
BN_CTX_end(ctx);
return ok;
}
int BN_mod_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
BN_CTX *ctx) {
if (!BN_sub(r, a, b)) {
return 0;
}
return BN_nnmod(r, r, m, ctx);
}
int bn_mod_sub_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
const BIGNUM *m, BN_CTX *ctx) {
BN_CTX_start(ctx);
a = bn_resized_from_ctx(a, m->width, ctx);
b = bn_resized_from_ctx(b, m->width, ctx);
BIGNUM *tmp = bn_scratch_space_from_ctx(m->width, ctx);
int ok = a != NULL && b != NULL && tmp != NULL &&
bn_wexpand(r, m->width);
if (ok) {
bn_mod_sub_words(r->d, a->d, b->d, m->d, tmp->d, m->width);
r->width = m->width;
r->neg = 0;
}
BN_CTX_end(ctx);
return ok;
}
int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
const BIGNUM *m) {
BN_CTX *ctx = BN_CTX_new();
int ok = ctx != NULL &&
bn_mod_sub_consttime(r, a, b, m, ctx);
BN_CTX_free(ctx);
return ok;
}
int BN_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, const BIGNUM *m,
BN_CTX *ctx) {
BIGNUM *t;
int ret = 0;
BN_CTX_start(ctx);
t = BN_CTX_get(ctx);
if (t == NULL) {
goto err;
}
if (a == b) {
if (!BN_sqr(t, a, ctx)) {
goto err;
}
} else {
if (!BN_mul(t, a, b, ctx)) {
goto err;
}
}
if (!BN_nnmod(r, t, m, ctx)) {
goto err;
}
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
int BN_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx) {
if (!BN_sqr(r, a, ctx)) {
return 0;
}
// r->neg == 0, thus we don't need BN_nnmod
return BN_mod(r, r, m, ctx);
}
int BN_mod_lshift(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
BN_CTX *ctx) {
BIGNUM *abs_m = NULL;
int ret;
if (!BN_nnmod(r, a, m, ctx)) {
return 0;
}
if (m->neg) {
abs_m = BN_dup(m);
if (abs_m == NULL) {
return 0;
}
abs_m->neg = 0;
}
ret = bn_mod_lshift_consttime(r, r, n, (abs_m ? abs_m : m), ctx);
BN_free(abs_m);
return ret;
}
int bn_mod_lshift_consttime(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m,
BN_CTX *ctx) {
if (!BN_copy(r, a) ||
!bn_resize_words(r, m->width)) {
return 0;
}
BN_CTX_start(ctx);
BIGNUM *tmp = bn_scratch_space_from_ctx(m->width, ctx);
int ok = tmp != NULL;
if (ok) {
for (int i = 0; i < n; i++) {
bn_mod_add_words(r->d, r->d, r->d, m->d, tmp->d, m->width);
}
r->neg = 0;
}
BN_CTX_end(ctx);
return ok;
}
int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m) {
BN_CTX *ctx = BN_CTX_new();
int ok = ctx != NULL &&
bn_mod_lshift_consttime(r, a, n, m, ctx);
BN_CTX_free(ctx);
return ok;
}
int BN_mod_lshift1(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx) {
if (!BN_lshift1(r, a)) {
return 0;
}
return BN_nnmod(r, r, m, ctx);
}
int bn_mod_lshift1_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *m,
BN_CTX *ctx) {
return bn_mod_add_consttime(r, a, a, m, ctx);
}
int BN_mod_lshift1_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m) {
BN_CTX *ctx = BN_CTX_new();
int ok = ctx != NULL &&
bn_mod_lshift1_consttime(r, a, m, ctx);
BN_CTX_free(ctx);
return ok;
}
BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w) {
BN_ULONG ret = 0;
int i, j;
if (!w) {
// actually this an error (division by zero)
return (BN_ULONG) - 1;
}
if (a->width == 0) {
return 0;
}
// normalize input for |bn_div_rem_words|.
j = BN_BITS2 - BN_num_bits_word(w);
w <<= j;
if (!BN_lshift(a, a, j)) {
return (BN_ULONG) - 1;
}
for (i = a->width - 1; i >= 0; i--) {
BN_ULONG l = a->d[i];
BN_ULONG d;
BN_ULONG unused_rem;
bn_div_rem_words(&d, &unused_rem, ret, l, w);
ret = l - (d * w);
a->d[i] = d;
}
bn_set_minimal_width(a);
ret >>= j;
return ret;
}
BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w) {
#ifndef BN_CAN_DIVIDE_ULLONG
BN_ULONG ret = 0;
#else
BN_ULLONG ret = 0;
#endif
int i;
if (w == 0) {
return (BN_ULONG) -1;
}
#ifndef BN_CAN_DIVIDE_ULLONG
// If |w| is too long and we don't have |BN_ULLONG| division then we need to
// fall back to using |BN_div_word|.
if (w > ((BN_ULONG)1 << BN_BITS4)) {
BIGNUM *tmp = BN_dup(a);
if (tmp == NULL) {
return (BN_ULONG)-1;
}
ret = BN_div_word(tmp, w);
BN_free(tmp);
return ret;
}
#endif
for (i = a->width - 1; i >= 0; i--) {
#ifndef BN_CAN_DIVIDE_ULLONG
ret = ((ret << BN_BITS4) | ((a->d[i] >> BN_BITS4) & BN_MASK2l)) % w;
ret = ((ret << BN_BITS4) | (a->d[i] & BN_MASK2l)) % w;
#else
ret = (BN_ULLONG)(((ret << (BN_ULLONG)BN_BITS2) | a->d[i]) % (BN_ULLONG)w);
#endif
}
return (BN_ULONG)ret;
}
int BN_mod_pow2(BIGNUM *r, const BIGNUM *a, size_t e) {
if (e == 0 || a->width == 0) {
BN_zero(r);
return 1;
}
size_t num_words = 1 + ((e - 1) / BN_BITS2);
// If |a| definitely has less than |e| bits, just BN_copy.
if ((size_t) a->width < num_words) {
return BN_copy(r, a) != NULL;
}
// Otherwise, first make sure we have enough space in |r|.
// Note that this will fail if num_words > INT_MAX.
if (!bn_wexpand(r, num_words)) {
return 0;
}
// Copy the content of |a| into |r|.
OPENSSL_memcpy(r->d, a->d, num_words * sizeof(BN_ULONG));
// If |e| isn't word-aligned, we have to mask off some of our bits.
size_t top_word_exponent = e % (sizeof(BN_ULONG) * 8);
if (top_word_exponent != 0) {
r->d[num_words - 1] &= (((BN_ULONG) 1) << top_word_exponent) - 1;
}
// Fill in the remaining fields of |r|.
r->neg = a->neg;
r->width = (int) num_words;
bn_set_minimal_width(r);
return 1;
}
int BN_nnmod_pow2(BIGNUM *r, const BIGNUM *a, size_t e) {
if (!BN_mod_pow2(r, a, e)) {
return 0;
}
// If the returned value was non-negative, we're done.
if (BN_is_zero(r) || !r->neg) {
return 1;
}
size_t num_words = 1 + (e - 1) / BN_BITS2;
// Expand |r| to the size of our modulus.
if (!bn_wexpand(r, num_words)) {
return 0;
}
// Clear the upper words of |r|.
OPENSSL_memset(&r->d[r->width], 0, (num_words - r->width) * BN_BYTES);
// Set parameters of |r|.
r->neg = 0;
r->width = (int) num_words;
// Now, invert every word. The idea here is that we want to compute 2^e-|x|,
// which is actually equivalent to the twos-complement representation of |x|
// in |e| bits, which is -x = ~x + 1.
for (int i = 0; i < r->width; i++) {
r->d[i] = ~r->d[i];
}
// If our exponent doesn't span the top word, we have to mask the rest.
size_t top_word_exponent = e % BN_BITS2;
if (top_word_exponent != 0) {
r->d[r->width - 1] &= (((BN_ULONG) 1) << top_word_exponent) - 1;
}
// Keep the minimal-width invariant for |BIGNUM|.
bn_set_minimal_width(r);
// Finally, add one, for the reason described above.
return BN_add(r, r, BN_value_one());
}