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/* 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"
#if !defined(BN_ULLONG)
/* bn_div_words divides a double-width |h|,|l| by |d| and returns the result,
* which must fit in a |BN_ULONG|. */
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)) & BN_MASK2;
l = (l & BN_MASK2l) << BN_BITS4;
}
ret |= q;
return ret;
}
#endif /* !defined(BN_ULLONG) */
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://llvm.org/bugs/show_bug.cgi?id=6397
* * https://llvm.org/bugs/show_bug.cgi?id=12418
*
* These issues aren't specific to x86 and x86_64, so it might be worthwhile
* to add more assembly language implementations. */
#if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86) && defined(__GNUC__)
__asm__ volatile (
"divl %4"
: "=a"(*quotient_out), "=d"(*rem_out)
: "a"(n1), "d"(n0), "rm"(d0)
: "cc" );
#elif !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && defined(__GNUC__)
__asm__ volatile (
"divq %4"
: "=a"(*quotient_out), "=d"(*rem_out)
: "a"(n1), "d"(n0), "rm"(d0)
: "cc" );
#else
#if defined(BN_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
}
/* BN_div computes dv := num / divisor, rounding towards
* zero, and sets up rm such that dv*divisor + rm = num holds.
* Thus:
* dv->neg == num->neg ^ divisor->neg (unless the result is zero)
* rm->neg == num->neg (unless the remainder is zero)
* If 'dv' or 'rm' is NULL, the respective value is not returned.
*
* This was specifically designed to contain fewer branches that may leak
* sensitive information; see "New Branch Prediction Vulnerabilities in OpenSSL
* and Necessary Software Countermeasures" by Onur Acıçmez, Shay Gueron, and
* Jean-Pierre Seifert. */
int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
BN_CTX *ctx) {
int norm_shift, i, loop;
BIGNUM *tmp, wnum, *snum, *sdiv, *res;
BN_ULONG *resp, *wnump;
BN_ULONG d0, d1;
int num_n, div_n;
/* Invalid zero-padding would have particularly bad consequences
* so don't just rely on bn_check_top() here */
if ((num->top > 0 && num->d[num->top - 1] == 0) ||
(divisor->top > 0 && divisor->d[divisor->top - 1] == 0)) {
OPENSSL_PUT_ERROR(BN, BN_R_NOT_INITIALIZED);
return 0;
}
if (BN_is_zero(divisor)) {
OPENSSL_PUT_ERROR(BN, BN_R_DIV_BY_ZERO);
return 0;
}
BN_CTX_start(ctx);
tmp = BN_CTX_get(ctx);
snum = BN_CTX_get(ctx);
sdiv = BN_CTX_get(ctx);
if (dv == NULL) {
res = BN_CTX_get(ctx);
} else {
res = dv;
}
if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL) {
goto err;
}
/* First we normalise the numbers */
norm_shift = BN_BITS2 - ((BN_num_bits(divisor)) % BN_BITS2);
if (!(BN_lshift(sdiv, divisor, norm_shift))) {
goto err;
}
sdiv->neg = 0;
norm_shift += BN_BITS2;
if (!(BN_lshift(snum, num, norm_shift))) {
goto err;
}
snum->neg = 0;
/* Since we don't want to have special-case logic for the case where snum is
* larger than sdiv, we pad snum with enough zeroes without changing its
* value. */
if (snum->top <= sdiv->top + 1) {
if (bn_wexpand(snum, sdiv->top + 2) == NULL) {
goto err;
}
for (i = snum->top; i < sdiv->top + 2; i++) {
snum->d[i] = 0;
}
snum->top = sdiv->top + 2;
} else {
if (bn_wexpand(snum, snum->top + 1) == NULL) {
goto err;
}
snum->d[snum->top] = 0;
snum->top++;
}
div_n = sdiv->top;
num_n = snum->top;
loop = num_n - div_n;
/* Lets setup a 'window' into snum
* This is the part that corresponds to the current
* 'area' being divided */
wnum.neg = 0;
wnum.d = &(snum->d[loop]);
wnum.top = div_n;
/* only needed when BN_ucmp messes up the values between top and max */
wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
/* Get the top 2 words of sdiv */
/* div_n=sdiv->top; */
d0 = sdiv->d[div_n - 1];
d1 = (div_n == 1) ? 0 : sdiv->d[div_n - 2];
/* pointer to the 'top' of snum */
wnump = &(snum->d[num_n - 1]);
/* Setup to 'res' */
res->neg = (num->neg ^ divisor->neg);
if (!bn_wexpand(res, (loop + 1))) {
goto err;
}
res->top = loop - 1;
resp = &(res->d[loop - 1]);
/* space for temp */
if (!bn_wexpand(tmp, (div_n + 1))) {
goto err;
}
/* if res->top == 0 then clear the neg value otherwise decrease
* the resp pointer */
if (res->top == 0) {
res->neg = 0;
} else {
resp--;
}
for (i = 0; i < loop - 1; i++, wnump--, resp--) {
BN_ULONG q, l0;
/* the first part of the loop uses the top two words of snum and sdiv to
* calculate a BN_ULONG q such that | wnum - sdiv * q | < sdiv */
BN_ULONG n0, n1, rem = 0;
n0 = wnump[0];
n1 = wnump[-1];
if (n0 == d0) {
q = BN_MASK2;
} else {
/* n0 < d0 */
bn_div_rem_words(&q, &rem, n0, n1, d0);
#ifdef BN_ULLONG
BN_ULLONG t2 = (BN_ULLONG)d1 * q;
for (;;) {
if (t2 <= ((((BN_ULLONG)rem) << BN_BITS2) | wnump[-2])) {
break;
}
q--;
rem += d0;
if (rem < d0) {
break; /* don't let rem overflow */
}
t2 -= d1;
}
#else /* !BN_ULLONG */
BN_ULONG t2l, t2h;
BN_UMULT_LOHI(t2l, t2h, d1, q);
for (;;) {
if ((t2h < rem) || ((t2h == rem) && (t2l <= wnump[-2]))) {
break;
}
q--;
rem += d0;
if (rem < d0) {
break; /* don't let rem overflow */
}
if (t2l < d1) {
t2h--;
}
t2l -= d1;
}
#endif /* !BN_ULLONG */
}
l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q);
tmp->d[div_n] = l0;
wnum.d--;
/* ingore top values of the bignums just sub the two
* BN_ULONG arrays with bn_sub_words */
if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n + 1)) {
/* Note: As we have considered only the leading
* two BN_ULONGs in the calculation of q, sdiv * q
* might be greater than wnum (but then (q-1) * sdiv
* is less or equal than wnum)
*/
q--;
if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n)) {
/* we can't have an overflow here (assuming
* that q != 0, but if q == 0 then tmp is
* zero anyway) */
(*wnump)++;
}
}
/* store part of the result */
*resp = q;
}
bn_correct_top(snum);
if (rm != NULL) {
/* Keep a copy of the neg flag in num because if rm==num
* BN_rshift() will overwrite it.
*/
int neg = num->neg;
if (!BN_rshift(rm, snum, norm_shift)) {
goto err;
}
if (!BN_is_zero(rm)) {
rm->neg = neg;
}
}
bn_correct_top(res);
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|. */
return (d->neg ? BN_sub : BN_add)(r, r, d);
}
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) {
if (!BN_uadd(r, a, b)) {
return 0;
}
if (BN_ucmp(r, m) >= 0) {
return BN_usub(r, r, m);
}
return 1;
}
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);
}
/* BN_mod_sub variant that may be used if both a and b are non-negative
* and less than m */
int BN_mod_sub_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
const BIGNUM *m) {
if (!BN_sub(r, a, b)) {
return 0;
}
if (r->neg) {
return BN_add(r, r, m);
}
return 1;
}
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_quick(r, r, n, (abs_m ? abs_m : m));
BN_free(abs_m);
return ret;
}
int BN_mod_lshift_quick(BIGNUM *r, const BIGNUM *a, int n, const BIGNUM *m) {
if (r != a) {
if (BN_copy(r, a) == NULL) {
return 0;
}
}
while (n > 0) {
int max_shift;
/* 0 < r < m */
max_shift = BN_num_bits(m) - BN_num_bits(r);
/* max_shift >= 0 */
if (max_shift < 0) {
OPENSSL_PUT_ERROR(BN, BN_R_INPUT_NOT_REDUCED);
return 0;
}
if (max_shift > n) {
max_shift = n;
}
if (max_shift) {
if (!BN_lshift(r, r, max_shift)) {
return 0;
}
n -= max_shift;
} else {
if (!BN_lshift1(r, r)) {
return 0;
}
--n;
}
/* BN_num_bits(r) <= BN_num_bits(m) */
if (BN_cmp(r, m) >= 0) {
if (!BN_sub(r, r, m)) {
return 0;
}
}
}
return 1;
}
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_quick(BIGNUM *r, const BIGNUM *a, const BIGNUM *m) {
if (!BN_lshift1(r, a)) {
return 0;
}
if (BN_cmp(r, m) >= 0) {
return BN_sub(r, r, m);
}
return 1;
}
BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w) {
BN_ULONG ret = 0;
int i, j;
w &= BN_MASK2;
if (!w) {
/* actually this an error (division by zero) */
return (BN_ULONG) - 1;
}
if (a->top == 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->top - 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) & BN_MASK2)) & BN_MASK2;
a->d[i] = d;
}
if ((a->top > 0) && (a->d[a->top - 1] == 0)) {
a->top--;
}
if (a->top == 0) {
a->neg = 0;
}
ret >>= j;
return ret;
}
BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w) {
#ifndef BN_ULLONG
BN_ULONG ret = 0;
#else
BN_ULLONG ret = 0;
#endif
int i;
if (w == 0) {
return (BN_ULONG) -1;
}
#ifndef BN_ULLONG
/* If |w| is too long and we don't have |BN_ULLONG| 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
w &= BN_MASK2;
for (i = a->top - 1; i >= 0; i--) {
#ifndef BN_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->top == 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->top < 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) == NULL) {
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->top = (int) num_words;
bn_correct_top(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) == NULL) {
return 0;
}
/* Clear the upper words of |r|. */
OPENSSL_memset(&r->d[r->top], 0, (num_words - r->top) * BN_BYTES);
/* Set parameters of |r|. */
r->neg = 0;
r->top = (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->top; 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->top - 1] &= (((BN_ULONG) 1) << top_word_exponent) - 1;
}
/* Keep the correct_top invariant for BN_add. */
bn_correct_top(r);
/* Finally, add one, for the reason described above. */
return BN_add(r, r, BN_value_one());
}