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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 <limits.h>
#include <openssl/err.h>
#include "internal.h"
#define asm __asm__
#if !defined(OPENSSL_NO_ASM)
# if defined(__GNUC__) && __GNUC__>=2
# if defined(OPENSSL_X86)
/*
* There were two reasons for implementing this template:
* - GNU C generates a call to a function (__udivdi3 to be exact)
* in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
* understand why...);
* - divl doesn't only calculate quotient, but also leaves
* remainder in %edx which we can definitely use here:-)
*
* <appro@fy.chalmers.se>
*/
#undef div_asm
# define div_asm(n0,n1,d0) \
({ asm volatile ( \
"divl %4" \
: "=a"(q), "=d"(rem) \
: "a"(n1), "d"(n0), "g"(d0) \
: "cc"); \
q; \
})
# define REMAINDER_IS_ALREADY_CALCULATED
# elif defined(OPENSSL_X86_64)
/*
* Same story here, but it's 128-bit by 64-bit division. Wow!
* <appro@fy.chalmers.se>
*/
# undef div_asm
# define div_asm(n0,n1,d0) \
({ asm volatile ( \
"divq %4" \
: "=a"(q), "=d"(rem) \
: "a"(n1), "d"(n0), "g"(d0) \
: "cc"); \
q; \
})
# define REMAINDER_IS_ALREADY_CALCULATED
# endif /* __<cpu> */
# endif /* __GNUC__ */
#endif /* OPENSSL_NO_ASM */
/* 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. */
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;
int no_branch = 0;
/* 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_div, BN_R_NOT_INITIALIZED);
return 0;
}
if ((num->flags & BN_FLG_CONSTTIME) != 0 ||
(divisor->flags & BN_FLG_CONSTTIME) != 0) {
no_branch = 1;
}
if (BN_is_zero(divisor)) {
OPENSSL_PUT_ERROR(BN, BN_div, BN_R_DIV_BY_ZERO);
return 0;
}
if (!no_branch && BN_ucmp(num, divisor) < 0) {
if (rm != NULL) {
if (BN_copy(rm, num) == NULL) {
return 0;
}
}
if (dv != NULL) {
BN_zero(dv);
}
return 1;
}
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;
if (no_branch) {
/* Since we don't know whether 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 - no_branch;
resp = &(res->d[loop - 1]);
/* space for temp */
if (!bn_wexpand(tmp, (div_n + 1))) {
goto err;
}
if (!no_branch) {
if (BN_ucmp(&wnum, sdiv) >= 0) {
bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
*resp = 1;
} else {
res->top--;
}
}
/* 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 */
#ifdef BN_LLONG
BN_ULLONG t2;
#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(div_asm)
q = (BN_ULONG)(((((BN_ULLONG)n0) << BN_BITS2) | n1) / d0);
#else
q = div_asm(n0, n1, d0);
#endif
#ifndef REMAINDER_IS_ALREADY_CALCULATED
/* rem doesn't have to be BN_ULLONG. The least we know it's less that d0,
* isn't it? */
rem = (n1 - q * d0) & BN_MASK2;
#endif
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_LLONG */
BN_ULONG t2l, t2h;
#if defined(div_asm)
q = div_asm(n0, n1, d0);
#else
q = bn_div_words(n0, n1, d0);
#endif
#ifndef REMAINDER_IS_ALREADY_CALCULATED
rem = (n1 - q * d0) & BN_MASK2;
#endif
#if defined(BN_UMULT_LOHI)
BN_UMULT_LOHI(t2l, t2h, d1, q);
#elif defined(BN_UMULT_HIGH)
t2l = d1 * q;
t2h = BN_UMULT_HIGH(d1, q);
#else
{
BN_ULONG ql, qh;
t2l = LBITS(d1);
t2h = HBITS(d1);
ql = LBITS(q);
qh = HBITS(q);
mul64(t2l, t2h, ql, qh); /* t2=(BN_ULLONG)d1*q; */
}
#endif
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_LLONG */
}
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;
BN_rshift(rm, snum, norm_shift);
if (!BN_is_zero(rm)) {
rm->neg = neg;
}
}
if (no_branch) {
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));
if (abs_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_mod_lshift_quick, 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 (so bn_div_words doesn't complain) */
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, d;
l = a->d[i];
d = bn_div_words(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--;
}
ret >>= j;
return ret;
}
BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w) {
#ifndef BN_LLONG
BN_ULONG ret = 0;
#else
BN_ULLONG ret = 0;
#endif
int i;
if (w == 0) {
return (BN_ULONG) -1;
}
w &= BN_MASK2;
for (i = a->top - 1; i >= 0; i--) {
#ifndef BN_LLONG
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;
}