You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
478 lines
15 KiB
478 lines
15 KiB
4 years ago
|
/* crypto/bn/bn_div.c */
|
||
|
/* 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 <stdio.h>
|
||
|
#include <openssl/bn.h>
|
||
|
#include "cryptlib.h"
|
||
|
#include "bn_lcl.h"
|
||
|
|
||
|
/* The old slow way */
|
||
|
#if 0
|
||
|
int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
|
||
|
BN_CTX *ctx)
|
||
|
{
|
||
|
int i, nm, nd;
|
||
|
int ret = 0;
|
||
|
BIGNUM *D;
|
||
|
|
||
|
bn_check_top(m);
|
||
|
bn_check_top(d);
|
||
|
if (BN_is_zero(d)) {
|
||
|
BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);
|
||
|
return (0);
|
||
|
}
|
||
|
|
||
|
if (BN_ucmp(m, d) < 0) {
|
||
|
if (rem != NULL) {
|
||
|
if (BN_copy(rem, m) == NULL)
|
||
|
return (0);
|
||
|
}
|
||
|
if (dv != NULL)
|
||
|
BN_zero(dv);
|
||
|
return (1);
|
||
|
}
|
||
|
|
||
|
BN_CTX_start(ctx);
|
||
|
D = BN_CTX_get(ctx);
|
||
|
if (dv == NULL)
|
||
|
dv = BN_CTX_get(ctx);
|
||
|
if (rem == NULL)
|
||
|
rem = BN_CTX_get(ctx);
|
||
|
if (D == NULL || dv == NULL || rem == NULL)
|
||
|
goto end;
|
||
|
|
||
|
nd = BN_num_bits(d);
|
||
|
nm = BN_num_bits(m);
|
||
|
if (BN_copy(D, d) == NULL)
|
||
|
goto end;
|
||
|
if (BN_copy(rem, m) == NULL)
|
||
|
goto end;
|
||
|
|
||
|
/*
|
||
|
* The next 2 are needed so we can do a dv->d[0]|=1 later since
|
||
|
* BN_lshift1 will only work once there is a value :-)
|
||
|
*/
|
||
|
BN_zero(dv);
|
||
|
if (bn_wexpand(dv, 1) == NULL)
|
||
|
goto end;
|
||
|
dv->top = 1;
|
||
|
|
||
|
if (!BN_lshift(D, D, nm - nd))
|
||
|
goto end;
|
||
|
for (i = nm - nd; i >= 0; i--) {
|
||
|
if (!BN_lshift1(dv, dv))
|
||
|
goto end;
|
||
|
if (BN_ucmp(rem, D) >= 0) {
|
||
|
dv->d[0] |= 1;
|
||
|
if (!BN_usub(rem, rem, D))
|
||
|
goto end;
|
||
|
}
|
||
|
/* CAN IMPROVE (and have now :=) */
|
||
|
if (!BN_rshift1(D, D))
|
||
|
goto end;
|
||
|
}
|
||
|
rem->neg = BN_is_zero(rem) ? 0 : m->neg;
|
||
|
dv->neg = m->neg ^ d->neg;
|
||
|
ret = 1;
|
||
|
end:
|
||
|
BN_CTX_end(ctx);
|
||
|
return (ret);
|
||
|
}
|
||
|
|
||
|
#else
|
||
|
|
||
|
# if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
|
||
|
&& !defined(PEDANTIC) && !defined(BN_DIV3W)
|
||
|
# if defined(__GNUC__) && __GNUC__>=2
|
||
|
# if defined(__i386) || defined (__i386__)
|
||
|
/*-
|
||
|
* 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 bn_div_words
|
||
|
# define bn_div_words(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(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
|
||
|
/*
|
||
|
* Same story here, but it's 128-bit by 64-bit division. Wow!
|
||
|
* <appro@fy.chalmers.se>
|
||
|
*/
|
||
|
# undef bn_div_words
|
||
|
# define bn_div_words(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 (bn_check_top() works only for
|
||
|
* BN_DEBUG builds)
|
||
|
*/
|
||
|
if ((num->top > 0 && num->d[num->top - 1] == 0) ||
|
||
|
(divisor->top > 0 && divisor->d[divisor->top - 1] == 0)) {
|
||
|
BNerr(BN_F_BN_DIV, BN_R_NOT_INITIALIZED);
|
||
|
return 0;
|
||
|
}
|
||
|
|
||
|
bn_check_top(num);
|
||
|
bn_check_top(divisor);
|
||
|
|
||
|
if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0)
|
||
|
|| (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0)) {
|
||
|
no_branch = 1;
|
||
|
}
|
||
|
|
||
|
bn_check_top(dv);
|
||
|
bn_check_top(rm);
|
||
|
/*- bn_check_top(num); *//*
|
||
|
* 'num' has been checked already
|
||
|
*/
|
||
|
/*- bn_check_top(divisor); *//*
|
||
|
* 'divisor' has been checked already
|
||
|
*/
|
||
|
|
||
|
if (BN_is_zero(divisor)) {
|
||
|
BNerr(BN_F_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) {
|
||
|
/*
|
||
|
* If BN_DEBUG_RAND is defined BN_ucmp changes (via bn_pollute)
|
||
|
* the const bignum arguments => clean the values between top and
|
||
|
* max again
|
||
|
*/
|
||
|
bn_clear_top2max(&wnum);
|
||
|
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
|
||
|
*/
|
||
|
# if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
|
||
|
BN_ULONG bn_div_3_words(BN_ULONG *, BN_ULONG, BN_ULONG);
|
||
|
q = bn_div_3_words(wnump, d1, d0);
|
||
|
# else
|
||
|
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(bn_div_words)
|
||
|
q = (BN_ULONG)(((((BN_ULLONG) n0) << BN_BITS2) | n1) / d0);
|
||
|
# else
|
||
|
q = bn_div_words(n0, n1, d0);
|
||
|
# ifdef BN_DEBUG_LEVITTE
|
||
|
fprintf(stderr, "DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
|
||
|
X) -> 0x%08X\n", n0, n1, d0, q);
|
||
|
# endif
|
||
|
# 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;
|
||
|
|
||
|
q = bn_div_words(n0, n1, d0);
|
||
|
# ifdef BN_DEBUG_LEVITTE
|
||
|
fprintf(stderr, "DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
|
||
|
X) -> 0x%08X\n", n0, n1, d0, q);
|
||
|
# 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 */
|
||
|
}
|
||
|
# endif /* !BN_DIV3W */
|
||
|
|
||
|
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;
|
||
|
bn_check_top(rm);
|
||
|
}
|
||
|
if (no_branch)
|
||
|
bn_correct_top(res);
|
||
|
BN_CTX_end(ctx);
|
||
|
return (1);
|
||
|
err:
|
||
|
bn_check_top(rm);
|
||
|
BN_CTX_end(ctx);
|
||
|
return (0);
|
||
|
}
|
||
|
#endif
|