/* crypto/bn/bn_lib.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.]
*/
#ifndef BN_DEBUG
# undef NDEBUG /* avoid conflicting definitions */
# define NDEBUG
#endif
#include <assert.h>
#include <limits.h>
#include <stdio.h>
#include "cryptlib.h"
#include "bn_lcl.h"
const char BN_version[]="Big Number" OPENSSL_VERSION_PTEXT;
/* This stuff appears to be completely unused, so is deprecated */
#ifndef OPENSSL_NO_DEPRECATED
/* For a 32 bit machine
* 2 - 4 == 128
* 3 - 8 == 256
* 4 - 16 == 512
* 5 - 32 == 1024
* 6 - 64 == 2048
* 7 - 128 == 4096
* 8 - 256 == 8192
*/
static int bn_limit_bits=0;
static int bn_limit_num=8; /* (1<<bn_limit_bits) */
static int bn_limit_bits_low=0;
static int bn_limit_num_low=8; /* (1<<bn_limit_bits_low) */
static int bn_limit_bits_high=0;
static int bn_limit_num_high=8; /* (1<<bn_limit_bits_high) */
static int bn_limit_bits_mont=0;
static int bn_limit_num_mont=8; /* (1<<bn_limit_bits_mont) */
void BN_set_params(int mult, int high, int low, int mont)
{
if (mult >= 0)
{
if (mult > (int)(sizeof(int)*8)-1)
mult=sizeof(int)*8-1;
bn_limit_bits=mult;
bn_limit_num=1<<mult;
}
if (high >= 0)
{
if (high > (int)(sizeof(int)*8)-1)
high=sizeof(int)*8-1;
bn_limit_bits_high=high;
bn_limit_num_high=1<<high;
}
if (low >= 0)
{
if (low > (int)(sizeof(int)*8)-1)
low=sizeof(int)*8-1;
bn_limit_bits_low=low;
bn_limit_num_low=1<<low;
}
if (mont >= 0)
{
if (mont > (int)(sizeof(int)*8)-1)
mont=sizeof(int)*8-1;
bn_limit_bits_mont=mont;
bn_limit_num_mont=1<<mont;
}
}
int BN_get_params(int which)
{
if (which == 0) return(bn_limit_bits);
else if (which == 1) return(bn_limit_bits_high);
else if (which == 2) return(bn_limit_bits_low);
else if (which == 3) return(bn_limit_bits_mont);
else return(0);
}
#endif
const BIGNUM *BN_value_one(void)
{
static BN_ULONG data_one=1L;
static BIGNUM const_one={&data_one,1,1,0,BN_FLG_STATIC_DATA};
return(&const_one);
}
char *BN_options(void)
{
static int init=0;
static char data[16];
if (!init)
{
init++;
#ifdef BN_LLONG
BIO_snprintf(data,sizeof data,"bn(%d,%d)",
(int)sizeof(BN_ULLONG)*8,(int)sizeof(BN_ULONG)*8);
#else
BIO_snprintf(data,sizeof data,"bn(%d,%d)",
(int)sizeof(BN_ULONG)*8,(int)sizeof(BN_ULONG)*8);
#endif
}
return(data);
}
int BN_num_bits_word(BN_ULONG l)
{
static const char bits[256]={
0,1,2,2,3,3,3,3,4,4,4,4,4,4,4,4,
5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,
6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,
8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
};
#if defined(SIXTY_FOUR_BIT_LONG)
if (l & 0xffffffff00000000L)
{
if (l & 0xffff000000000000L)
{
if (l & 0xff00000000000000L)
{
return(bits[(int)(l>>56)]+56);
}
else return(bits[(int)(l>>48)]+48);
}
else
{
if (l & 0x0000ff0000000000L)
{
return(bits[(int)(l>>40)]+40);
}
else return(bits[(int)(l>>32)]+32);
}
}
else
#else
#ifdef SIXTY_FOUR_BIT
if (l & 0xffffffff00000000LL)
{
if (l & 0xffff000000000000LL)
{
if (l & 0xff00000000000000LL)
{
return(bits[(int)(l>>56)]+56);
}
else return(bits[(int)(l>>48)]+48);
}
else
{
if (l & 0x0000ff0000000000LL)
{
return(bits[(int)(l>>40)]+40);
}
else return(bits[(int)(l>>32)]+32);
}
}
else
#endif
#endif
{
#if defined(THIRTY_TWO_BIT) || defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
if (l & 0xffff0000L)
{
if (l & 0xff000000L)
return(bits[(int)(l>>24L)]+24);
else return(bits[(int)(l>>16L)]+16);
}
else
#endif
{
#if defined(SIXTEEN_BIT) || defined(THIRTY_TWO_BIT) || defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
if (l & 0xff00L)
return(bits[(int)(l>>8)]+8);
else
#endif
return(bits[(int)(l )] );
}
}
}
int BN_num_bits(const BIGNUM *a)
{
int i = a->top - 1;
bn_check_top(a);
if (BN_is_zero(a)) return 0;
return ((i*BN_BITS2) + BN_num_bits_word(a->d[i]));
}
void BN_clear_free(BIGNUM *a)
{
int i;
if (a == NULL) return;
bn_check_top(a);
if (a->d != NULL)
{
OPENSSL_cleanse(a->d,a->dmax*sizeof(a->d[0]));
if (!(BN_get_flags(a,BN_FLG_STATIC_DATA)))
OPENSSL_free(a->d);
}
i=BN_get_flags(a,BN_FLG_MALLOCED);
OPENSSL_cleanse(a,sizeof(BIGNUM));
if (i)
OPENSSL_free(a);
}
void BN_free(BIGNUM *a)
{
if (a == NULL) return;
bn_check_top(a);
if ((a->d != NULL) && !(BN_get_flags(a,BN_FLG_STATIC_DATA)))
OPENSSL_free(a->d);
if (a->flags & BN_FLG_MALLOCED)
OPENSSL_free(a);
else
{
#ifndef OPENSSL_NO_DEPRECATED
a->flags|=BN_FLG_FREE;
#endif
a->d = NULL;
}
}
void BN_init(BIGNUM *a)
{
memset(a,0,sizeof(BIGNUM));
bn_check_top(a);
}
BIGNUM *BN_new(void)
{
BIGNUM *ret;
if ((ret=(BIGNUM *)OPENSSL_malloc(sizeof(BIGNUM))) == NULL)
{
BNerr(BN_F_BN_NEW,ERR_R_MALLOC_FAILURE);
return(NULL);
}
ret->flags=BN_FLG_MALLOCED;
ret->top=0;
ret->neg=0;
ret->dmax=0;
ret->d=NULL;
bn_check_top(ret);
return(ret);
}
/* This is used both by bn_expand2() and bn_dup_expand() */
/* The caller MUST check that words > b->dmax before calling this */
static BN_ULONG *bn_expand_internal(const BIGNUM *b, int words)
{
BN_ULONG *A,*a = NULL;
const BN_ULONG *B;
int i;
bn_check_top(b);
if (words > (INT_MAX/(4*BN_BITS2)))
{
BNerr(BN_F_BN_EXPAND_INTERNAL,BN_R_BIGNUM_TOO_LONG);
return NULL;
}
if (BN_get_flags(b,BN_FLG_STATIC_DATA))
{
BNerr(BN_F_BN_EXPAND_INTERNAL,BN_R_EXPAND_ON_STATIC_BIGNUM_DATA);
return(NULL);
}
a=A=(BN_ULONG *)OPENSSL_malloc(sizeof(BN_ULONG)*words);
if (A == NULL)
{
BNerr(BN_F_BN_EXPAND_INTERNAL,ERR_R_MALLOC_FAILURE);
return(NULL);
}
#if 1
B=b->d;
/* Check if the previous number needs to be copied */
if (B != NULL)
{
for (i=b->top>>2; i>0; i--,A+=4,B+=4)
{
/*
* The fact that the loop is unrolled
* 4-wise is a tribute to Intel. It's
* the one that doesn't have enough
* registers to accomodate more data.
* I'd unroll it 8-wise otherwise:-)
*
* <appro@fy.chalmers.se>
*/
BN_ULONG a0,a1,a2,a3;
a0=B[0]; a1=B[1]; a2=B[2]; a3=B[3];
A[0]=a0; A[1]=a1; A[2]=a2; A[3]=a3;
}
switch (b->top&3)
{
case 3: A[2]=B[2];
case 2: A[1]=B[1];
case 1: A[0]=B[0];
case 0: /* workaround for ultrix cc: without 'case 0', the optimizer does
* the switch table by doing a=top&3; a--; goto jump_table[a];
* which fails for top== 0 */
;
}
}
#else
memset(A,0,sizeof(BN_ULONG)*words);
memcpy(A,b->d,sizeof(b->d[0])*b->top);
#endif
return(a);
}
/* This is an internal function that can be used instead of bn_expand2()
* when there is a need to copy BIGNUMs instead of only expanding the
* data part, while still expanding them.
* Especially useful when needing to expand BIGNUMs that are declared
* 'const' and should therefore not be changed.
* The reason to use this instead of a BN_dup() followed by a bn_expand2()
* is memory allocation overhead. A BN_dup() followed by a bn_expand2()
* will allocate new memory for the BIGNUM data twice, and free it once,
* while bn_dup_expand() makes sure allocation is made only once.
*/
#ifndef OPENSSL_NO_DEPRECATED
BIGNUM *bn_dup_expand(const BIGNUM *b, int words)
{
BIGNUM *r = NULL;
bn_check_top(b);
/* This function does not work if
* words <= b->dmax && top < words
* because BN_dup() does not preserve 'dmax'!
* (But bn_dup_expand() is not used anywhere yet.)
*/
if (words > b->dmax)
{
BN_ULONG *a = bn_expand_internal(b, words);
if (a)
{
r = BN_new();
if (r)
{
r->top = b->top;
r->dmax = words;
r->neg = b->neg;
r->d = a;
}
else
{
/* r == NULL, BN_new failure */
OPENSSL_free(a);
}
}
/* If a == NULL, there was an error in allocation in
bn_expand_internal(), and NULL should be returned */
}
else
{
r = BN_dup(b);
}
bn_check_top(r);
return r;
}
#endif
/* This is an internal function that should not be used in applications.
* It ensures that 'b' has enough room for a 'words' word number
* and initialises any unused part of b->d with leading zeros.
* It is mostly used by the various BIGNUM routines. If there is an error,
* NULL is returned. If not, 'b' is returned. */
BIGNUM *bn_expand2(BIGNUM *b, int words)
{
bn_check_top(b);
if (words > b->dmax)
{
BN_ULONG *a = bn_expand_internal(b, words);
if(!a) return NULL;
if(b->d) OPENSSL_free(b->d);
b->d=a;
b->dmax=words;
}
/* None of this should be necessary because of what b->top means! */
#if 0
/* NB: bn_wexpand() calls this only if the BIGNUM really has to grow */
if (b->top < b->dmax)
{
int i;
BN_ULONG *A = &(b->d[b->top]);
for (i=(b->dmax - b->top)>>3; i>0; i--,A+=8)
{
A[0]=0; A[1]=0; A[2]=0; A[3]=0;
A[4]=0; A[5]=0; A[6]=0; A[7]=0;
}
for (i=(b->dmax - b->top)&7; i>0; i--,A++)
A[0]=0;
assert(A == &(b->d[b->dmax]));
}
#endif
bn_check_top(b);
return b;
}
BIGNUM *BN_dup(const BIGNUM *a)
{
BIGNUM *t;
if (a == NULL) return NULL;
bn_check_top(a);
t = BN_new();
if (t == NULL) return NULL;
if(!BN_copy(t, a))
{
BN_free(t);
return NULL;
}
bn_check_top(t);
return t;
}
BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b)
{
int i;
BN_ULONG *A;
const BN_ULONG *B;
bn_check_top(b);
if (a == b) return(a);
if (bn_wexpand(a,b->top) == NULL) return(NULL);
#if 1
A=a->d;
B=b->d;
for (i=b->top>>2; i>0; i--,A+=4,B+=4)
{
BN_ULONG a0,a1,a2,a3;
a0=B[0]; a1=B[1]; a2=B[2]; a3=B[3];
A[0]=a0; A[1]=a1; A[2]=a2; A[3]=a3;
}
switch (b->top&3)
{
case 3: A[2]=B[2];
case 2: A[1]=B[1];
case 1: A[0]=B[0];
case 0: ; /* ultrix cc workaround, see comments in bn_expand_internal */
}
#else
memcpy(a->d,b->d,sizeof(b->d[0])*b->top);
#endif
a->top=b->top;
a->neg=b->neg;
bn_check_top(a);
return(a);
}
void BN_swap(BIGNUM *a, BIGNUM *b)
{
int flags_old_a, flags_old_b;
BN_ULONG *tmp_d;
int tmp_top, tmp_dmax, tmp_neg;
bn_check_top(a);
bn_check_top(b);
flags_old_a = a->flags;
flags_old_b = b->flags;
tmp_d = a->d;
tmp_top = a->top;
tmp_dmax = a->dmax;
tmp_neg = a->neg;
a->d = b->d;
a->top = b->top;
a->dmax = b->dmax;
a->neg = b->neg;
b->d = tmp_d;
b->top = tmp_top;
b->dmax = tmp_dmax;
b->neg = tmp_neg;
a->flags = (flags_old_a & BN_FLG_MALLOCED) | (flags_old_b & BN_FLG_STATIC_DATA);
b->flags = (flags_old_b & BN_FLG_MALLOCED) | (flags_old_a & BN_FLG_STATIC_DATA);
bn_check_top(a);
bn_check_top(b);
}
void BN_clear(BIGNUM *a)
{
bn_check_top(a);
if (a->d != NULL)
memset(a->d,0,a->dmax*sizeof(a->d[0]));
a->top=0;
a->neg=0;
}
BN_ULONG BN_get_word(const BIGNUM *a)
{
if (a->top > 1)
return BN_MASK2;
else if (a->top == 1)
return a->d[0];
/* a->top == 0 */
return 0;
}
int BN_set_word(BIGNUM *a, BN_ULONG w)
{
bn_check_top(a);
if (bn_expand(a,(int)sizeof(BN_ULONG)*8) == NULL) return(0);
a->neg = 0;
a->d[0] = w;
a->top = (w ? 1 : 0);
bn_check_top(a);
return(1);
}
BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret)
{
unsigned int i,m;
unsigned int n;
BN_ULONG l;
BIGNUM *bn = NULL;
if (ret == NULL)
ret = bn = BN_new();
if (ret == NULL) return(NULL);
bn_check_top(ret);
l=0;
n=len;
if (n == 0)
{
ret->top=0;
return(ret);
}
i=((n-1)/BN_BYTES)+1;
m=((n-1)%(BN_BYTES));
if (bn_wexpand(ret, (int)i) == NULL)
{
if (bn) BN_free(bn);
return NULL;
}
ret->top=i;
ret->neg=0;
while (n--)
{
l=(l<<8L)| *(s++);
if (m-- == 0)
{
ret->d[--i]=l;
l=0;
m=BN_BYTES-1;
}
}
/* need to call this due to clear byte at top if avoiding
* having the top bit set (-ve number) */
bn_correct_top(ret);
return(ret);
}
/* ignore negative */
int BN_bn2bin(const BIGNUM *a, unsigned char *to)
{
int n,i;
BN_ULONG l;
bn_check_top(a);
n=i=BN_num_bytes(a);
while (i--)
{
l=a->d[i/BN_BYTES];
*(to++)=(unsigned char)(l>>(8*(i%BN_BYTES)))&0xff;
}
return(n);
}
int BN_ucmp(const BIGNUM *a, const BIGNUM *b)
{
int i;
BN_ULONG t1,t2,*ap,*bp;
bn_check_top(a);
bn_check_top(b);
i=a->top-b->top;
if (i != 0) return(i);
ap=a->d;
bp=b->d;
for (i=a->top-1; i>=0; i--)
{
t1= ap[i];
t2= bp[i];
if (t1 != t2)
return((t1 > t2) ? 1 : -1);
}
return(0);
}
int BN_cmp(const BIGNUM *a, const BIGNUM *b)
{
int i;
int gt,lt;
BN_ULONG t1,t2;
if ((a == NULL) || (b == NULL))
{
if (a != NULL)
return(-1);
else if (b != NULL)
return(1);
else
return(0);
}
bn_check_top(a);
bn_check_top(b);
if (a->neg != b->neg)
{
if (a->neg)
return(-1);
else return(1);
}
if (a->neg == 0)
{ gt=1; lt= -1; }
else { gt= -1; lt=1; }
if (a->top > b->top) return(gt);
if (a->top < b->top) return(lt);
for (i=a->top-1; i>=0; i--)
{
t1=a->d[i];
t2=b->d[i];
if (t1 > t2) return(gt);
if (t1 < t2) return(lt);
}
return(0);
}
int BN_set_bit(BIGNUM *a, int n)
{
int i,j,k;
if (n < 0)
return 0;
i=n/BN_BITS2;
j=n%BN_BITS2;
if (a->top <= i)
{
if (bn_wexpand(a,i+1) == NULL) return(0);
for(k=a->top; k<i+1; k++)
a->d[k]=0;
a->top=i+1;
}
a->d[i]|=(((BN_ULONG)1)<<j);
bn_check_top(a);
return(1);
}
int BN_clear_bit(BIGNUM *a, int n)
{
int i,j;
bn_check_top(a);
if (n < 0) return 0;
i=n/BN_BITS2;
j=n%BN_BITS2;
if (a->top <= i) return(0);
a->d[i]&=(~(((BN_ULONG)1)<<j));
bn_correct_top(a);
return(1);
}
int BN_is_bit_set(const BIGNUM *a, int n)
{
int i,j;
bn_check_top(a);
if (n < 0) return 0;
i=n/BN_BITS2;
j=n%BN_BITS2;
if (a->top <= i) return 0;
return(((a->d[i])>>j)&((BN_ULONG)1));
}
int BN_mask_bits(BIGNUM *a, int n)
{
int b,w;
bn_check_top(a);
if (n < 0) return 0;
w=n/BN_BITS2;
b=n%BN_BITS2;
if (w >= a->top) return 0;
if (b == 0)
a->top=w;
else
{
a->top=w+1;
a->d[w]&= ~(BN_MASK2<<b);
}
bn_correct_top(a);
return(1);
}
void BN_set_negative(BIGNUM *a, int b)
{
if (b && !BN_is_zero(a))
a->neg = 1;
else
a->neg = 0;
}
int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n)
{
int i;
BN_ULONG aa,bb;
aa=a[n-1];
bb=b[n-1];
if (aa != bb) return((aa > bb)?1:-1);
for (i=n-2; i>=0; i--)
{
aa=a[i];
bb=b[i];
if (aa != bb) return((aa > bb)?1:-1);
}
return(0);
}
/* Here follows a specialised variants of bn_cmp_words(). It has the
property of performing the operation on arrays of different sizes.
The sizes of those arrays is expressed through cl, which is the
common length ( basicall, min(len(a),len(b)) ), and dl, which is the
delta between the two lengths, calculated as len(a)-len(b).
All lengths are the number of BN_ULONGs... */
int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b,
int cl, int dl)
{
int n,i;
n = cl-1;
if (dl < 0)
{
for (i=dl; i<0; i++)
{
if (b[n-i] != 0)
return -1; /* a < b */
}
}
if (dl > 0)
{
for (i=dl; i>0; i--)
{
if (a[n+i] != 0)
return 1; /* a > b */
}
}
return bn_cmp_words(a,b,cl);
}
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