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/* 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 <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "bn_lcl.h"
const char *BN_version="Big Number";
/* 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) */
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)
{
BN_ULONG l;
int i;
bn_check_top(a);
if (a->top == 0) return(0);
l=a->d[a->top-1];
assert(l != 0);
i=(a->top-1)*BN_BITS2;
return(i+BN_num_bits_word(l));
}
void BN_clear_free(BIGNUM *a)
{
int i;
if (a == NULL) return;
if (a->d != NULL)
{
memset(a->d,0,a->dmax*sizeof(a->d[0]));
if (!(BN_get_flags(a,BN_FLG_STATIC_DATA)))
free(a->d);
}
i=BN_get_flags(a,BN_FLG_MALLOCED);
memset(a,0,sizeof(BIGNUM));
if (i)
free(a);
}
void BN_free(BIGNUM *a)
{
if (a == NULL) return;
if ((a->d != NULL) && !(BN_get_flags(a,BN_FLG_STATIC_DATA)))
free(a->d);
a->flags|=BN_FLG_FREE; /* REMOVE? */
if (a->flags & BN_FLG_MALLOCED)
free(a);
}
void BN_init(BIGNUM *a)
{
memset(a,0,sizeof(BIGNUM));
}
BIGNUM *BN_new(void)
{
BIGNUM *ret;
if ((ret=(BIGNUM *)malloc(sizeof(BIGNUM))) == NULL)
{
return(NULL);
}
ret->flags=BN_FLG_MALLOCED;
ret->top=0;
ret->neg=0;
ret->dmax=0;
ret->d=NULL;
return(ret);
}
/* This is an internal function that should not be used in applications.
* It ensures that 'b' has enough room for a 'words' word number number.
* 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_ULONG *A,*a;
const BN_ULONG *B;
int i;
bn_check_top(b);
if (words > b->dmax)
{
bn_check_top(b);
if (BN_get_flags(b,BN_FLG_STATIC_DATA))
{
return(NULL);
}
a=A=(BN_ULONG *)malloc(sizeof(BN_ULONG)*(words+1));
if (A == NULL)
{
return(NULL);
}
#if 1
B=b->d;
/* Check if the previous number needs to be copied */
if (B != NULL)
{
#if 0
/* This lot is an unrolled loop to copy b->top
* BN_ULONGs from B to A
*/
/*
* I have nothing against unrolling but it's usually done for
* several reasons, namely:
* - minimize percentage of decision making code, i.e. branches;
* - avoid cache trashing;
* - make it possible to schedule loads earlier;
* Now let's examine the code below. The cornerstone of C is
* "programmer is always right" and that's what we love it for:-)
* For this very reason C compilers have to be paranoid when it
* comes to data aliasing and assume the worst. Yeah, but what
* does it mean in real life? This means that loop body below will
* be compiled to sequence of loads immediately followed by stores
* as compiler assumes the worst, something in A==B+1 style. As a
* result CPU pipeline is going to starve for incoming data. Secondly
* if A and B happen to share same cache line such code is going to
* cause severe cache trashing. Both factors have severe impact on
* performance of modern CPUs and this is the reason why this
* particular piece of code is #ifdefed away and replaced by more
* "friendly" version found in #else section below. This comment
* also applies to BN_copy function.
*
* <appro@fy.chalmers.se>
*/
for (i=b->top&(~7); i>0; i-=8)
{
A[0]=B[0]; A[1]=B[1]; A[2]=B[2]; A[3]=B[3];
A[4]=B[4]; A[5]=B[5]; A[6]=B[6]; A[7]=B[7];
A+=8;
B+=8;
}
switch (b->top&7)
{
case 7:
A[6]=B[6];
case 6:
A[5]=B[5];
case 5:
A[4]=B[4];
case 4:
A[3]=B[3];
case 3:
A[2]=B[2];
case 2:
A[1]=B[1];
case 1:
A[0]=B[0];
case 0:
/* I need the 'case 0' entry for utrix cc.
* If the optimizer is turned on, it does the
* switch table by doing
* a=top&7
* a--;
* goto jump_table[a];
* If top is 0, this makes us jump to 0xffffffc
* which is rather bad :-(.
* eric 23-Apr-1998
*/
;
}
#else
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: ; /* ultrix cc workaround, see above */
}
#endif
free(b->d);
}
b->d=a;
b->dmax=words;
/* Now need to zero any data between b->top and b->max */
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;
#else
memset(A,0,sizeof(BN_ULONG)*(words+1));
memcpy(A,b->d,sizeof(b->d[0])*b->top);
b->d=a;
b->max=words;
#endif
/* memset(&(p[b->max]),0,((words+1)-b->max)*sizeof(BN_ULONG)); */
/* { int i; for (i=b->max; i<words+1; i++) p[i]=i;} */
}
return(b);
}
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_expand2 */
}
#else
memcpy(a->d,b->d,sizeof(b->d[0])*b->top);
#endif
/* memset(&(a->d[b->top]),0,sizeof(a->d[0])*(a->max-b->top));*/
a->top=b->top;
if ((a->top == 0) && (a->d != NULL))
a->d[0]=0;
a->neg=b->neg;
return(a);
}
int BN_set_word(BIGNUM *a, BN_ULONG w)
{
int i,n;
if (bn_expand(a,sizeof(BN_ULONG)*8) == NULL) return(0);
n=sizeof(BN_ULONG)/BN_BYTES;
a->neg=0;
a->top=0;
a->d[0]=(BN_ULONG)w&BN_MASK2;
if (a->d[0] != 0) a->top=1;
for (i=1; i<n; i++)
{
/* the following is done instead of
* w>>=BN_BITS2 so compilers don't complain
* on builds where sizeof(long) == BN_TYPES */
#ifndef SIXTY_FOUR_BIT /* the data item > unsigned long */
w>>=BN_BITS4;
w>>=BN_BITS4;
#else
w=0;
#endif
a->d[i]=(BN_ULONG)w&BN_MASK2;
if (a->d[i] != 0) a->top=i+1;
}
return(1);
}
/* ignore negative */
BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret)
{
unsigned int i,m;
unsigned int n;
BN_ULONG l;
if (ret == NULL) ret=BN_new();
if (ret == NULL) return(NULL);
l=0;
n=len;
if (n == 0)
{
ret->top=0;
return(ret);
}
if (bn_expand(ret,(int)(n+2)*8) == NULL)
return(NULL);
i=((n-1)/BN_BYTES)+1;
m=((n-1)%(BN_BYTES));
ret->top=i;
while (n-- > 0)
{
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_fix_top(ret);
return(ret);
}
/* ignore negative */
int BN_bn2bin(const BIGNUM *a, unsigned char *to)
{
int n,i;
BN_ULONG l;
n=i=BN_num_bytes(a);
while (i-- > 0)
{
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_is_bit_set(const BIGNUM *a, int n)
{
int i,j;
if (n < 0) return(0);
i=n/BN_BITS2;
j=n%BN_BITS2;
if (a->top <= i) return(0);
return((a->d[i]&(((BN_ULONG)1)<<j))?1:0);
}