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[thirdparty/openssl.git] / crypto / bn / bn_lib.c

/* 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 const BN_ULONG data_one=1L;
        static const BIGNUM const_one={(BN_ULONG *)&data_one,1,1,0,BN_FLG_STATIC_DATA};

        return(&const_one);
        }

int BN_num_bits_word(BN_ULONG l)
        {
        static const unsigned 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(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);
                }
#ifdef PURIFY
        /* Valgrind complains in BN_consttime_swap because we process the whole
         * array even if it's not initialised yet. This doesn't matter in that
         * function - what's important is constant time operation (we're not
         * actually going to use the data)
        */
        memset(a, 0, sizeof(BN_ULONG)*words);
#endif

#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 (int)(((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);
        }

/* 
 * Constant-time conditional swap of a and b.  
 * a and b are swapped if condition is not 0.  The code assumes that at most one bit of condition is set.
 * nwords is the number of words to swap.  The code assumes that at least nwords are allocated in both a and b,
 * and that no more than nwords are used by either a or b.
 * a and b cannot be the same number
 */
void BN_consttime_swap(BN_ULONG condition, BIGNUM *a, BIGNUM *b, int nwords)
        {
        BN_ULONG t;
        int i;

        bn_wcheck_size(a, nwords);
        bn_wcheck_size(b, nwords);

        assert(a != b);
        assert((condition & (condition - 1)) == 0);
        assert(sizeof(BN_ULONG) >= sizeof(int));

        condition = ((condition - 1) >> (BN_BITS2 - 1)) - 1;

        t = (a->top^b->top) & condition;
        a->top ^= t;
        b->top ^= t;

#define BN_CONSTTIME_SWAP(ind) \
        do { \
                t = (a->d[ind] ^ b->d[ind]) & condition; \
                a->d[ind] ^= t; \
                b->d[ind] ^= t; \
        } while (0)


        switch (nwords) {
        default:
                for (i = 10; i < nwords; i++) 
                        BN_CONSTTIME_SWAP(i);
                /* Fallthrough */
        case 10: BN_CONSTTIME_SWAP(9); /* Fallthrough */
        case 9: BN_CONSTTIME_SWAP(8); /* Fallthrough */
        case 8: BN_CONSTTIME_SWAP(7); /* Fallthrough */
        case 7: BN_CONSTTIME_SWAP(6); /* Fallthrough */
        case 6: BN_CONSTTIME_SWAP(5); /* Fallthrough */
        case 5: BN_CONSTTIME_SWAP(4); /* Fallthrough */
        case 4: BN_CONSTTIME_SWAP(3); /* Fallthrough */
        case 3: BN_CONSTTIME_SWAP(2); /* Fallthrough */
        case 2: BN_CONSTTIME_SWAP(1); /* Fallthrough */
        case 1: BN_CONSTTIME_SWAP(0);
        }
#undef BN_CONSTTIME_SWAP
}