rdesktop/crypto/bn_exp.c

/* crypto/bn/bn_exp.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.]
 */
/* ====================================================================
 * Copyright (c) 1998-2000 The OpenSSL Project.  All rights reserved.
 *
 * 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 above 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 acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
 *
 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
 *    endorse or promote products derived from this software without
 *    prior written permission. For written permission, please contact
 *    openssl-core@openssl.org.
 *
 * 5. Products derived from this software may not be called "OpenSSL"
 *    nor may "OpenSSL" appear in their names without prior written
 *    permission of the OpenSSL Project.
 *
 * 6. Redistributions of any form whatsoever must retain the following
 *    acknowledgment:
 *    "This product includes software developed by the OpenSSL Project
 *    for use in the OpenSSL Toolkit (http://www.openssl.org/)"
 *
 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
 * EXPRESSED 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 OpenSSL PROJECT OR
 * ITS 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.
 * ====================================================================
 *
 * This product includes cryptographic software written by Eric Young
 * (eay@cryptsoft.com).  This product includes software written by Tim
 * Hudson (tjh@cryptsoft.com).
 *
 */


#include <stdio.h>
#include "bn_lcl.h"
#ifdef ATALLA
# include <alloca.h>
# include <atasi.h>
# include <assert.h>
# include <dlfcn.h>
#endif


#define TABLE_SIZE      32

/* slow but works */
int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx)
        {
        BIGNUM *t;
        int r=0;

        bn_check_top(a);
        bn_check_top(b);
        bn_check_top(m);

        BN_CTX_start(ctx);
        if ((t = BN_CTX_get(ctx)) == 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_mod(ret,t,m,ctx)) goto err;
        r=1;
err:
        BN_CTX_end(ctx);
        return(r);
        }

#if 0
/* this one works - simple but works */
int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx)
        {
        int i,bits,ret=0;
        BIGNUM *v,*rr;

        BN_CTX_start(ctx);
        if ((r == a) || (r == p))
                rr = BN_CTX_get(ctx);
        else
                rr = r;
        if ((v = BN_CTX_get(ctx)) == NULL) goto err;

        if (BN_copy(v,a) == NULL) goto err;
        bits=BN_num_bits(p);

        if (BN_is_odd(p))
                { if (BN_copy(rr,a) == NULL) goto err; }
        else    { if (!BN_one(rr)) goto err; }

        for (i=1; i<bits; i++)
                {
                if (!BN_sqr(v,v,ctx)) goto err;
                if (BN_is_bit_set(p,i))
                        {
                        if (!BN_mul(rr,rr,v,ctx)) goto err;
                        }
                }
        ret=1;
err:
        if (r != rr) BN_copy(r,rr);
        BN_CTX_end(ctx);
        return(ret);
        }
#endif

#ifdef ATALLA

/*
 * This routine will dynamically check for the existance of an Atalla AXL-200
 * SSL accelerator module.  If one is found, the variable
 * asi_accelerator_present is set to 1 and the function pointers
 * ptr_ASI_xxxxxx above will be initialized to corresponding ASI API calls.
 */
typedef int tfnASI_GetPerformanceStatistics(int reset_flag,
                                            unsigned int *ret_buf);
typedef int tfnASI_GetHardwareConfig(long card_num, unsigned int *ret_buf);
typedef int tfnASI_RSAPrivateKeyOpFn(RSAPrivateKey * rsaKey,
                                     unsigned char *output,
                                     unsigned char *input,
                                     unsigned int modulus_len);

static tfnASI_GetHardwareConfig *ptr_ASI_GetHardwareConfig;
static tfnASI_RSAPrivateKeyOpFn *ptr_ASI_RSAPrivateKeyOpFn;
static tfnASI_GetPerformanceStatistics *ptr_ASI_GetPerformanceStatistics;
static int asi_accelerator_present;
static int tried_atalla;

void atalla_initialize_accelerator_handle(void)
        {
        void *dl_handle;
        int status;
        unsigned int config_buf[1024]; 
        static int tested;

        if(tested)
                return;

        tested=1;

        bzero((void *)config_buf, 1024);

        /*
         * Check to see if the library is present on the system
         */
        dl_handle = dlopen("atasi.so", RTLD_NOW);
        if (dl_handle == (void *) NULL)
                {
/*              printf("atasi.so library is not present on the system\n");
                printf("No HW acceleration available\n");*/
                return;
                }

        /*
         * The library is present.  Now we'll check to insure that the
         * LDM is up and running. First we'll get the address of the
         * function in the atasi library that we need to see if the
         * LDM is operating.
         */

        ptr_ASI_GetHardwareConfig =
          (tfnASI_GetHardwareConfig *)dlsym(dl_handle,"ASI_GetHardwareConfig");

        if (ptr_ASI_GetHardwareConfig)
                {
                /*
                 * We found the call, now we'll get our config
                 * status.  If we get a non 0 result, the LDM is not
                 * running and we cannot use the Atalla ASI *
                 * library.
                 */
                status = (*ptr_ASI_GetHardwareConfig)(0L, config_buf);
                if (status != 0)
                        {
                        printf("atasi.so library is present but not initialized\n");
                        printf("No HW acceleration available\n");
                        return;
                        }    
                }
        else
                {
/*              printf("We found the library, but not the function. Very Strange!\n");*/
                return ;
                }

        /* 
         * It looks like we have acceleration capabilities.  Load up the
         * pointers to our ASI API calls.
         */
        ptr_ASI_RSAPrivateKeyOpFn=
          (tfnASI_RSAPrivateKeyOpFn *)dlsym(dl_handle, "ASI_RSAPrivateKeyOpFn");
        if (ptr_ASI_RSAPrivateKeyOpFn == NULL)
                {
/*              printf("We found the library, but no RSA function. Very Strange!\n");*/
                return;
                }

        ptr_ASI_GetPerformanceStatistics =
          (tfnASI_GetPerformanceStatistics *)dlsym(dl_handle, "ASI_GetPerformanceStatistics");
        if (ptr_ASI_GetPerformanceStatistics == NULL)
                {
/*              printf("We found the library, but no stat function. Very Strange!\n");*/
                return;
              }

        /*
         * Indicate that acceleration is available
         */
        asi_accelerator_present = 1;

/*      printf("This system has acceleration!\n");*/

        return;
        }

/* make sure this only gets called once when bn_mod_exp calls bn_mod_exp_mont */
int BN_mod_exp_atalla(BIGNUM *r, BIGNUM *a, const BIGNUM *p, const BIGNUM *m)
        {
        unsigned char *abin;
        unsigned char *pbin;
        unsigned char *mbin;
        unsigned char *rbin;
        int an,pn,mn,ret;
        RSAPrivateKey keydata;

        atalla_initialize_accelerator_handle();
        if(!asi_accelerator_present)
                return 0;


/* We should be able to run without size testing */
# define ASIZE  128
        an=BN_num_bytes(a);
        pn=BN_num_bytes(p);
        mn=BN_num_bytes(m);

        if(an <= ASIZE && pn <= ASIZE && mn <= ASIZE)
            {
            int size=mn;

            assert(an <= mn);
            abin=alloca(size);
            memset(abin,'\0',mn);
            BN_bn2bin(a,abin+size-an);

            pbin=alloca(pn);
            BN_bn2bin(p,pbin);

            mbin=alloca(size);
            memset(mbin,'\0',mn);
            BN_bn2bin(m,mbin+size-mn);

            rbin=alloca(size);

            memset(&keydata,'\0',sizeof keydata);
            keydata.privateExponent.data=pbin;
            keydata.privateExponent.len=pn;
            keydata.modulus.data=mbin;
            keydata.modulus.len=size;

            ret=(*ptr_ASI_RSAPrivateKeyOpFn)(&keydata,rbin,abin,keydata.modulus.len);
/*fprintf(stderr,"!%s\n",BN_bn2hex(a));*/
            if(!ret)
                {
                BN_bin2bn(rbin,keydata.modulus.len,r);
/*fprintf(stderr,"?%s\n",BN_bn2hex(r));*/
                return 1;
                }
            }
        return 0;
        }
#endif /* def ATALLA */


int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p, const BIGNUM *m,
               BN_CTX *ctx)
        {
        int ret;

        bn_check_top(a);
        bn_check_top(p);
        bn_check_top(m);

#ifdef ATALLA
        if(BN_mod_exp_atalla(r,a,p,m))
            return 1;
/* If it fails, try the other methods (but don't try atalla again) */
        tried_atalla=1;
#endif

#ifdef MONT_MUL_MOD
        /* I have finally been able to take out this pre-condition of
         * the top bit being set.  It was caused by an error in BN_div
         * with negatives.  There was also another problem when for a^b%m
         * a >= m.  eay 07-May-97 */
/*      if ((m->d[m->top-1]&BN_TBIT) && BN_is_odd(m)) */

        if (BN_is_odd(m))
                {
                if (a->top == 1)
                        {
                        BN_ULONG A = a->d[0];
                        ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);
                        }
                else
                        ret=BN_mod_exp_mont(r,a,p,m,ctx,NULL);
                }
        else
#endif
#ifdef RECP_MUL_MOD
                { ret=BN_mod_exp_recp(r,a,p,m,ctx); }
#else
                { ret=BN_mod_exp_simple(r,a,p,m,ctx); }
#endif

#ifdef ATALLA
        tried_atalla=0;
#endif

        return(ret);
        }

#ifdef RECP_MUL_MOD
int BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
                    const BIGNUM *m, BN_CTX *ctx)
        {
        int i,j,bits,ret=0,wstart,wend,window,wvalue;
        int start=1,ts=0;
        BIGNUM *aa;
        BIGNUM val[TABLE_SIZE];
        BN_RECP_CTX recp;

        bits=BN_num_bits(p);

        if (bits == 0)
                {
                BN_one(r);
                return(1);
                }

        BN_CTX_start(ctx);
        if ((aa = BN_CTX_get(ctx)) == NULL) goto err;

        BN_RECP_CTX_init(&recp);
        if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;

        BN_init(&(val[0]));
        ts=1;

        if (!BN_mod(&(val[0]),a,m,ctx)) goto err;               /* 1 */

        window = BN_window_bits_for_exponent_size(bits);
        if (window > 1)
                {
                if (!BN_mod_mul_reciprocal(aa,&(val[0]),&(val[0]),&recp,ctx))
                        goto err;                               /* 2 */
                j=1<<(window-1);
                for (i=1; i<j; i++)
                        {
                        BN_init(&val[i]);
                        if (!BN_mod_mul_reciprocal(&(val[i]),&(val[i-1]),aa,&recp,ctx))
                                goto err;
                        }
                ts=i;
                }
                
        start=1;        /* This is used to avoid multiplication etc
                         * when there is only the value '1' in the
                         * buffer. */
        wvalue=0;       /* The 'value' of the window */
        wstart=bits-1;  /* The top bit of the window */
        wend=0;         /* The bottom bit of the window */

        if (!BN_one(r)) goto err;

        for (;;)
                {
                if (BN_is_bit_set(p,wstart) == 0)
                        {
                        if (!start)
                                if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
                                goto err;
                        if (wstart == 0) break;
                        wstart--;
                        continue;
                        }
                /* We now have wstart on a 'set' bit, we now need to work out
                 * how bit a window to do.  To do this we need to scan
                 * forward until the last set bit before the end of the
                 * window */
                j=wstart;
                wvalue=1;
                wend=0;
                for (i=1; i<window; i++)
                        {
                        if (wstart-i < 0) break;
                        if (BN_is_bit_set(p,wstart-i))
                                {
                                wvalue<<=(i-wend);
                                wvalue|=1;
                                wend=i;
                                }
                        }

                /* wend is the size of the current window */
                j=wend+1;
                /* add the 'bytes above' */
                if (!start)
                        for (i=0; i<j; i++)
                                {
                                if (!BN_mod_mul_reciprocal(r,r,r,&recp,ctx))
                                        goto err;
                                }
                
                /* wvalue will be an odd number < 2^window */
                if (!BN_mod_mul_reciprocal(r,r,&(val[wvalue>>1]),&recp,ctx))
                        goto err;

                /* move the 'window' down further */
                wstart-=wend+1;
                wvalue=0;
                start=0;
                if (wstart < 0) break;
                }
        ret=1;
err:
        BN_CTX_end(ctx);
        for (i=0; i<ts; i++)
                BN_clear_free(&(val[i]));
        BN_RECP_CTX_free(&recp);
        return(ret);
        }
#endif

#ifdef MONT_MUL_MOD
int BN_mod_exp_mont(BIGNUM *rr, BIGNUM *a, const BIGNUM *p,
                    const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
        {
        int i,j,bits,ret=0,wstart,wend,window,wvalue;
        int start=1,ts=0;
        BIGNUM *d,*r;
        BIGNUM *aa;
        BIGNUM val[TABLE_SIZE];
        BN_MONT_CTX *mont=NULL;

        bn_check_top(a);
        bn_check_top(p);
        bn_check_top(m);

#ifdef ATALLA
        if(!tried_atalla && BN_mod_exp_atalla(rr,a,p,m))
            return 1;
/* If it fails, try the other methods */
#endif

        if (!(m->d[0] & 1))
                {
                BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
                return(0);
                }
        bits=BN_num_bits(p);
        if (bits == 0)
                {
                BN_one(rr);
                return(1);
                }
        BN_CTX_start(ctx);
        d = BN_CTX_get(ctx);
        r = BN_CTX_get(ctx);
        if (d == NULL || r == NULL) goto err;

        /* If this is not done, things will break in the montgomery
         * part */

        if (in_mont != NULL)
                mont=in_mont;
        else
                {
                if ((mont=BN_MONT_CTX_new()) == NULL) goto err;
                if (!BN_MONT_CTX_set(mont,m,ctx)) goto err;
                }

        BN_init(&val[0]);
        ts=1;
        if (BN_ucmp(a,m) >= 0)
                {
                if (!BN_mod(&(val[0]),a,m,ctx))
                        goto err;
                aa= &(val[0]);
                }
        else
                aa=a;
        if (!BN_to_montgomery(&(val[0]),aa,mont,ctx)) goto err; /* 1 */

        window = BN_window_bits_for_exponent_size(bits);
        if (window > 1)
                {
                if (!BN_mod_mul_montgomery(d,&(val[0]),&(val[0]),mont,ctx)) goto err; /* 2 */
                j=1<<(window-1);
                for (i=1; i<j; i++)
                        {
                        BN_init(&(val[i]));
                        if (!BN_mod_mul_montgomery(&(val[i]),&(val[i-1]),d,mont,ctx))
                                goto err;
                        }
                ts=i;
                }

        start=1;        /* This is used to avoid multiplication etc
                         * when there is only the value '1' in the
                         * buffer. */
        wvalue=0;       /* The 'value' of the window */
        wstart=bits-1;  /* The top bit of the window */
        wend=0;         /* The bottom bit of the window */

        if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
        for (;;)
                {
                if (BN_is_bit_set(p,wstart) == 0)
                        {
                        if (!start)
                                {
                                if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
                                goto err;
                                }
                        if (wstart == 0) break;
                        wstart--;
                        continue;
                        }
                /* We now have wstart on a 'set' bit, we now need to work out
                 * how bit a window to do.  To do this we need to scan
                 * forward until the last set bit before the end of the
                 * window */
                j=wstart;
                wvalue=1;
                wend=0;
                for (i=1; i<window; i++)
                        {
                        if (wstart-i < 0) break;
                        if (BN_is_bit_set(p,wstart-i))
                                {
                                wvalue<<=(i-wend);
                                wvalue|=1;
                                wend=i;
                                }
                        }

                /* wend is the size of the current window */
                j=wend+1;
                /* add the 'bytes above' */
                if (!start)
                        for (i=0; i<j; i++)
                                {
                                if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))
                                        goto err;
                                }
                
                /* wvalue will be an odd number < 2^window */
                if (!BN_mod_mul_montgomery(r,r,&(val[wvalue>>1]),mont,ctx))
                        goto err;

                /* move the 'window' down further */
                wstart-=wend+1;
                wvalue=0;
                start=0;
                if (wstart < 0) break;
                }
        if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
        ret=1;
err:
        if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
        BN_CTX_end(ctx);
        for (i=0; i<ts; i++)
                BN_clear_free(&(val[i]));
        return(ret);
        }

int BN_mod_exp_mont_word(BIGNUM *rr, BN_ULONG a, const BIGNUM *p,
                         const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
        {
        BN_MONT_CTX *mont = NULL;
        int b, bits, ret=0;
        int r_is_one;
        BN_ULONG w, next_w;
        BIGNUM *d, *r, *t;
        BIGNUM *swap_tmp;
#define BN_MOD_MUL_WORD(r, w, m) \
                (BN_mul_word(r, (w)) && \
                (/* BN_ucmp(r, (m)) < 0 ? 1 :*/  \
                        (BN_mod(t, r, m, ctx) && (swap_tmp = r, r = t, t = swap_tmp, 1))))
                /* BN_MOD_MUL_WORD is only used with 'w' large,
                  * so the BN_ucmp test is probably more overhead
                  * than always using BN_mod (which uses BN_copy if
                  * a similar test returns true). */
#define BN_TO_MONTGOMERY_WORD(r, w, mont) \
                (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))

        bn_check_top(p);
        bn_check_top(m);

        if (!(m->d[0] & 1))
                {
                BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
                return(0);
                }
        bits = BN_num_bits(p);
        if (bits == 0)
                {
                BN_one(rr);
                return(1);
                }
        BN_CTX_start(ctx);
        d = BN_CTX_get(ctx);
        r = BN_CTX_get(ctx);
        t = BN_CTX_get(ctx);
        if (d == NULL || r == NULL || t == NULL) goto err;

#ifdef ATALLA
        if (!tried_atalla)
                {
                BN_set_word(t, a);
                if (BN_mod_exp_atalla(rr, t, p, m))
                        {
                        BN_CTX_end(ctx);
                        return 1;
                        }
                }
/* If it fails, try the other methods */
#endif

        if (in_mont != NULL)
                mont=in_mont;
        else
                {
                if ((mont = BN_MONT_CTX_new()) == NULL) goto err;
                if (!BN_MONT_CTX_set(mont, m, ctx)) goto err;
                }

        r_is_one = 1; /* except for Montgomery factor */

        /* bits-1 >= 0 */

        /* The result is accumulated in the product r*w. */
        w = a; /* bit 'bits-1' of 'p' is always set */
        for (b = bits-2; b >= 0; b--)
                {
                /* First, square r*w. */
                next_w = w*w;
                if ((next_w/w) != w) /* overflow */
                        {
                        if (r_is_one)
                                {
                                if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
                                r_is_one = 0;
                                }
                        else
                                {
                                if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
                                }
                        next_w = 1;
                        }
                w = next_w;
                if (!r_is_one)
                        {
                        if (!BN_mod_mul_montgomery(r, r, r, mont, ctx)) goto err;
                        }

                /* Second, multiply r*w by 'a' if exponent bit is set. */
                if (BN_is_bit_set(p, b))
                        {
                        next_w = w*a;
                        if ((next_w/a) != w) /* overflow */
                                {
                                if (r_is_one)
                                        {
                                        if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
                                        r_is_one = 0;
                                        }
                                else
                                        {
                                        if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
                                        }
                                next_w = a;
                                }
                        w = next_w;
                        }
                }

        /* Finally, set r:=r*w. */
        if (w != 1)
                {
                if (r_is_one)
                        {
                        if (!BN_TO_MONTGOMERY_WORD(r, w, mont)) goto err;
                        r_is_one = 0;
                        }
                else
                        {
                        if (!BN_MOD_MUL_WORD(r, w, m)) goto err;
                        }
                }

        if (r_is_one) /* can happen only if a == 1*/
                {
                if (!BN_one(rr)) goto err;
                }
        else
                {
                if (!BN_from_montgomery(rr, r, mont, ctx)) goto err;
                }
        ret = 1;
err:
        if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
        BN_CTX_end(ctx);
        return(ret);
        }
#endif

/* The old fallback, simple version :-) */
int BN_mod_exp_simple(BIGNUM *r, BIGNUM *a, BIGNUM *p, BIGNUM *m,
             BN_CTX *ctx)
        {
        int i,j,bits,ret=0,wstart,wend,window,wvalue,ts=0;
        int start=1;
        BIGNUM *d;
        BIGNUM val[TABLE_SIZE];

        bits=BN_num_bits(p);

        if (bits == 0)
                {
                BN_one(r);
                return(1);
                }

        BN_CTX_start(ctx);
        if ((d = BN_CTX_get(ctx)) == NULL) goto err;

        BN_init(&(val[0]));
        ts=1;
        if (!BN_mod(&(val[0]),a,m,ctx)) goto err;               /* 1 */

        window = BN_window_bits_for_exponent_size(bits);
        if (window > 1)
                {
                if (!BN_mod_mul(d,&(val[0]),&(val[0]),m,ctx))
                        goto err;                               /* 2 */
                j=1<<(window-1);
                for (i=1; i<j; i++)
                        {
                        BN_init(&(val[i]));
                        if (!BN_mod_mul(&(val[i]),&(val[i-1]),d,m,ctx))
                                goto err;
                        }
                ts=i;
                }

        start=1;        /* This is used to avoid multiplication etc
                         * when there is only the value '1' in the
                         * buffer. */
        wvalue=0;       /* The 'value' of the window */
        wstart=bits-1;  /* The top bit of the window */
        wend=0;         /* The bottom bit of the window */

        if (!BN_one(r)) goto err;

        for (;;)
                {
                if (BN_is_bit_set(p,wstart) == 0)
                        {
                        if (!start)
                                if (!BN_mod_mul(r,r,r,m,ctx))
                                goto err;
                        if (wstart == 0) break;
                        wstart--;
                        continue;
                        }
                /* We now have wstart on a 'set' bit, we now need to work out
                 * how bit a window to do.  To do this we need to scan
                 * forward until the last set bit before the end of the
                 * window */
                j=wstart;
                wvalue=1;
                wend=0;
                for (i=1; i<window; i++)
                        {
                        if (wstart-i < 0) break;
                        if (BN_is_bit_set(p,wstart-i))
                                {
                                wvalue<<=(i-wend);
                                wvalue|=1;
                                wend=i;
                                }
                        }

                /* wend is the size of the current window */
                j=wend+1;
                /* add the 'bytes above' */
                if (!start)
                        for (i=0; i<j; i++)
                                {
                                if (!BN_mod_mul(r,r,r,m,ctx))
                                        goto err;
                                }
                
                /* wvalue will be an odd number < 2^window */
                if (!BN_mod_mul(r,r,&(val[wvalue>>1]),m,ctx))
                        goto err;

                /* move the 'window' down further */
                wstart-=wend+1;
                wvalue=0;
                start=0;
                if (wstart < 0) break;
                }
        ret=1;
err:
        BN_CTX_end(ctx);
        for (i=0; i<ts; i++)
                BN_clear_free(&(val[i]));
        return(ret);
        }
