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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) 1998-2005 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 "cryptlib.h"
#include "bn_lcl.h"

/* maximum precomputation table size for *variable* sliding windows */
#define TABLE_SIZE      32

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

      if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
            {
            /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
            BNerr(BN_F_BN_EXP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
            return -1;
            }

      BN_CTX_start(ctx);
      if ((r == a) || (r == p))
            rr = BN_CTX_get(ctx);
      else
            rr = r;
      v = BN_CTX_get(ctx);
      if (rr == NULL || v == 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);
      bn_check_top(r);
      return(ret);
      }


int BN_mod_exp(BIGNUM *r, const 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);

      /* For even modulus  m = 2^k*m_odd,  it might make sense to compute
       * a^p mod m_odd  and  a^p mod 2^k  separately (with Montgomery
       * exponentiation for the odd part), using appropriate exponent
       * reductions, and combine the results using the CRT.
       *
       * For now, we use Montgomery only if the modulus is odd; otherwise,
       * exponentiation using the reciprocal-based quick remaindering
       * algorithm is used.
       *
       * (Timing obtained with expspeed.c [computations  a^p mod m
       * where  a, p, m  are of the same length: 256, 512, 1024, 2048,
       * 4096, 8192 bits], compared to the running time of the
       * standard algorithm:
       *
       *   BN_mod_exp_mont   33 .. 40 %  [AMD K6-2, Linux, debug configuration]
         *                     55 .. 77 %  [UltraSparc processor, but
       *                                  debug-solaris-sparcv8-gcc conf.]
       * 
       *   BN_mod_exp_recp   50 .. 70 %  [AMD K6-2, Linux, debug configuration]
       *                     62 .. 118 % [UltraSparc, debug-solaris-sparcv8-gcc]
       *
       * On the Sparc, BN_mod_exp_recp was faster than BN_mod_exp_mont
       * at 2048 and more bits, but at 512 and 1024 bits, it was
       * slower even than the standard algorithm!
       *
       * "Real" timings [linux-elf, solaris-sparcv9-gcc configurations]
       * should be obtained when the new Montgomery reduction code
       * has been integrated into OpenSSL.)
       */

#define MONT_MUL_MOD
#define MONT_EXP_WORD
#define RECP_MUL_MOD

#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))
            {
#  ifdef MONT_EXP_WORD
            if (a->top == 1 && !a->neg && (BN_get_flags(p, BN_FLG_CONSTTIME) == 0))
                  {
                  BN_ULONG A = a->d[0];
                  ret=BN_mod_exp_mont_word(r,A,p,m,ctx,NULL);
                  }
            else
#  endif
                  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

      bn_check_top(r);
      return(ret);
      }


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;
      BIGNUM *aa;
      /* Table of variables obtained from 'ctx' */
      BIGNUM *val[TABLE_SIZE];
      BN_RECP_CTX recp;

      if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
            {
            /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
            BNerr(BN_F_BN_MOD_EXP_RECP,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
            return -1;
            }

      bits=BN_num_bits(p);

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

      BN_CTX_start(ctx);
      aa = BN_CTX_get(ctx);
      val[0] = BN_CTX_get(ctx);
      if(!aa || !val[0]) goto err;

      BN_RECP_CTX_init(&recp);
      if (m->neg)
            {
            /* ignore sign of 'm' */
            if (!BN_copy(aa, m)) goto err;
            aa->neg = 0;
            if (BN_RECP_CTX_set(&recp,aa,ctx) <= 0) goto err;
            }
      else
            {
            if (BN_RECP_CTX_set(&recp,m,ctx) <= 0) goto err;
            }

      if (!BN_nnmod(val[0],a,m,ctx)) goto err;        /* 1 */
      if (BN_is_zero(val[0]))
            {
            BN_zero(r);
            ret = 1;
            goto err;
            }

      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++)
                  {
                  if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
                              !BN_mod_mul_reciprocal(val[i],val[i-1],
                                    aa,&recp,ctx))
                        goto err;
                  }
            }
            
      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);
      BN_RECP_CTX_free(&recp);
      bn_check_top(r);
      return(ret);
      }


int BN_mod_exp_mont(BIGNUM *rr, const 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;
      BIGNUM *d,*r;
      const BIGNUM *aa;
      /* Table of variables obtained from 'ctx' */
      BIGNUM *val[TABLE_SIZE];
      BN_MONT_CTX *mont=NULL;

      if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
            {
            return BN_mod_exp_mont_consttime(rr, a, p, m, ctx, in_mont);
            }

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

      if (!BN_is_odd(m))
            {
            BNerr(BN_F_BN_MOD_EXP_MONT,BN_R_CALLED_WITH_EVEN_MODULUS);
            return(0);
            }
      bits=BN_num_bits(p);
      if (bits == 0)
            {
            ret = BN_one(rr);
            return ret;
            }

      BN_CTX_start(ctx);
      d = BN_CTX_get(ctx);
      r = BN_CTX_get(ctx);
      val[0] = BN_CTX_get(ctx);
      if (!d || !r || !val[0]) 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;
            }

      if (a->neg || BN_ucmp(a,m) >= 0)
            {
            if (!BN_nnmod(val[0],a,m,ctx))
                  goto err;
            aa= val[0];
            }
      else
            aa=a;
      if (BN_is_zero(aa))
            {
            BN_zero(rr);
            ret = 1;
            goto err;
            }
      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++)
                  {
                  if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
                              !BN_mod_mul_montgomery(val[i],val[i-1],
                                    d,mont,ctx))
                        goto err;
                  }
            }

      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);
      bn_check_top(rr);
      return(ret);
      }


/* BN_mod_exp_mont_consttime() stores the precomputed powers in a specific layout
 * so that accessing any of these table values shows the same access pattern as far
 * as cache lines are concerned.  The following functions are used to transfer a BIGNUM
 * from/to that table. */

static int MOD_EXP_CTIME_COPY_TO_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
      {
      size_t i, j;

      if (bn_wexpand(b, top) == NULL)
            return 0;
      while (b->top < top)
            {
            b->d[b->top++] = 0;
            }
      
      for (i = 0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
            {
            buf[j] = ((unsigned char*)b->d)[i];
            }

      bn_correct_top(b);
      return 1;
      }

static int MOD_EXP_CTIME_COPY_FROM_PREBUF(BIGNUM *b, int top, unsigned char *buf, int idx, int width)
      {
      size_t i, j;

      if (bn_wexpand(b, top) == NULL)
            return 0;

      for (i=0, j=idx; i < top * sizeof b->d[0]; i++, j+=width)
            {
            ((unsigned char*)b->d)[i] = buf[j];
            }

      b->top = top;
      bn_correct_top(b);
      return 1;
      }     

/* Given a pointer value, compute the next address that is a cache line multiple. */
#define MOD_EXP_CTIME_ALIGN(x_) \
      ((unsigned char*)(x_) + (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - (((BN_ULONG)(x_)) & (MOD_EXP_CTIME_MIN_CACHE_LINE_MASK))))

/* This variant of BN_mod_exp_mont() uses fixed windows and the special
 * precomputation memory layout to limit data-dependency to a minimum
 * to protect secret exponents (cf. the hyper-threading timing attacks
 * pointed out by Colin Percival,
 * http://www.daemonology.net/hyperthreading-considered-harmful/)
 */
int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
                const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *in_mont)
      {
      int i,bits,ret=0,idx,window,wvalue;
      int top;
      BIGNUM *r;
      const BIGNUM *aa;
      BN_MONT_CTX *mont=NULL;

      int numPowers;
      unsigned char *powerbufFree=NULL;
      int powerbufLen = 0;
      unsigned char *powerbuf=NULL;
      BIGNUM *computeTemp=NULL, *am=NULL;

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

      top = m->top;

      if (!(m->d[0] & 1))
            {
            BNerr(BN_F_BN_MOD_EXP_MONT_CONSTTIME,BN_R_CALLED_WITH_EVEN_MODULUS);
            return(0);
            }
      bits=BN_num_bits(p);
      if (bits == 0)
            {
            ret = BN_one(rr);
            return ret;
            }

      /* Initialize BIGNUM context and allocate intermediate result */
      BN_CTX_start(ctx);
      r = BN_CTX_get(ctx);
      if (r == NULL) goto err;

      /* Allocate a montgomery context if it was not supplied by the caller.
       * 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;
            }

      /* Get the window size to use with size of p. */
      window = BN_window_bits_for_ctime_exponent_size(bits);

      /* Allocate a buffer large enough to hold all of the pre-computed
       * powers of a.
       */
      numPowers = 1 << window;
      powerbufLen = sizeof(m->d[0])*top*numPowers;
      if ((powerbufFree=(unsigned char*)OPENSSL_malloc(powerbufLen+MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH)) == NULL)
            goto err;
            
      powerbuf = MOD_EXP_CTIME_ALIGN(powerbufFree);
      memset(powerbuf, 0, powerbufLen);

      /* Initialize the intermediate result. Do this early to save double conversion,
       * once each for a^0 and intermediate result.
       */
      if (!BN_to_montgomery(r,BN_value_one(),mont,ctx)) goto err;
      if (!MOD_EXP_CTIME_COPY_TO_PREBUF(r, top, powerbuf, 0, numPowers)) goto err;

      /* Initialize computeTemp as a^1 with montgomery precalcs */
      computeTemp = BN_CTX_get(ctx);
      am = BN_CTX_get(ctx);
      if (computeTemp==NULL || am==NULL) goto err;

      if (a->neg || BN_ucmp(a,m) >= 0)
            {
            if (!BN_mod(am,a,m,ctx))
                  goto err;
            aa= am;
            }
      else
            aa=a;
      if (!BN_to_montgomery(am,aa,mont,ctx)) goto err;
      if (!BN_copy(computeTemp, am)) goto err;
      if (!MOD_EXP_CTIME_COPY_TO_PREBUF(am, top, powerbuf, 1, numPowers)) goto err;

      /* If the window size is greater than 1, then calculate
       * val[i=2..2^winsize-1]. Powers are computed as a*a^(i-1)
       * (even powers could instead be computed as (a^(i/2))^2
       * to use the slight performance advantage of sqr over mul).
       */
      if (window > 1)
            {
            for (i=2; i<numPowers; i++)
                  {
                  /* Calculate a^i = a^(i-1) * a */
                  if (!BN_mod_mul_montgomery(computeTemp,am,computeTemp,mont,ctx))
                        goto err;
                  if (!MOD_EXP_CTIME_COPY_TO_PREBUF(computeTemp, top, powerbuf, i, numPowers)) goto err;
                  }
            }

      /* Adjust the number of bits up to a multiple of the window size.
       * If the exponent length is not a multiple of the window size, then
       * this pads the most significant bits with zeros to normalize the
       * scanning loop to there's no special cases.
       *
       * * NOTE: Making the window size a power of two less than the native
       * * word size ensures that the padded bits won't go past the last
       * * word in the internal BIGNUM structure. Going past the end will
       * * still produce the correct result, but causes a different branch
       * * to be taken in the BN_is_bit_set function.
       */
      bits = ((bits+window-1)/window)*window;
      idx=bits-1; /* The top bit of the window */

      /* Scan the exponent one window at a time starting from the most
       * significant bits.
       */
      while (idx >= 0)
            {
            wvalue=0; /* The 'value' of the window */
            
            /* Scan the window, squaring the result as we go */
            for (i=0; i<window; i++,idx--)
                  {
                  if (!BN_mod_mul_montgomery(r,r,r,mont,ctx))     goto err;
                  wvalue = (wvalue<<1)+BN_is_bit_set(p,idx);
                  }
            
            /* Fetch the appropriate pre-computed value from the pre-buf */
            if (!MOD_EXP_CTIME_COPY_FROM_PREBUF(computeTemp, top, powerbuf, wvalue, numPowers)) goto err;

            /* Multiply the result into the intermediate result */
            if (!BN_mod_mul_montgomery(r,r,computeTemp,mont,ctx)) goto err;
            }

      /* Convert the final result from montgomery to standard format */
      if (!BN_from_montgomery(rr,r,mont,ctx)) goto err;
      ret=1;
err:
      if ((in_mont == NULL) && (mont != NULL)) BN_MONT_CTX_free(mont);
      if (powerbuf!=NULL)
            {
            OPENSSL_cleanse(powerbuf,powerbufLen);
            OPENSSL_free(powerbufFree);
            }
      if (am!=NULL) BN_clear(am);
      if (computeTemp!=NULL) BN_clear(computeTemp);
      BN_CTX_end(ctx);
      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). */
            /* We can use BN_mod and do not need BN_nnmod because our
             * accumulator is never negative (the result of BN_mod does
             * not depend on the sign of the modulus).
             */
#define BN_TO_MONTGOMERY_WORD(r, w, mont) \
            (BN_set_word(r, (w)) && BN_to_montgomery(r, r, (mont), ctx))

      if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
            {
            /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
            BNerr(BN_F_BN_MOD_EXP_MONT_WORD,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
            return -1;
            }

      bn_check_top(p);
      bn_check_top(m);

      if (!BN_is_odd(m))
            {
            BNerr(BN_F_BN_MOD_EXP_MONT_WORD,BN_R_CALLED_WITH_EVEN_MODULUS);
            return(0);
            }
      if (m->top == 1)
            a %= m->d[0]; /* make sure that 'a' is reduced */

      bits = BN_num_bits(p);
      if (bits == 0)
            {
            ret = BN_one(rr);
            return ret;
            }
      if (a == 0)
            {
            BN_zero(rr);
            ret = 1;
            return ret;
            }

      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;

      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);
      bn_check_top(rr);
      return(ret);
      }


/* The old fallback, simple version :-) */
int BN_mod_exp_simple(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;
      BIGNUM *d;
      /* Table of variables obtained from 'ctx' */
      BIGNUM *val[TABLE_SIZE];

      if (BN_get_flags(p, BN_FLG_CONSTTIME) != 0)
            {
            /* BN_FLG_CONSTTIME only supported by BN_mod_exp_mont() */
            BNerr(BN_F_BN_MOD_EXP_SIMPLE,ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
            return -1;
            }

      bits=BN_num_bits(p);

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

      BN_CTX_start(ctx);
      d = BN_CTX_get(ctx);
      val[0] = BN_CTX_get(ctx);
      if(!d || !val[0]) goto err;

      if (!BN_nnmod(val[0],a,m,ctx)) goto err;        /* 1 */
      if (BN_is_zero(val[0]))
            {
            BN_zero(r);
            ret = 1;
            goto err;
            }

      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++)
                  {
                  if(((val[i] = BN_CTX_get(ctx)) == NULL) ||
                              !BN_mod_mul(val[i],val[i-1],d,m,ctx))
                        goto err;
                  }
            }

      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);
      bn_check_top(r);
      return(ret);
      }


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