diff --git a/mpi.c b/mpi.c
deleted file mode 100644
index 2ddd0de..0000000
--- a/mpi.c
+++ /dev/null
@@ -1,8813 +0,0 @@
-/* Start: bn_error.c */
-#include <ltc_tommath.h>
-#ifdef BN_ERROR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-static const struct {
-     int code;
-     char *msg;
-} msgs[] = {
-     { MP_OKAY, "Successful" },
-     { MP_MEM,  "Out of heap" },
-     { MP_VAL,  "Value out of range" }
-};
-
-/* return a char * string for a given code */
-char *mp_error_to_string(int code)
-{
-   int x;
-
-   /* scan the lookup table for the given message */
-   for (x = 0; x < (int)(sizeof(msgs) / sizeof(msgs[0])); x++) {
-       if (msgs[x].code == code) {
-          return msgs[x].msg;
-       }
-   }
-
-   /* generic reply for invalid code */
-   return "Invalid error code";
-}
-
-#endif
-
-/* End: bn_error.c */
-
-/* Start: bn_fast_mp_invmod.c */
-#include <ltc_tommath.h>
-#ifdef BN_FAST_MP_INVMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* computes the modular inverse via binary extended euclidean algorithm, 
- * that is c = 1/a mod b 
- *
- * Based on slow invmod except this is optimized for the case where b is 
- * odd as per HAC Note 14.64 on pp. 610
- */
-int
-fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
-{
-  mp_int  x, y, u, v, B, D;
-  int     res, neg;
-
-  /* 2. [modified] b must be odd   */
-  if (mp_iseven (b) == 1) {
-    return MP_VAL;
-  }
-
-  /* init all our temps */
-  if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
-     return res;
-  }
-
-  /* x == modulus, y == value to invert */
-  if ((res = mp_copy (b, &x)) != MP_OKAY) {
-    goto __ERR;
-  }
-
-  /* we need y = |a| */
-  if ((res = mp_abs (a, &y)) != MP_OKAY) {
-    goto __ERR;
-  }
-
-  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
-  if ((res = mp_copy (&x, &u)) != MP_OKAY) {
-    goto __ERR;
-  }
-  if ((res = mp_copy (&y, &v)) != MP_OKAY) {
-    goto __ERR;
-  }
-  mp_set (&D, 1);
-
-top:
-  /* 4.  while u is even do */
-  while (mp_iseven (&u) == 1) {
-    /* 4.1 u = u/2 */
-    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
-      goto __ERR;
-    }
-    /* 4.2 if B is odd then */
-    if (mp_isodd (&B) == 1) {
-      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
-        goto __ERR;
-      }
-    }
-    /* B = B/2 */
-    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
-      goto __ERR;
-    }
-  }
-
-  /* 5.  while v is even do */
-  while (mp_iseven (&v) == 1) {
-    /* 5.1 v = v/2 */
-    if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
-      goto __ERR;
-    }
-    /* 5.2 if D is odd then */
-    if (mp_isodd (&D) == 1) {
-      /* D = (D-x)/2 */
-      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
-        goto __ERR;
-      }
-    }
-    /* D = D/2 */
-    if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
-      goto __ERR;
-    }
-  }
-
-  /* 6.  if u >= v then */
-  if (mp_cmp (&u, &v) != MP_LT) {
-    /* u = u - v, B = B - D */
-    if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
-      goto __ERR;
-    }
-
-    if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
-      goto __ERR;
-    }
-  } else {
-    /* v - v - u, D = D - B */
-    if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
-      goto __ERR;
-    }
-
-    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
-      goto __ERR;
-    }
-  }
-
-  /* if not zero goto step 4 */
-  if (mp_iszero (&u) == 0) {
-    goto top;
-  }
-
-  /* now a = C, b = D, gcd == g*v */
-
-  /* if v != 1 then there is no inverse */
-  if (mp_cmp_d (&v, 1) != MP_EQ) {
-    res = MP_VAL;
-    goto __ERR;
-  }
-
-  /* b is now the inverse */
-  neg = a->sign;
-  while (D.sign == MP_NEG) {
-    if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
-      goto __ERR;
-    }
-  }
-  mp_exch (&D, c);
-  c->sign = neg;
-  res = MP_OKAY;
-
-__ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
-  return res;
-}
-#endif
-
-/* End: bn_fast_mp_invmod.c */
-
-/* Start: bn_fast_mp_montgomery_reduce.c */
-#include <ltc_tommath.h>
-#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* computes xR**-1 == x (mod N) via Montgomery Reduction
- *
- * This is an optimized implementation of montgomery_reduce
- * which uses the comba method to quickly calculate the columns of the
- * reduction.
- *
- * Based on Algorithm 14.32 on pp.601 of HAC.
-*/
-int
-fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
-{
-  int     ix, res, olduse;
-  mp_word W[MP_WARRAY];
-
-  /* get old used count */
-  olduse = x->used;
-
-  /* grow a as required */
-  if (x->alloc < n->used + 1) {
-    if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
-      return res;
-    }
-  }
-
-  /* first we have to get the digits of the input into
-   * an array of double precision words W[...]
-   */
-  {
-    register mp_word *_W;
-    register mp_digit *tmpx;
-
-    /* alias for the W[] array */
-    _W   = W;
-
-    /* alias for the digits of  x*/
-    tmpx = x->dp;
-
-    /* copy the digits of a into W[0..a->used-1] */
-    for (ix = 0; ix < x->used; ix++) {
-      *_W++ = *tmpx++;
-    }
-
-    /* zero the high words of W[a->used..m->used*2] */
-    for (; ix < n->used * 2 + 1; ix++) {
-      *_W++ = 0;
-    }
-  }
-
-  /* now we proceed to zero successive digits
-   * from the least significant upwards
-   */
-  for (ix = 0; ix < n->used; ix++) {
-    /* mu = ai * m' mod b
-     *
-     * We avoid a double precision multiplication (which isn't required)
-     * by casting the value down to a mp_digit.  Note this requires
-     * that W[ix-1] have  the carry cleared (see after the inner loop)
-     */
-    register mp_digit mu;
-    mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
-
-    /* a = a + mu * m * b**i
-     *
-     * This is computed in place and on the fly.  The multiplication
-     * by b**i is handled by offseting which columns the results
-     * are added to.
-     *
-     * Note the comba method normally doesn't handle carries in the
-     * inner loop In this case we fix the carry from the previous
-     * column since the Montgomery reduction requires digits of the
-     * result (so far) [see above] to work.  This is
-     * handled by fixing up one carry after the inner loop.  The
-     * carry fixups are done in order so after these loops the
-     * first m->used words of W[] have the carries fixed
-     */
-    {
-      register int iy;
-      register mp_digit *tmpn;
-      register mp_word *_W;
-
-      /* alias for the digits of the modulus */
-      tmpn = n->dp;
-
-      /* Alias for the columns set by an offset of ix */
-      _W = W + ix;
-
-      /* inner loop */
-      for (iy = 0; iy < n->used; iy++) {
-          *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
-      }
-    }
-
-    /* now fix carry for next digit, W[ix+1] */
-    W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
-  }
-
-  /* now we have to propagate the carries and
-   * shift the words downward [all those least
-   * significant digits we zeroed].
-   */
-  {
-    register mp_digit *tmpx;
-    register mp_word *_W, *_W1;
-
-    /* nox fix rest of carries */
-
-    /* alias for current word */
-    _W1 = W + ix;
-
-    /* alias for next word, where the carry goes */
-    _W = W + ++ix;
-
-    for (; ix <= n->used * 2 + 1; ix++) {
-      *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
-    }
-
-    /* copy out, A = A/b**n
-     *
-     * The result is A/b**n but instead of converting from an
-     * array of mp_word to mp_digit than calling mp_rshd
-     * we just copy them in the right order
-     */
-
-    /* alias for destination word */
-    tmpx = x->dp;
-
-    /* alias for shifted double precision result */
-    _W = W + n->used;
-
-    for (ix = 0; ix < n->used + 1; ix++) {
-      *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
-    }
-
-    /* zero oldused digits, if the input a was larger than
-     * m->used+1 we'll have to clear the digits
-     */
-    for (; ix < olduse; ix++) {
-      *tmpx++ = 0;
-    }
-  }
-
-  /* set the max used and clamp */
-  x->used = n->used + 1;
-  mp_clamp (x);
-
-  /* if A >= m then A = A - m */
-  if (mp_cmp_mag (x, n) != MP_LT) {
-    return s_mp_sub (x, n, x);
-  }
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_fast_mp_montgomery_reduce.c */
-
-/* Start: bn_fast_s_mp_mul_digs.c */
-#include <ltc_tommath.h>
-#ifdef BN_FAST_S_MP_MUL_DIGS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* Fast (comba) multiplier
- *
- * This is the fast column-array [comba] multiplier.  It is 
- * designed to compute the columns of the product first 
- * then handle the carries afterwards.  This has the effect 
- * of making the nested loops that compute the columns very
- * simple and schedulable on super-scalar processors.
- *
- * This has been modified to produce a variable number of 
- * digits of output so if say only a half-product is required 
- * you don't have to compute the upper half (a feature 
- * required for fast Barrett reduction).
- *
- * Based on Algorithm 14.12 on pp.595 of HAC.
- *
- */
-int
-fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
-{
-  int     olduse, res, pa, ix, iz;
-  mp_digit W[MP_WARRAY];
-  register mp_word  _W;
-
-  /* grow the destination as required */
-  if (c->alloc < digs) {
-    if ((res = mp_grow (c, digs)) != MP_OKAY) {
-      return res;
-    }
-  }
-
-  /* number of output digits to produce */
-  pa = MIN(digs, a->used + b->used);
-
-  /* clear the carry */
-  _W = 0;
-  for (ix = 0; ix <= pa; ix++) { 
-      int      tx, ty;
-      int      iy;
-      mp_digit *tmpx, *tmpy;
-
-      /* get offsets into the two bignums */
-      ty = MIN(b->used-1, ix);
-      tx = ix - ty;
-
-      /* setup temp aliases */
-      tmpx = a->dp + tx;
-      tmpy = b->dp + ty;
-
-      /* this is the number of times the loop will iterrate, essentially its 
-         while (tx++ < a->used && ty-- >= 0) { ... }
-       */
-      iy = MIN(a->used-tx, ty+1);
-
-      /* execute loop */
-      for (iz = 0; iz < iy; ++iz) {
-         _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
-      }
-
-      /* store term */
-      W[ix] = ((mp_digit)_W) & MP_MASK;
-
-      /* make next carry */
-      _W = _W >> ((mp_word)DIGIT_BIT);
-  }
-
-  /* setup dest */
-  olduse  = c->used;
-  c->used = digs;
-
-  {
-    register mp_digit *tmpc;
-    tmpc = c->dp;
-    for (ix = 0; ix < digs; ix++) {
-      /* now extract the previous digit [below the carry] */
-      *tmpc++ = W[ix];
-    }
-
-    /* clear unused digits [that existed in the old copy of c] */
-    for (; ix < olduse; ix++) {
-      *tmpc++ = 0;
-    }
-  }
-  mp_clamp (c);
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_fast_s_mp_mul_digs.c */
-
-/* Start: bn_fast_s_mp_mul_high_digs.c */
-#include <ltc_tommath.h>
-#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* this is a modified version of fast_s_mul_digs that only produces
- * output digits *above* digs.  See the comments for fast_s_mul_digs
- * to see how it works.
- *
- * This is used in the Barrett reduction since for one of the multiplications
- * only the higher digits were needed.  This essentially halves the work.
- *
- * Based on Algorithm 14.12 on pp.595 of HAC.
- */
-int
-fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
-{
-  int     olduse, res, pa, ix, iz;
-  mp_digit W[MP_WARRAY];
-  mp_word  _W;
-
-  /* grow the destination as required */
-  pa = a->used + b->used;
-  if (c->alloc < pa) {
-    if ((res = mp_grow (c, pa)) != MP_OKAY) {
-      return res;
-    }
-  }
-
-  /* number of output digits to produce */
-  pa = a->used + b->used;
-  _W = 0;
-  for (ix = digs; ix <= pa; ix++) { 
-      int      tx, ty, iy;
-      mp_digit *tmpx, *tmpy;
-
-      /* get offsets into the two bignums */
-      ty = MIN(b->used-1, ix);
-      tx = ix - ty;
-
-      /* setup temp aliases */
-      tmpx = a->dp + tx;
-      tmpy = b->dp + ty;
-
-      /* this is the number of times the loop will iterrate, essentially its 
-         while (tx++ < a->used && ty-- >= 0) { ... }
-       */
-      iy = MIN(a->used-tx, ty+1);
-
-      /* execute loop */
-      for (iz = 0; iz < iy; iz++) {
-         _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
-      }
-
-      /* store term */
-      W[ix] = ((mp_digit)_W) & MP_MASK;
-
-      /* make next carry */
-      _W = _W >> ((mp_word)DIGIT_BIT);
-  }
-
-  /* setup dest */
-  olduse  = c->used;
-  c->used = pa;
-
-  {
-    register mp_digit *tmpc;
-
-    tmpc = c->dp + digs;
-    for (ix = digs; ix <= pa; ix++) {
-      /* now extract the previous digit [below the carry] */
-      *tmpc++ = W[ix];
-    }
-
-    /* clear unused digits [that existed in the old copy of c] */
-    for (; ix < olduse; ix++) {
-      *tmpc++ = 0;
-    }
-  }
-  mp_clamp (c);
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_fast_s_mp_mul_high_digs.c */
-
-/* Start: bn_fast_s_mp_sqr.c */
-#include <ltc_tommath.h>
-#ifdef BN_FAST_S_MP_SQR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* fast squaring
- *
- * This is the comba method where the columns of the product
- * are computed first then the carries are computed.  This
- * has the effect of making a very simple inner loop that
- * is executed the most
- *
- * W2 represents the outer products and W the inner.
- *
- * A further optimizations is made because the inner
- * products are of the form "A * B * 2".  The *2 part does
- * not need to be computed until the end which is good
- * because 64-bit shifts are slow!
- *
- * Based on Algorithm 14.16 on pp.597 of HAC.
- *
- */
-/* the jist of squaring...
-
-you do like mult except the offset of the tmpx [one that starts closer to zero]
-can't equal the offset of tmpy.  So basically you set up iy like before then you min it with
-(ty-tx) so that it never happens.  You double all those you add in the inner loop
-
-After that loop you do the squares and add them in.
-
-Remove W2 and don't memset W
-
-*/
-
-int fast_s_mp_sqr (mp_int * a, mp_int * b)
-{
-  int       olduse, res, pa, ix, iz;
-  mp_digit   W[MP_WARRAY], *tmpx;
-  mp_word   W1;
-
-  /* grow the destination as required */
-  pa = a->used + a->used;
-  if (b->alloc < pa) {
-    if ((res = mp_grow (b, pa)) != MP_OKAY) {
-      return res;
-    }
-  }
-
-  /* number of output digits to produce */
-  W1 = 0;
-  for (ix = 0; ix <= pa; ix++) { 
-      int      tx, ty, iy;
-      mp_word  _W;
-      mp_digit *tmpy;
-
-      /* clear counter */
-      _W = 0;
-
-      /* get offsets into the two bignums */
-      ty = MIN(a->used-1, ix);
-      tx = ix - ty;
-
-      /* setup temp aliases */
-      tmpx = a->dp + tx;
-      tmpy = a->dp + ty;
-
-      /* this is the number of times the loop will iterrate, essentially its 
-         while (tx++ < a->used && ty-- >= 0) { ... }
-       */
-      iy = MIN(a->used-tx, ty+1);
-
-      /* now for squaring tx can never equal ty 
-       * we halve the distance since they approach at a rate of 2x
-       * and we have to round because odd cases need to be executed
-       */
-      iy = MIN(iy, (ty-tx+1)>>1);
-
-      /* execute loop */
-      for (iz = 0; iz < iy; iz++) {
-         _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--);
-      }
-
-      /* double the inner product and add carry */
-      _W = _W + _W + W1;
-
-      /* even columns have the square term in them */
-      if ((ix&1) == 0) {
-         _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]);
-      }
-
-      /* store it */
-      W[ix] = _W;
-
-      /* make next carry */
-      W1 = _W >> ((mp_word)DIGIT_BIT);
-  }
-
-  /* setup dest */
-  olduse  = b->used;
-  b->used = a->used+a->used;
-
-  {
-    mp_digit *tmpb;
-    tmpb = b->dp;
-    for (ix = 0; ix < pa; ix++) {
-      *tmpb++ = W[ix] & MP_MASK;
-    }
-
-    /* clear unused digits [that existed in the old copy of c] */
-    for (; ix < olduse; ix++) {
-      *tmpb++ = 0;
-    }
-  }
-  mp_clamp (b);
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_fast_s_mp_sqr.c */
-
-/* Start: bn_mp_2expt.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_2EXPT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* computes a = 2**b 
- *
- * Simple algorithm which zeroes the int, grows it then just sets one bit
- * as required.
- */
-int
-mp_2expt (mp_int * a, int b)
-{
-  int     res;
-
-  /* zero a as per default */
-  mp_zero (a);
-
-  /* grow a to accomodate the single bit */
-  if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) {
-    return res;
-  }
-
-  /* set the used count of where the bit will go */
-  a->used = b / DIGIT_BIT + 1;
-
-  /* put the single bit in its place */
-  a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
-
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_2expt.c */
-
-/* Start: bn_mp_abs.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_ABS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* b = |a| 
- *
- * Simple function copies the input and fixes the sign to positive
- */
-int
-mp_abs (mp_int * a, mp_int * b)
-{
-  int     res;
-
-  /* copy a to b */
-  if (a != b) {
-     if ((res = mp_copy (a, b)) != MP_OKAY) {
-       return res;
-     }
-  }
-
-  /* force the sign of b to positive */
-  b->sign = MP_ZPOS;
-
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_abs.c */
-
-/* Start: bn_mp_add.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_ADD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* high level addition (handles signs) */
-int mp_add (mp_int * a, mp_int * b, mp_int * c)
-{
-  int     sa, sb, res;
-
-  /* get sign of both inputs */
-  sa = a->sign;
-  sb = b->sign;
-
-  /* handle two cases, not four */
-  if (sa == sb) {
-    /* both positive or both negative */
-    /* add their magnitudes, copy the sign */
-    c->sign = sa;
-    res = s_mp_add (a, b, c);
-  } else {
-    /* one positive, the other negative */
-    /* subtract the one with the greater magnitude from */
-    /* the one of the lesser magnitude.  The result gets */
-    /* the sign of the one with the greater magnitude. */
-    if (mp_cmp_mag (a, b) == MP_LT) {
-      c->sign = sb;
-      res = s_mp_sub (b, a, c);
-    } else {
-      c->sign = sa;
-      res = s_mp_sub (a, b, c);
-    }
-  }
-  return res;
-}
-
-#endif
-
-/* End: bn_mp_add.c */
-
-/* Start: bn_mp_add_d.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_ADD_D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* single digit addition */
-int
-mp_add_d (mp_int * a, mp_digit b, mp_int * c)
-{
-  int     res, ix, oldused;
-  mp_digit *tmpa, *tmpc, mu;
-
-  /* grow c as required */
-  if (c->alloc < a->used + 1) {
-     if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
-        return res;
-     }
-  }
-
-  /* if a is negative and |a| >= b, call c = |a| - b */
-  if (a->sign == MP_NEG && (a->used > 1 || a->dp[0] >= b)) {
-     /* temporarily fix sign of a */
-     a->sign = MP_ZPOS;
-
-     /* c = |a| - b */
-     res = mp_sub_d(a, b, c);
-
-     /* fix sign  */
-     a->sign = c->sign = MP_NEG;
-
-     return res;
-  }
-
-  /* old number of used digits in c */
-  oldused = c->used;
-
-  /* sign always positive */
-  c->sign = MP_ZPOS;
-
-  /* source alias */
-  tmpa    = a->dp;
-
-  /* destination alias */
-  tmpc    = c->dp;
-
-  /* if a is positive */
-  if (a->sign == MP_ZPOS) {
-     /* add digit, after this we're propagating
-      * the carry.
-      */
-     *tmpc   = *tmpa++ + b;
-     mu      = *tmpc >> DIGIT_BIT;
-     *tmpc++ &= MP_MASK;
-
-     /* now handle rest of the digits */
-     for (ix = 1; ix < a->used; ix++) {
-        *tmpc   = *tmpa++ + mu;
-        mu      = *tmpc >> DIGIT_BIT;
-        *tmpc++ &= MP_MASK;
-     }
-     /* set final carry */
-     ix++;
-     *tmpc++  = mu;
-
-     /* setup size */
-     c->used = a->used + 1;
-  } else {
-     /* a was negative and |a| < b */
-     c->used  = 1;
-
-     /* the result is a single digit */
-     if (a->used == 1) {
-        *tmpc++  =  b - a->dp[0];
-     } else {
-        *tmpc++  =  b;
-     }
-
-     /* setup count so the clearing of oldused
-      * can fall through correctly
-      */
-     ix       = 1;
-  }
-
-  /* now zero to oldused */
-  while (ix++ < oldused) {
-     *tmpc++ = 0;
-  }
-  mp_clamp(c);
-
-  return MP_OKAY;
-}
-
-#endif
-
-/* End: bn_mp_add_d.c */
-
-/* Start: bn_mp_addmod.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_ADDMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* d = a + b (mod c) */
-int
-mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
-{
-  int     res;
-  mp_int  t;
-
-  if ((res = mp_init (&t)) != MP_OKAY) {
-    return res;
-  }
-
-  if ((res = mp_add (a, b, &t)) != MP_OKAY) {
-    mp_clear (&t);
-    return res;
-  }
-  res = mp_mod (&t, c, d);
-  mp_clear (&t);
-  return res;
-}
-#endif
-
-/* End: bn_mp_addmod.c */
-
-/* Start: bn_mp_and.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_AND_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* AND two ints together */
-int
-mp_and (mp_int * a, mp_int * b, mp_int * c)
-{
-  int     res, ix, px;
-  mp_int  t, *x;
-
-  if (a->used > b->used) {
-    if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
-      return res;
-    }
-    px = b->used;
-    x = b;
-  } else {
-    if ((res = mp_init_copy (&t, b)) != MP_OKAY) {
-      return res;
-    }
-    px = a->used;
-    x = a;
-  }
-
-  for (ix = 0; ix < px; ix++) {
-    t.dp[ix] &= x->dp[ix];
-  }
-
-  /* zero digits above the last from the smallest mp_int */
-  for (; ix < t.used; ix++) {
-    t.dp[ix] = 0;
-  }
-
-  mp_clamp (&t);
-  mp_exch (c, &t);
-  mp_clear (&t);
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_and.c */
-
-/* Start: bn_mp_clamp.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_CLAMP_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* trim unused digits 
- *
- * This is used to ensure that leading zero digits are
- * trimed and the leading "used" digit will be non-zero
- * Typically very fast.  Also fixes the sign if there
- * are no more leading digits
- */
-void
-mp_clamp (mp_int * a)
-{
-  /* decrease used while the most significant digit is
-   * zero.
-   */
-  while (a->used > 0 && a->dp[a->used - 1] == 0) {
-    --(a->used);
-  }
-
-  /* reset the sign flag if used == 0 */
-  if (a->used == 0) {
-    a->sign = MP_ZPOS;
-  }
-}
-#endif
-
-/* End: bn_mp_clamp.c */
-
-/* Start: bn_mp_clear.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_CLEAR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* clear one (frees)  */
-void
-mp_clear (mp_int * a)
-{
-  int i;
-
-  /* only do anything if a hasn't been freed previously */
-  if (a->dp != NULL) {
-    /* first zero the digits */
-    for (i = 0; i < a->used; i++) {
-        a->dp[i] = 0;
-    }
-
-    /* free ram */
-    XFREE(a->dp);
-
-    /* reset members to make debugging easier */
-    a->dp    = NULL;
-    a->alloc = a->used = 0;
-    a->sign  = MP_ZPOS;
-  }
-}
-#endif
-
-/* End: bn_mp_clear.c */
-
-/* Start: bn_mp_clear_multi.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_CLEAR_MULTI_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-#include <stdarg.h>
-
-void mp_clear_multi(mp_int *mp, ...) 
-{
-    mp_int* next_mp = mp;
-    va_list args;
-    va_start(args, mp);
-    while (next_mp != NULL) {
-        mp_clear(next_mp);
-        next_mp = va_arg(args, mp_int*);
-    }
-    va_end(args);
-}
-#endif
-
-/* End: bn_mp_clear_multi.c */
-
-/* Start: bn_mp_cmp.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_CMP_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* compare two ints (signed)*/
-int
-mp_cmp (mp_int * a, mp_int * b)
-{
-  /* compare based on sign */
-  if (a->sign != b->sign) {
-     if (a->sign == MP_NEG) {
-        return MP_LT;
-     } else {
-        return MP_GT;
-     }
-  }
-  
-  /* compare digits */
-  if (a->sign == MP_NEG) {
-     /* if negative compare opposite direction */
-     return mp_cmp_mag(b, a);
-  } else {
-     return mp_cmp_mag(a, b);
-  }
-}
-#endif
-
-/* End: bn_mp_cmp.c */
-
-/* Start: bn_mp_cmp_d.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_CMP_D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* compare a digit */
-int mp_cmp_d(mp_int * a, mp_digit b)
-{
-  /* compare based on sign */
-  if (a->sign == MP_NEG) {
-    return MP_LT;
-  }
-
-  /* compare based on magnitude */
-  if (a->used > 1) {
-    return MP_GT;
-  }
-
-  /* compare the only digit of a to b */
-  if (a->dp[0] > b) {
-    return MP_GT;
-  } else if (a->dp[0] < b) {
-    return MP_LT;
-  } else {
-    return MP_EQ;
-  }
-}
-#endif
-
-/* End: bn_mp_cmp_d.c */
-
-/* Start: bn_mp_cmp_mag.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_CMP_MAG_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* compare maginitude of two ints (unsigned) */
-int mp_cmp_mag (mp_int * a, mp_int * b)
-{
-  int     n;
-  mp_digit *tmpa, *tmpb;
-
-  /* compare based on # of non-zero digits */
-  if (a->used > b->used) {
-    return MP_GT;
-  }
-  
-  if (a->used < b->used) {
-    return MP_LT;
-  }
-
-  /* alias for a */
-  tmpa = a->dp + (a->used - 1);
-
-  /* alias for b */
-  tmpb = b->dp + (a->used - 1);
-
-  /* compare based on digits  */
-  for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
-    if (*tmpa > *tmpb) {
-      return MP_GT;
-    }
-
-    if (*tmpa < *tmpb) {
-      return MP_LT;
-    }
-  }
-  return MP_EQ;
-}
-#endif
-
-/* End: bn_mp_cmp_mag.c */
-
-/* Start: bn_mp_cnt_lsb.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_CNT_LSB_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-static const int lnz[16] = { 
-   4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
-};
-
-/* Counts the number of lsbs which are zero before the first zero bit */
-int mp_cnt_lsb(mp_int *a)
-{
-   int x;
-   mp_digit q, qq;
-
-   /* easy out */
-   if (mp_iszero(a) == 1) {
-      return 0;
-   }
-
-   /* scan lower digits until non-zero */
-   for (x = 0; x < a->used && a->dp[x] == 0; x++);
-   q = a->dp[x];
-   x *= DIGIT_BIT;
-
-   /* now scan this digit until a 1 is found */
-   if ((q & 1) == 0) {
-      do {
-         qq  = q & 15;
-         x  += lnz[qq];
-         q >>= 4;
-      } while (qq == 0);
-   }
-   return x;
-}
-
-#endif
-
-/* End: bn_mp_cnt_lsb.c */
-
-/* Start: bn_mp_copy.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_COPY_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* copy, b = a */
-int
-mp_copy (mp_int * a, mp_int * b)
-{
-  int     res, n;
-
-  /* if dst == src do nothing */
-  if (a == b) {
-    return MP_OKAY;
-  }
-
-  /* grow dest */
-  if (b->alloc < a->used) {
-     if ((res = mp_grow (b, a->used)) != MP_OKAY) {
-        return res;
-     }
-  }
-
-  /* zero b and copy the parameters over */
-  {
-    register mp_digit *tmpa, *tmpb;
-
-    /* pointer aliases */
-
-    /* source */
-    tmpa = a->dp;
-
-    /* destination */
-    tmpb = b->dp;
-
-    /* copy all the digits */
-    for (n = 0; n < a->used; n++) {
-      *tmpb++ = *tmpa++;
-    }
-
-    /* clear high digits */
-    for (; n < b->used; n++) {
-      *tmpb++ = 0;
-    }
-  }
-
-  /* copy used count and sign */
-  b->used = a->used;
-  b->sign = a->sign;
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_copy.c */
-
-/* Start: bn_mp_count_bits.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_COUNT_BITS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* returns the number of bits in an int */
-int
-mp_count_bits (mp_int * a)
-{
-  int     r;
-  mp_digit q;
-
-  /* shortcut */
-  if (a->used == 0) {
-    return 0;
-  }
-
-  /* get number of digits and add that */
-  r = (a->used - 1) * DIGIT_BIT;
-  
-  /* take the last digit and count the bits in it */
-  q = a->dp[a->used - 1];
-  while (q > ((mp_digit) 0)) {
-    ++r;
-    q >>= ((mp_digit) 1);
-  }
-  return r;
-}
-#endif
-
-/* End: bn_mp_count_bits.c */
-
-/* Start: bn_mp_div.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_DIV_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-#ifdef BN_MP_DIV_SMALL
-
-/* slower bit-bang division... also smaller */
-int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d)
-{
-   mp_int ta, tb, tq, q;
-   int    res, n, n2;
-
-  /* is divisor zero ? */
-  if (mp_iszero (b) == 1) {
-    return MP_VAL;
-  }
-
-  /* if a < b then q=0, r = a */
-  if (mp_cmp_mag (a, b) == MP_LT) {
-    if (d != NULL) {
-      res = mp_copy (a, d);
-    } else {
-      res = MP_OKAY;
-    }
-    if (c != NULL) {
-      mp_zero (c);
-    }
-    return res;
-  }
-	
-  /* init our temps */
-  if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) {
-     return res;
-  }
-
-
-  mp_set(&tq, 1);
-  n = mp_count_bits(a) - mp_count_bits(b);
-  if (((res = mp_copy(a, &ta)) != MP_OKAY) ||
-      ((res = mp_copy(b, &tb)) != MP_OKAY) || 
-      ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) ||
-      ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) {
-      goto __ERR;
-  }
-
-  while (n-- >= 0) {
-     if (mp_cmp(&tb, &ta) != MP_GT) {
-        if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) ||
-            ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) {
-           goto __ERR;
-        }
-     }
-     if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) ||
-         ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) {
-           goto __ERR;
-     }
-  }
-
-  /* now q == quotient and ta == remainder */
-  n  = a->sign;
-  n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG);
-  if (c != NULL) {
-     mp_exch(c, &q);
-     c->sign  = n2;
-  }
-  if (d != NULL) {
-     mp_exch(d, &ta);
-     d->sign = n;
-  }
-__ERR:
-   mp_clear_multi(&ta, &tb, &tq, &q, NULL);
-   return res;
-}
-
-#else
-
-/* integer signed division. 
- * c*b + d == a [e.g. a/b, c=quotient, d=remainder]
- * HAC pp.598 Algorithm 14.20
- *
- * Note that the description in HAC is horribly 
- * incomplete.  For example, it doesn't consider 
- * the case where digits are removed from 'x' in 
- * the inner loop.  It also doesn't consider the 
- * case that y has fewer than three digits, etc..
- *
- * The overall algorithm is as described as 
- * 14.20 from HAC but fixed to treat these cases.
-*/
-int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
-{
-  mp_int  q, x, y, t1, t2;
-  int     res, n, t, i, norm, neg;
-
-  /* is divisor zero ? */
-  if (mp_iszero (b) == 1) {
-    return MP_VAL;
-  }
-
-  /* if a < b then q=0, r = a */
-  if (mp_cmp_mag (a, b) == MP_LT) {
-    if (d != NULL) {
-      res = mp_copy (a, d);
-    } else {
-      res = MP_OKAY;
-    }
-    if (c != NULL) {
-      mp_zero (c);
-    }
-    return res;
-  }
-
-  if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) {
-    return res;
-  }
-  q.used = a->used + 2;
-
-  if ((res = mp_init (&t1)) != MP_OKAY) {
-    goto __Q;
-  }
-
-  if ((res = mp_init (&t2)) != MP_OKAY) {
-    goto __T1;
-  }
-
-  if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
-    goto __T2;
-  }
-
-  if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
-    goto __X;
-  }
-
-  /* fix the sign */
-  neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
-  x.sign = y.sign = MP_ZPOS;
-
-  /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */
-  norm = mp_count_bits(&y) % DIGIT_BIT;
-  if (norm < (int)(DIGIT_BIT-1)) {
-     norm = (DIGIT_BIT-1) - norm;
-     if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) {
-       goto __Y;
-     }
-     if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
-       goto __Y;
-     }
-  } else {
-     norm = 0;
-  }
-
-  /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */
-  n = x.used - 1;
-  t = y.used - 1;
-
-  /* while (x >= y*b**n-t) do { q[n-t] += 1; x -= y*b**{n-t} } */
-  if ((res = mp_lshd (&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
-    goto __Y;
-  }
-
-  while (mp_cmp (&x, &y) != MP_LT) {
-    ++(q.dp[n - t]);
-    if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
-      goto __Y;
-    }
-  }
-
-  /* reset y by shifting it back down */
-  mp_rshd (&y, n - t);
-
-  /* step 3. for i from n down to (t + 1) */
-  for (i = n; i >= (t + 1); i--) {
-    if (i > x.used) {
-      continue;
-    }
-
-    /* step 3.1 if xi == yt then set q{i-t-1} to b-1, 
-     * otherwise set q{i-t-1} to (xi*b + x{i-1})/yt */
-    if (x.dp[i] == y.dp[t]) {
-      q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1);
-    } else {
-      mp_word tmp;
-      tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT);
-      tmp |= ((mp_word) x.dp[i - 1]);
-      tmp /= ((mp_word) y.dp[t]);
-      if (tmp > (mp_word) MP_MASK)
-        tmp = MP_MASK;
-      q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK));
-    }
-
-    /* while (q{i-t-1} * (yt * b + y{t-1})) > 
-             xi * b**2 + xi-1 * b + xi-2 
-     
-       do q{i-t-1} -= 1; 
-    */
-    q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK;
-    do {
-      q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK;
-
-      /* find left hand */
-      mp_zero (&t1);
-      t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1];
-      t1.dp[1] = y.dp[t];
-      t1.used = 2;
-      if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
-        goto __Y;
-      }
-
-      /* find right hand */
-      t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2];
-      t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1];
-      t2.dp[2] = x.dp[i];
-      t2.used = 3;
-    } while (mp_cmp_mag(&t1, &t2) == MP_GT);
-
-    /* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
-    if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
-      goto __Y;
-    }
-
-    if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
-      goto __Y;
-    }
-
-    if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
-      goto __Y;
-    }
-
-    /* if x < 0 then { x = x + y*b**{i-t-1}; q{i-t-1} -= 1; } */
-    if (x.sign == MP_NEG) {
-      if ((res = mp_copy (&y, &t1)) != MP_OKAY) {
-        goto __Y;
-      }
-      if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
-        goto __Y;
-      }
-      if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
-        goto __Y;
-      }
-
-      q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK;
-    }
-  }
-
-  /* now q is the quotient and x is the remainder 
-   * [which we have to normalize] 
-   */
-  
-  /* get sign before writing to c */
-  x.sign = x.used == 0 ? MP_ZPOS : a->sign;
-
-  if (c != NULL) {
-    mp_clamp (&q);
-    mp_exch (&q, c);
-    c->sign = neg;
-  }
-
-  if (d != NULL) {
-    mp_div_2d (&x, norm, &x, NULL);
-    mp_exch (&x, d);
-  }
-
-  res = MP_OKAY;
-
-__Y:mp_clear (&y);
-__X:mp_clear (&x);
-__T2:mp_clear (&t2);
-__T1:mp_clear (&t1);
-__Q:mp_clear (&q);
-  return res;
-}
-
-#endif
-
-#endif
-
-/* End: bn_mp_div.c */
-
-/* Start: bn_mp_div_2.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_DIV_2_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* b = a/2 */
-int mp_div_2(mp_int * a, mp_int * b)
-{
-  int     x, res, oldused;
-
-  /* copy */
-  if (b->alloc < a->used) {
-    if ((res = mp_grow (b, a->used)) != MP_OKAY) {
-      return res;
-    }
-  }
-
-  oldused = b->used;
-  b->used = a->used;
-  {
-    register mp_digit r, rr, *tmpa, *tmpb;
-
-    /* source alias */
-    tmpa = a->dp + b->used - 1;
-
-    /* dest alias */
-    tmpb = b->dp + b->used - 1;
-
-    /* carry */
-    r = 0;
-    for (x = b->used - 1; x >= 0; x--) {
-      /* get the carry for the next iteration */
-      rr = *tmpa & 1;
-
-      /* shift the current digit, add in carry and store */
-      *tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
-
-      /* forward carry to next iteration */
-      r = rr;
-    }
-
-    /* zero excess digits */
-    tmpb = b->dp + b->used;
-    for (x = b->used; x < oldused; x++) {
-      *tmpb++ = 0;
-    }
-  }
-  b->sign = a->sign;
-  mp_clamp (b);
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_div_2.c */
-
-/* Start: bn_mp_div_2d.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_DIV_2D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* shift right by a certain bit count (store quotient in c, optional remainder in d) */
-int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
-{
-  mp_digit D, r, rr;
-  int     x, res;
-  mp_int  t;
-
-
-  /* if the shift count is <= 0 then we do no work */
-  if (b <= 0) {
-    res = mp_copy (a, c);
-    if (d != NULL) {
-      mp_zero (d);
-    }
-    return res;
-  }
-
-  if ((res = mp_init (&t)) != MP_OKAY) {
-    return res;
-  }
-
-  /* get the remainder */
-  if (d != NULL) {
-    if ((res = mp_mod_2d (a, b, &t)) != MP_OKAY) {
-      mp_clear (&t);
-      return res;
-    }
-  }
-
-  /* copy */
-  if ((res = mp_copy (a, c)) != MP_OKAY) {
-    mp_clear (&t);
-    return res;
-  }
-
-  /* shift by as many digits in the bit count */
-  if (b >= (int)DIGIT_BIT) {
-    mp_rshd (c, b / DIGIT_BIT);
-  }
-
-  /* shift any bit count < DIGIT_BIT */
-  D = (mp_digit) (b % DIGIT_BIT);
-  if (D != 0) {
-    register mp_digit *tmpc, mask, shift;
-
-    /* mask */
-    mask = (((mp_digit)1) << D) - 1;
-
-    /* shift for lsb */
-    shift = DIGIT_BIT - D;
-
-    /* alias */
-    tmpc = c->dp + (c->used - 1);
-
-    /* carry */
-    r = 0;
-    for (x = c->used - 1; x >= 0; x--) {
-      /* get the lower  bits of this word in a temp */
-      rr = *tmpc & mask;
-
-      /* shift the current word and mix in the carry bits from the previous word */
-      *tmpc = (*tmpc >> D) | (r << shift);
-      --tmpc;
-
-      /* set the carry to the carry bits of the current word found above */
-      r = rr;
-    }
-  }
-  mp_clamp (c);
-  if (d != NULL) {
-    mp_exch (&t, d);
-  }
-  mp_clear (&t);
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_div_2d.c */
-
-/* Start: bn_mp_div_3.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_DIV_3_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* divide by three (based on routine from MPI and the GMP manual) */
-int
-mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
-{
-  mp_int   q;
-  mp_word  w, t;
-  mp_digit b;
-  int      res, ix;
-  
-  /* b = 2**DIGIT_BIT / 3 */
-  b = (((mp_word)1) << ((mp_word)DIGIT_BIT)) / ((mp_word)3);
-
-  if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
-     return res;
-  }
-  
-  q.used = a->used;
-  q.sign = a->sign;
-  w = 0;
-  for (ix = a->used - 1; ix >= 0; ix--) {
-     w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
-
-     if (w >= 3) {
-        /* multiply w by [1/3] */
-        t = (w * ((mp_word)b)) >> ((mp_word)DIGIT_BIT);
-
-        /* now subtract 3 * [w/3] from w, to get the remainder */
-        w -= t+t+t;
-
-        /* fixup the remainder as required since
-         * the optimization is not exact.
-         */
-        while (w >= 3) {
-           t += 1;
-           w -= 3;
-        }
-      } else {
-        t = 0;
-      }
-      q.dp[ix] = (mp_digit)t;
-  }
-
-  /* [optional] store the remainder */
-  if (d != NULL) {
-     *d = (mp_digit)w;
-  }
-
-  /* [optional] store the quotient */
-  if (c != NULL) {
-     mp_clamp(&q);
-     mp_exch(&q, c);
-  }
-  mp_clear(&q);
-  
-  return res;
-}
-
-#endif
-
-/* End: bn_mp_div_3.c */
-
-/* Start: bn_mp_div_d.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_DIV_D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-static int s_is_power_of_two(mp_digit b, int *p)
-{
-   int x;
-
-   for (x = 1; x < DIGIT_BIT; x++) {
-      if (b == (((mp_digit)1)<<x)) {
-         *p = x;
-         return 1;
-      }
-   }
-   return 0;
-}
-
-/* single digit division (based on routine from MPI) */
-int mp_div_d (mp_int * a, mp_digit b, mp_int * c, mp_digit * d)
-{
-  mp_int  q;
-  mp_word w;
-  mp_digit t;
-  int     res, ix;
-
-  /* cannot divide by zero */
-  if (b == 0) {
-     return MP_VAL;
-  }
-
-  /* quick outs */
-  if (b == 1 || mp_iszero(a) == 1) {
-     if (d != NULL) {
-        *d = 0;
-     }
-     if (c != NULL) {
-        return mp_copy(a, c);
-     }
-     return MP_OKAY;
-  }
-
-  /* power of two ? */
-  if (s_is_power_of_two(b, &ix) == 1) {
-     if (d != NULL) {
-        *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
-     }
-     if (c != NULL) {
-        return mp_div_2d(a, ix, c, NULL);
-     }
-     return MP_OKAY;
-  }
-
-#ifdef BN_MP_DIV_3_C
-  /* three? */
-  if (b == 3) {
-     return mp_div_3(a, c, d);
-  }
-#endif
-
-  /* no easy answer [c'est la vie].  Just division */
-  if ((res = mp_init_size(&q, a->used)) != MP_OKAY) {
-     return res;
-  }
-  
-  q.used = a->used;
-  q.sign = a->sign;
-  w = 0;
-  for (ix = a->used - 1; ix >= 0; ix--) {
-     w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]);
-     
-     if (w >= b) {
-        t = (mp_digit)(w / b);
-        w -= ((mp_word)t) * ((mp_word)b);
-      } else {
-        t = 0;
-      }
-      q.dp[ix] = (mp_digit)t;
-  }
-  
-  if (d != NULL) {
-     *d = (mp_digit)w;
-  }
-  
-  if (c != NULL) {
-     mp_clamp(&q);
-     mp_exch(&q, c);
-  }
-  mp_clear(&q);
-  
-  return res;
-}
-
-#endif
-
-/* End: bn_mp_div_d.c */
-
-/* Start: bn_mp_dr_is_modulus.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_DR_IS_MODULUS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* determines if a number is a valid DR modulus */
-int mp_dr_is_modulus(mp_int *a)
-{
-   int ix;
-
-   /* must be at least two digits */
-   if (a->used < 2) {
-      return 0;
-   }
-
-   /* must be of the form b**k - a [a <= b] so all
-    * but the first digit must be equal to -1 (mod b).
-    */
-   for (ix = 1; ix < a->used; ix++) {
-       if (a->dp[ix] != MP_MASK) {
-          return 0;
-       }
-   }
-   return 1;
-}
-
-#endif
-
-/* End: bn_mp_dr_is_modulus.c */
-
-/* Start: bn_mp_dr_reduce.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_DR_REDUCE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* reduce "x" in place modulo "n" using the Diminished Radix algorithm.
- *
- * Based on algorithm from the paper
- *
- * "Generating Efficient Primes for Discrete Log Cryptosystems"
- *                 Chae Hoon Lim, Pil Loong Lee,
- *          POSTECH Information Research Laboratories
- *
- * The modulus must be of a special format [see manual]
- *
- * Has been modified to use algorithm 7.10 from the LTM book instead
- *
- * Input x must be in the range 0 <= x <= (n-1)**2
- */
-int
-mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k)
-{
-  int      err, i, m;
-  mp_word  r;
-  mp_digit mu, *tmpx1, *tmpx2;
-
-  /* m = digits in modulus */
-  m = n->used;
-
-  /* ensure that "x" has at least 2m digits */
-  if (x->alloc < m + m) {
-    if ((err = mp_grow (x, m + m)) != MP_OKAY) {
-      return err;
-    }
-  }
-
-/* top of loop, this is where the code resumes if
- * another reduction pass is required.
- */
-top:
-  /* aliases for digits */
-  /* alias for lower half of x */
-  tmpx1 = x->dp;
-
-  /* alias for upper half of x, or x/B**m */
-  tmpx2 = x->dp + m;
-
-  /* set carry to zero */
-  mu = 0;
-
-  /* compute (x mod B**m) + k * [x/B**m] inline and inplace */
-  for (i = 0; i < m; i++) {
-      r         = ((mp_word)*tmpx2++) * ((mp_word)k) + *tmpx1 + mu;
-      *tmpx1++  = (mp_digit)(r & MP_MASK);
-      mu        = (mp_digit)(r >> ((mp_word)DIGIT_BIT));
-  }
-
-  /* set final carry */
-  *tmpx1++ = mu;
-
-  /* zero words above m */
-  for (i = m + 1; i < x->used; i++) {
-      *tmpx1++ = 0;
-  }
-
-  /* clamp, sub and return */
-  mp_clamp (x);
-
-  /* if x >= n then subtract and reduce again
-   * Each successive "recursion" makes the input smaller and smaller.
-   */
-  if (mp_cmp_mag (x, n) != MP_LT) {
-    s_mp_sub(x, n, x);
-    goto top;
-  }
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_dr_reduce.c */
-
-/* Start: bn_mp_dr_setup.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_DR_SETUP_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* determines the setup value */
-void mp_dr_setup(mp_int *a, mp_digit *d)
-{
-   /* the casts are required if DIGIT_BIT is one less than
-    * the number of bits in a mp_digit [e.g. DIGIT_BIT==31]
-    */
-   *d = (mp_digit)((((mp_word)1) << ((mp_word)DIGIT_BIT)) - 
-        ((mp_word)a->dp[0]));
-}
-
-#endif
-
-/* End: bn_mp_dr_setup.c */
-
-/* Start: bn_mp_exch.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_EXCH_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* swap the elements of two integers, for cases where you can't simply swap the 
- * mp_int pointers around
- */
-void
-mp_exch (mp_int * a, mp_int * b)
-{
-  mp_int  t;
-
-  t  = *a;
-  *a = *b;
-  *b = t;
-}
-#endif
-
-/* End: bn_mp_exch.c */
-
-/* Start: bn_mp_expt_d.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_EXPT_D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* calculate c = a**b  using a square-multiply algorithm */
-int mp_expt_d (mp_int * a, mp_digit b, mp_int * c)
-{
-  int     res, x;
-  mp_int  g;
-
-  if ((res = mp_init_copy (&g, a)) != MP_OKAY) {
-    return res;
-  }
-
-  /* set initial result */
-  mp_set (c, 1);
-
-  for (x = 0; x < (int) DIGIT_BIT; x++) {
-    /* square */
-    if ((res = mp_sqr (c, c)) != MP_OKAY) {
-      mp_clear (&g);
-      return res;
-    }
-
-    /* if the bit is set multiply */
-    if ((b & (mp_digit) (((mp_digit)1) << (DIGIT_BIT - 1))) != 0) {
-      if ((res = mp_mul (c, &g, c)) != MP_OKAY) {
-         mp_clear (&g);
-         return res;
-      }
-    }
-
-    /* shift to next bit */
-    b <<= 1;
-  }
-
-  mp_clear (&g);
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_expt_d.c */
-
-/* Start: bn_mp_exptmod.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_EXPTMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-
-/* this is a shell function that calls either the normal or Montgomery
- * exptmod functions.  Originally the call to the montgomery code was
- * embedded in the normal function but that wasted alot of stack space
- * for nothing (since 99% of the time the Montgomery code would be called)
- */
-int mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
-{
-  int dr;
-
-  /* modulus P must be positive */
-  if (P->sign == MP_NEG) {
-     return MP_VAL;
-  }
-
-  /* if exponent X is negative we have to recurse */
-  if (X->sign == MP_NEG) {
-#ifdef BN_MP_INVMOD_C
-     mp_int tmpG, tmpX;
-     int err;
-
-     /* first compute 1/G mod P */
-     if ((err = mp_init(&tmpG)) != MP_OKAY) {
-        return err;
-     }
-     if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) {
-        mp_clear(&tmpG);
-        return err;
-     }
-
-     /* now get |X| */
-     if ((err = mp_init(&tmpX)) != MP_OKAY) {
-        mp_clear(&tmpG);
-        return err;
-     }
-     if ((err = mp_abs(X, &tmpX)) != MP_OKAY) {
-        mp_clear_multi(&tmpG, &tmpX, NULL);
-        return err;
-     }
-
-     /* and now compute (1/G)**|X| instead of G**X [X < 0] */
-     err = mp_exptmod(&tmpG, &tmpX, P, Y);
-     mp_clear_multi(&tmpG, &tmpX, NULL);
-     return err;
-#else 
-     /* no invmod */
-     return MP_VAL
-#endif
-  }
-
-#ifdef BN_MP_DR_IS_MODULUS_C
-  /* is it a DR modulus? */
-  dr = mp_dr_is_modulus(P);
-#else
-  dr = 0;
-#endif
-
-#ifdef BN_MP_REDUCE_IS_2K_C
-  /* if not, is it a uDR modulus? */
-  if (dr == 0) {
-     dr = mp_reduce_is_2k(P) << 1;
-  }
-#endif
-    
-  /* if the modulus is odd or dr != 0 use the fast method */
-#ifdef BN_MP_EXPTMOD_FAST_C
-  if (mp_isodd (P) == 1 || dr !=  0) {
-    return mp_exptmod_fast (G, X, P, Y, dr);
-  } else {
-#endif
-#ifdef BN_S_MP_EXPTMOD_C
-    /* otherwise use the generic Barrett reduction technique */
-    return s_mp_exptmod (G, X, P, Y);
-#else
-    /* no exptmod for evens */
-    return MP_VAL;
-#endif
-#ifdef BN_MP_EXPTMOD_FAST_C
-  }
-#endif
-}
-
-#endif
-
-/* End: bn_mp_exptmod.c */
-
-/* Start: bn_mp_exptmod_fast.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_EXPTMOD_FAST_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
- *
- * Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
- * The value of k changes based on the size of the exponent.
- *
- * Uses Montgomery or Diminished Radix reduction [whichever appropriate]
- */
-
-#ifdef MP_LOW_MEM
-   #define TAB_SIZE 32
-#else
-   #define TAB_SIZE 256
-#endif
-
-int
-mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
-{
-  mp_int  M[TAB_SIZE], res;
-  mp_digit buf, mp;
-  int     err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
-
-  /* use a pointer to the reduction algorithm.  This allows us to use
-   * one of many reduction algorithms without modding the guts of
-   * the code with if statements everywhere.
-   */
-  int     (*redux)(mp_int*,mp_int*,mp_digit);
-
-  /* find window size */
-  x = mp_count_bits (X);
-  if (x <= 7) {
-    winsize = 2;
-  } else if (x <= 36) {
-    winsize = 3;
-  } else if (x <= 140) {
-    winsize = 4;
-  } else if (x <= 450) {
-    winsize = 5;
-  } else if (x <= 1303) {
-    winsize = 6;
-  } else if (x <= 3529) {
-    winsize = 7;
-  } else {
-    winsize = 8;
-  }
-
-#ifdef MP_LOW_MEM
-  if (winsize > 5) {
-     winsize = 5;
-  }
-#endif
-
-  /* init M array */
-  /* init first cell */
-  if ((err = mp_init(&M[1])) != MP_OKAY) {
-     return err;
-  }
-
-  /* now init the second half of the array */
-  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
-    if ((err = mp_init(&M[x])) != MP_OKAY) {
-      for (y = 1<<(winsize-1); y < x; y++) {
-        mp_clear (&M[y]);
-      }
-      mp_clear(&M[1]);
-      return err;
-    }
-  }
-
-  /* determine and setup reduction code */
-  if (redmode == 0) {
-#ifdef BN_MP_MONTGOMERY_SETUP_C     
-     /* now setup montgomery  */
-     if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
-        goto __M;
-     }
-#else
-     err = MP_VAL;
-     goto __M;
-#endif
-
-     /* automatically pick the comba one if available (saves quite a few calls/ifs) */
-#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C
-     if (((P->used * 2 + 1) < MP_WARRAY) &&
-          P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
-        redux = fast_mp_montgomery_reduce;
-     } else 
-#endif
-     {
-#ifdef BN_MP_MONTGOMERY_REDUCE_C
-        /* use slower baseline Montgomery method */
-        redux = mp_montgomery_reduce;
-#else
-        err = MP_VAL;
-        goto __M;
-#endif
-     }
-  } else if (redmode == 1) {
-#if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C)
-     /* setup DR reduction for moduli of the form B**k - b */
-     mp_dr_setup(P, &mp);
-     redux = mp_dr_reduce;
-#else
-     err = MP_VAL;
-     goto __M;
-#endif
-  } else {
-#if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C)
-     /* setup DR reduction for moduli of the form 2**k - b */
-     if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
-        goto __M;
-     }
-     redux = mp_reduce_2k;
-#else
-     err = MP_VAL;
-     goto __M;
-#endif
-  }
-
-  /* setup result */
-  if ((err = mp_init (&res)) != MP_OKAY) {
-    goto __M;
-  }
-
-  /* create M table
-   *
-
-   *
-   * The first half of the table is not computed though accept for M[0] and M[1]
-   */
-
-  if (redmode == 0) {
-#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
-     /* now we need R mod m */
-     if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
-       goto __RES;
-     }
-#else 
-     err = MP_VAL;
-     goto __RES;
-#endif
-
-     /* now set M[1] to G * R mod m */
-     if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
-       goto __RES;
-     }
-  } else {
-     mp_set(&res, 1);
-     if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
-        goto __RES;
-     }
-  }
-
-  /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
-  if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
-    goto __RES;
-  }
-
-  for (x = 0; x < (winsize - 1); x++) {
-    if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
-      goto __RES;
-    }
-    if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
-      goto __RES;
-    }
-  }
-
-  /* create upper table */
-  for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
-    if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
-      goto __RES;
-    }
-    if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
-      goto __RES;
-    }
-  }
-
-  /* set initial mode and bit cnt */
-  mode   = 0;
-  bitcnt = 1;
-  buf    = 0;
-  digidx = X->used - 1;
-  bitcpy = 0;
-  bitbuf = 0;
-
-  for (;;) {
-    /* grab next digit as required */
-    if (--bitcnt == 0) {
-      /* if digidx == -1 we are out of digits so break */
-      if (digidx == -1) {
-        break;
-      }
-      /* read next digit and reset bitcnt */
-      buf    = X->dp[digidx--];
-      bitcnt = (int)DIGIT_BIT;
-    }
-
-    /* grab the next msb from the exponent */
-    y     = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
-    buf <<= (mp_digit)1;
-
-    /* if the bit is zero and mode == 0 then we ignore it
-     * These represent the leading zero bits before the first 1 bit
-     * in the exponent.  Technically this opt is not required but it
-     * does lower the # of trivial squaring/reductions used
-     */
-    if (mode == 0 && y == 0) {
-      continue;
-    }
-
-    /* if the bit is zero and mode == 1 then we square */
-    if (mode == 1 && y == 0) {
-      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
-        goto __RES;
-      }
-      if ((err = redux (&res, P, mp)) != MP_OKAY) {
-        goto __RES;
-      }
-      continue;
-    }
-
-    /* else we add it to the window */
-    bitbuf |= (y << (winsize - ++bitcpy));
-    mode    = 2;
-
-    if (bitcpy == winsize) {
-      /* ok window is filled so square as required and multiply  */
-      /* square first */
-      for (x = 0; x < winsize; x++) {
-        if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
-          goto __RES;
-        }
-        if ((err = redux (&res, P, mp)) != MP_OKAY) {
-          goto __RES;
-        }
-      }
-
-      /* then multiply */
-      if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
-        goto __RES;
-      }
-      if ((err = redux (&res, P, mp)) != MP_OKAY) {
-        goto __RES;
-      }
-
-      /* empty window and reset */
-      bitcpy = 0;
-      bitbuf = 0;
-      mode   = 1;
-    }
-  }
-
-  /* if bits remain then square/multiply */
-  if (mode == 2 && bitcpy > 0) {
-    /* square then multiply if the bit is set */
-    for (x = 0; x < bitcpy; x++) {
-      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
-        goto __RES;
-      }
-      if ((err = redux (&res, P, mp)) != MP_OKAY) {
-        goto __RES;
-      }
-
-      /* get next bit of the window */
-      bitbuf <<= 1;
-      if ((bitbuf & (1 << winsize)) != 0) {
-        /* then multiply */
-        if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
-          goto __RES;
-        }
-        if ((err = redux (&res, P, mp)) != MP_OKAY) {
-          goto __RES;
-        }
-      }
-    }
-  }
-
-  if (redmode == 0) {
-     /* fixup result if Montgomery reduction is used
-      * recall that any value in a Montgomery system is
-      * actually multiplied by R mod n.  So we have
-      * to reduce one more time to cancel out the factor
-      * of R.
-      */
-     if ((err = redux(&res, P, mp)) != MP_OKAY) {
-       goto __RES;
-     }
-  }
-
-  /* swap res with Y */
-  mp_exch (&res, Y);
-  err = MP_OKAY;
-__RES:mp_clear (&res);
-__M:
-  mp_clear(&M[1]);
-  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
-    mp_clear (&M[x]);
-  }
-  return err;
-}
-#endif
-
-
-/* End: bn_mp_exptmod_fast.c */
-
-/* Start: bn_mp_exteuclid.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_EXTEUCLID_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* Extended euclidean algorithm of (a, b) produces 
-   a*u1 + b*u2 = u3
- */
-int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3)
-{
-   mp_int u1,u2,u3,v1,v2,v3,t1,t2,t3,q,tmp;
-   int err;
-
-   if ((err = mp_init_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL)) != MP_OKAY) {
-      return err;
-   }
-
-   /* initialize, (u1,u2,u3) = (1,0,a) */
-   mp_set(&u1, 1);
-   if ((err = mp_copy(a, &u3)) != MP_OKAY)                                        { goto _ERR; }
-
-   /* initialize, (v1,v2,v3) = (0,1,b) */
-   mp_set(&v2, 1);
-   if ((err = mp_copy(b, &v3)) != MP_OKAY)                                        { goto _ERR; }
-
-   /* loop while v3 != 0 */
-   while (mp_iszero(&v3) == MP_NO) {
-       /* q = u3/v3 */
-       if ((err = mp_div(&u3, &v3, &q, NULL)) != MP_OKAY)                         { goto _ERR; }
-
-       /* (t1,t2,t3) = (u1,u2,u3) - (v1,v2,v3)q */
-       if ((err = mp_mul(&v1, &q, &tmp)) != MP_OKAY)                              { goto _ERR; }
-       if ((err = mp_sub(&u1, &tmp, &t1)) != MP_OKAY)                             { goto _ERR; }
-       if ((err = mp_mul(&v2, &q, &tmp)) != MP_OKAY)                              { goto _ERR; }
-       if ((err = mp_sub(&u2, &tmp, &t2)) != MP_OKAY)                             { goto _ERR; }
-       if ((err = mp_mul(&v3, &q, &tmp)) != MP_OKAY)                              { goto _ERR; }
-       if ((err = mp_sub(&u3, &tmp, &t3)) != MP_OKAY)                             { goto _ERR; }
-
-       /* (u1,u2,u3) = (v1,v2,v3) */
-       if ((err = mp_copy(&v1, &u1)) != MP_OKAY)                                  { goto _ERR; }
-       if ((err = mp_copy(&v2, &u2)) != MP_OKAY)                                  { goto _ERR; }
-       if ((err = mp_copy(&v3, &u3)) != MP_OKAY)                                  { goto _ERR; }
-
-       /* (v1,v2,v3) = (t1,t2,t3) */
-       if ((err = mp_copy(&t1, &v1)) != MP_OKAY)                                  { goto _ERR; }
-       if ((err = mp_copy(&t2, &v2)) != MP_OKAY)                                  { goto _ERR; }
-       if ((err = mp_copy(&t3, &v3)) != MP_OKAY)                                  { goto _ERR; }
-   }
-
-   /* copy result out */
-   if (U1 != NULL) { mp_exch(U1, &u1); }
-   if (U2 != NULL) { mp_exch(U2, &u2); }
-   if (U3 != NULL) { mp_exch(U3, &u3); }
-
-   err = MP_OKAY;
-_ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL);
-   return err;
-}
-#endif
-
-/* End: bn_mp_exteuclid.c */
-
-/* Start: bn_mp_fread.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_FREAD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* read a bigint from a file stream in ASCII */
-int mp_fread(mp_int *a, int radix, FILE *stream)
-{
-   int err, ch, neg, y;
-   
-   /* clear a */
-   mp_zero(a);
-   
-   /* if first digit is - then set negative */
-   ch = fgetc(stream);
-   if (ch == '-') {
-      neg = MP_NEG;
-      ch = fgetc(stream);
-   } else {
-      neg = MP_ZPOS;
-   }
-   
-   for (;;) {
-      /* find y in the radix map */
-      for (y = 0; y < radix; y++) {
-          if (mp_s_rmap[y] == ch) {
-             break;
-          }
-      }
-      if (y == radix) {
-         break;
-      }
-      
-      /* shift up and add */
-      if ((err = mp_mul_d(a, radix, a)) != MP_OKAY) {
-         return err;
-      }
-      if ((err = mp_add_d(a, y, a)) != MP_OKAY) {
-         return err;
-      }
-      
-      ch = fgetc(stream);
-   }
-   if (mp_cmp_d(a, 0) != MP_EQ) {
-      a->sign = neg;
-   }
-   
-   return MP_OKAY;
-}
-
-#endif
-
-/* End: bn_mp_fread.c */
-
-/* Start: bn_mp_fwrite.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_FWRITE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-int mp_fwrite(mp_int *a, int radix, FILE *stream)
-{
-   char *buf;
-   int err, len, x;
-   
-   if ((err = mp_radix_size(a, radix, &len)) != MP_OKAY) {
-      return err;
-   }
-
-   buf = OPT_CAST(char) XMALLOC (len);
-   if (buf == NULL) {
-      return MP_MEM;
-   }
-   
-   if ((err = mp_toradix(a, buf, radix)) != MP_OKAY) {
-      XFREE (buf);
-      return err;
-   }
-   
-   for (x = 0; x < len; x++) {
-       if (fputc(buf[x], stream) == EOF) {
-          XFREE (buf);
-          return MP_VAL;
-       }
-   }
-   
-   XFREE (buf);
-   return MP_OKAY;
-}
-
-#endif
-
-/* End: bn_mp_fwrite.c */
-
-/* Start: bn_mp_gcd.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_GCD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* Greatest Common Divisor using the binary method */
-int mp_gcd (mp_int * a, mp_int * b, mp_int * c)
-{
-  mp_int  u, v;
-  int     k, u_lsb, v_lsb, res;
-
-  /* either zero than gcd is the largest */
-  if (mp_iszero (a) == 1 && mp_iszero (b) == 0) {
-    return mp_abs (b, c);
-  }
-  if (mp_iszero (a) == 0 && mp_iszero (b) == 1) {
-    return mp_abs (a, c);
-  }
-
-  /* optimized.  At this point if a == 0 then
-   * b must equal zero too
-   */
-  if (mp_iszero (a) == 1) {
-    mp_zero(c);
-    return MP_OKAY;
-  }
-
-  /* get copies of a and b we can modify */
-  if ((res = mp_init_copy (&u, a)) != MP_OKAY) {
-    return res;
-  }
-
-  if ((res = mp_init_copy (&v, b)) != MP_OKAY) {
-    goto __U;
-  }
-
-  /* must be positive for the remainder of the algorithm */
-  u.sign = v.sign = MP_ZPOS;
-
-  /* B1.  Find the common power of two for u and v */
-  u_lsb = mp_cnt_lsb(&u);
-  v_lsb = mp_cnt_lsb(&v);
-  k     = MIN(u_lsb, v_lsb);
-
-  if (k > 0) {
-     /* divide the power of two out */
-     if ((res = mp_div_2d(&u, k, &u, NULL)) != MP_OKAY) {
-        goto __V;
-     }
-
-     if ((res = mp_div_2d(&v, k, &v, NULL)) != MP_OKAY) {
-        goto __V;
-     }
-  }
-
-  /* divide any remaining factors of two out */
-  if (u_lsb != k) {
-     if ((res = mp_div_2d(&u, u_lsb - k, &u, NULL)) != MP_OKAY) {
-        goto __V;
-     }
-  }
-
-  if (v_lsb != k) {
-     if ((res = mp_div_2d(&v, v_lsb - k, &v, NULL)) != MP_OKAY) {
-        goto __V;
-     }
-  }
-
-  while (mp_iszero(&v) == 0) {
-     /* make sure v is the largest */
-     if (mp_cmp_mag(&u, &v) == MP_GT) {
-        /* swap u and v to make sure v is >= u */
-        mp_exch(&u, &v);
-     }
-     
-     /* subtract smallest from largest */
-     if ((res = s_mp_sub(&v, &u, &v)) != MP_OKAY) {
-        goto __V;
-     }
-     
-     /* Divide out all factors of two */
-     if ((res = mp_div_2d(&v, mp_cnt_lsb(&v), &v, NULL)) != MP_OKAY) {
-        goto __V;
-     } 
-  } 
-
-  /* multiply by 2**k which we divided out at the beginning */
-  if ((res = mp_mul_2d (&u, k, c)) != MP_OKAY) {
-     goto __V;
-  }
-  c->sign = MP_ZPOS;
-  res = MP_OKAY;
-__V:mp_clear (&u);
-__U:mp_clear (&v);
-  return res;
-}
-#endif
-
-/* End: bn_mp_gcd.c */
-
-/* Start: bn_mp_get_int.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_GET_INT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* get the lower 32-bits of an mp_int */
-unsigned long mp_get_int(mp_int * a) 
-{
-  int i;
-  unsigned long res;
-
-  if (a->used == 0) {
-     return 0;
-  }
-
-  /* get number of digits of the lsb we have to read */
-  i = MIN(a->used,(int)((sizeof(unsigned long)*CHAR_BIT+DIGIT_BIT-1)/DIGIT_BIT))-1;
-
-  /* get most significant digit of result */
-  res = DIGIT(a,i);
-   
-  while (--i >= 0) {
-    res = (res << DIGIT_BIT) | DIGIT(a,i);
-  }
-
-  /* force result to 32-bits always so it is consistent on non 32-bit platforms */
-  return res & 0xFFFFFFFFUL;
-}
-#endif
-
-/* End: bn_mp_get_int.c */
-
-/* Start: bn_mp_grow.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_GROW_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* grow as required */
-int mp_grow (mp_int * a, int size)
-{
-  int     i;
-  mp_digit *tmp;
-
-  /* if the alloc size is smaller alloc more ram */
-  if (a->alloc < size) {
-    /* ensure there are always at least MP_PREC digits extra on top */
-    size += (MP_PREC * 2) - (size % MP_PREC);
-
-    /* reallocate the array a->dp
-     *
-     * We store the return in a temporary variable
-     * in case the operation failed we don't want
-     * to overwrite the dp member of a.
-     */
-    tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * size);
-    if (tmp == NULL) {
-      /* reallocation failed but "a" is still valid [can be freed] */
-      return MP_MEM;
-    }
-
-    /* reallocation succeeded so set a->dp */
-    a->dp = tmp;
-
-    /* zero excess digits */
-    i        = a->alloc;
-    a->alloc = size;
-    for (; i < a->alloc; i++) {
-      a->dp[i] = 0;
-    }
-  }
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_grow.c */
-
-/* Start: bn_mp_init.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_INIT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* init a new mp_int */
-int mp_init (mp_int * a)
-{
-  int i;
-
-  /* allocate memory required and clear it */
-  a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC);
-  if (a->dp == NULL) {
-    return MP_MEM;
-  }
-
-  /* set the digits to zero */
-  for (i = 0; i < MP_PREC; i++) {
-      a->dp[i] = 0;
-  }
-
-  /* set the used to zero, allocated digits to the default precision
-   * and sign to positive */
-  a->used  = 0;
-  a->alloc = MP_PREC;
-  a->sign  = MP_ZPOS;
-
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_init.c */
-
-/* Start: bn_mp_init_copy.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_INIT_COPY_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* creates "a" then copies b into it */
-int mp_init_copy (mp_int * a, mp_int * b)
-{
-  int     res;
-
-  if ((res = mp_init (a)) != MP_OKAY) {
-    return res;
-  }
-  return mp_copy (b, a);
-}
-#endif
-
-/* End: bn_mp_init_copy.c */
-
-/* Start: bn_mp_init_multi.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_INIT_MULTI_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-#include <stdarg.h>
-
-int mp_init_multi(mp_int *mp, ...) 
-{
-    mp_err res = MP_OKAY;      /* Assume ok until proven otherwise */
-    int n = 0;                 /* Number of ok inits */
-    mp_int* cur_arg = mp;
-    va_list args;
-
-    va_start(args, mp);        /* init args to next argument from caller */
-    while (cur_arg != NULL) {
-        if (mp_init(cur_arg) != MP_OKAY) {
-            /* Oops - error! Back-track and mp_clear what we already
-               succeeded in init-ing, then return error.
-            */
-            va_list clean_args;
-            
-            /* end the current list */
-            va_end(args);
-            
-            /* now start cleaning up */            
-            cur_arg = mp;
-            va_start(clean_args, mp);
-            while (n--) {
-                mp_clear(cur_arg);
-                cur_arg = va_arg(clean_args, mp_int*);
-            }
-            va_end(clean_args);
-            res = MP_MEM;
-            break;
-        }
-        n++;
-        cur_arg = va_arg(args, mp_int*);
-    }
-    va_end(args);
-    return res;                /* Assumed ok, if error flagged above. */
-}
-
-#endif
-
-/* End: bn_mp_init_multi.c */
-
-/* Start: bn_mp_init_set.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_INIT_SET_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* initialize and set a digit */
-int mp_init_set (mp_int * a, mp_digit b)
-{
-  int err;
-  if ((err = mp_init(a)) != MP_OKAY) {
-     return err;
-  }
-  mp_set(a, b);
-  return err;
-}
-#endif
-
-/* End: bn_mp_init_set.c */
-
-/* Start: bn_mp_init_set_int.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_INIT_SET_INT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* initialize and set a digit */
-int mp_init_set_int (mp_int * a, unsigned long b)
-{
-  int err;
-  if ((err = mp_init(a)) != MP_OKAY) {
-     return err;
-  }
-  return mp_set_int(a, b);
-}
-#endif
-
-/* End: bn_mp_init_set_int.c */
-
-/* Start: bn_mp_init_size.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_INIT_SIZE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* init an mp_init for a given size */
-int mp_init_size (mp_int * a, int size)
-{
-  int x;
-
-  /* pad size so there are always extra digits */
-  size += (MP_PREC * 2) - (size % MP_PREC);	
-  
-  /* alloc mem */
-  a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size);
-  if (a->dp == NULL) {
-    return MP_MEM;
-  }
-
-  /* set the members */
-  a->used  = 0;
-  a->alloc = size;
-  a->sign  = MP_ZPOS;
-
-  /* zero the digits */
-  for (x = 0; x < size; x++) {
-      a->dp[x] = 0;
-  }
-
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_init_size.c */
-
-/* Start: bn_mp_invmod.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_INVMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* hac 14.61, pp608 */
-int mp_invmod (mp_int * a, mp_int * b, mp_int * c)
-{
-  /* b cannot be negative */
-  if (b->sign == MP_NEG || mp_iszero(b) == 1) {
-    return MP_VAL;
-  }
-
-#ifdef BN_FAST_MP_INVMOD_C
-  /* if the modulus is odd we can use a faster routine instead */
-  if (mp_isodd (b) == 1) {
-    return fast_mp_invmod (a, b, c);
-  }
-#endif
-
-#ifdef BN_MP_INVMOD_SLOW_C
-  return mp_invmod_slow(a, b, c);
-#endif
-
-  return MP_VAL;
-}
-#endif
-
-/* End: bn_mp_invmod.c */
-
-/* Start: bn_mp_invmod_slow.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_INVMOD_SLOW_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* hac 14.61, pp608 */
-int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c)
-{
-  mp_int  x, y, u, v, A, B, C, D;
-  int     res;
-
-  /* b cannot be negative */
-  if (b->sign == MP_NEG || mp_iszero(b) == 1) {
-    return MP_VAL;
-  }
-
-  /* init temps */
-  if ((res = mp_init_multi(&x, &y, &u, &v, 
-                           &A, &B, &C, &D, NULL)) != MP_OKAY) {
-     return res;
-  }
-
-  /* x = a, y = b */
-  if ((res = mp_copy (a, &x)) != MP_OKAY) {
-    goto __ERR;
-  }
-  if ((res = mp_copy (b, &y)) != MP_OKAY) {
-    goto __ERR;
-  }
-
-  /* 2. [modified] if x,y are both even then return an error! */
-  if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
-    res = MP_VAL;
-    goto __ERR;
-  }
-
-  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
-  if ((res = mp_copy (&x, &u)) != MP_OKAY) {
-    goto __ERR;
-  }
-  if ((res = mp_copy (&y, &v)) != MP_OKAY) {
-    goto __ERR;
-  }
-  mp_set (&A, 1);
-  mp_set (&D, 1);
-
-top:
-  /* 4.  while u is even do */
-  while (mp_iseven (&u) == 1) {
-    /* 4.1 u = u/2 */
-    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
-      goto __ERR;
-    }
-    /* 4.2 if A or B is odd then */
-    if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) {
-      /* A = (A+y)/2, B = (B-x)/2 */
-      if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
-         goto __ERR;
-      }
-      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
-         goto __ERR;
-      }
-    }
-    /* A = A/2, B = B/2 */
-    if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
-      goto __ERR;
-    }
-    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
-      goto __ERR;
-    }
-  }
-
-  /* 5.  while v is even do */
-  while (mp_iseven (&v) == 1) {
-    /* 5.1 v = v/2 */
-    if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
-      goto __ERR;
-    }
-    /* 5.2 if C or D is odd then */
-    if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) {
-      /* C = (C+y)/2, D = (D-x)/2 */
-      if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
-         goto __ERR;
-      }
-      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
-         goto __ERR;
-      }
-    }
-    /* C = C/2, D = D/2 */
-    if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
-      goto __ERR;
-    }
-    if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
-      goto __ERR;
-    }
-  }
-
-  /* 6.  if u >= v then */
-  if (mp_cmp (&u, &v) != MP_LT) {
-    /* u = u - v, A = A - C, B = B - D */
-    if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
-      goto __ERR;
-    }
-
-    if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
-      goto __ERR;
-    }
-
-    if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
-      goto __ERR;
-    }
-  } else {
-    /* v - v - u, C = C - A, D = D - B */
-    if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
-      goto __ERR;
-    }
-
-    if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
-      goto __ERR;
-    }
-
-    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
-      goto __ERR;
-    }
-  }
-
-  /* if not zero goto step 4 */
-  if (mp_iszero (&u) == 0)
-    goto top;
-
-  /* now a = C, b = D, gcd == g*v */
-
-  /* if v != 1 then there is no inverse */
-  if (mp_cmp_d (&v, 1) != MP_EQ) {
-    res = MP_VAL;
-    goto __ERR;
-  }
-
-  /* if its too low */
-  while (mp_cmp_d(&C, 0) == MP_LT) {
-      if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
-         goto __ERR;
-      }
-  }
-  
-  /* too big */
-  while (mp_cmp_mag(&C, b) != MP_LT) {
-      if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
-         goto __ERR;
-      }
-  }
-  
-  /* C is now the inverse */
-  mp_exch (&C, c);
-  res = MP_OKAY;
-__ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
-  return res;
-}
-#endif
-
-/* End: bn_mp_invmod_slow.c */
-
-/* Start: bn_mp_is_square.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_IS_SQUARE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* Check if remainders are possible squares - fast exclude non-squares */
-static const char rem_128[128] = {
- 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
- 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
- 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
- 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
- 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
- 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
- 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1,
- 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1
-};
-
-static const char rem_105[105] = {
- 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1,
- 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1,
- 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1,
- 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1,
- 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1,
- 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1,
- 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1
-};
-
-/* Store non-zero to ret if arg is square, and zero if not */
-int mp_is_square(mp_int *arg,int *ret) 
-{
-  int           res;
-  mp_digit      c;
-  mp_int        t;
-  unsigned long r;
-
-  /* Default to Non-square :) */
-  *ret = MP_NO; 
-
-  if (arg->sign == MP_NEG) {
-    return MP_VAL;
-  }
-
-  /* digits used?  (TSD) */
-  if (arg->used == 0) {
-     return MP_OKAY;
-  }
-
-  /* First check mod 128 (suppose that DIGIT_BIT is at least 7) */
-  if (rem_128[127 & DIGIT(arg,0)] == 1) {
-     return MP_OKAY;
-  }
-
-  /* Next check mod 105 (3*5*7) */
-  if ((res = mp_mod_d(arg,105,&c)) != MP_OKAY) {
-     return res;
-  }
-  if (rem_105[c] == 1) {
-     return MP_OKAY;
-  }
-
-
-  if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) {
-     return res;
-  }
-  if ((res = mp_mod(arg,&t,&t)) != MP_OKAY) {
-     goto ERR;
-  }
-  r = mp_get_int(&t);
-  /* Check for other prime modules, note it's not an ERROR but we must
-   * free "t" so the easiest way is to goto ERR.  We know that res
-   * is already equal to MP_OKAY from the mp_mod call 
-   */ 
-  if ( (1L<<(r%11)) & 0x5C4L )             goto ERR;
-  if ( (1L<<(r%13)) & 0x9E4L )             goto ERR;
-  if ( (1L<<(r%17)) & 0x5CE8L )            goto ERR;
-  if ( (1L<<(r%19)) & 0x4F50CL )           goto ERR;
-  if ( (1L<<(r%23)) & 0x7ACCA0L )          goto ERR;
-  if ( (1L<<(r%29)) & 0xC2EDD0CL )         goto ERR;
-  if ( (1L<<(r%31)) & 0x6DE2B848L )        goto ERR;
-
-  /* Final check - is sqr(sqrt(arg)) == arg ? */
-  if ((res = mp_sqrt(arg,&t)) != MP_OKAY) {
-     goto ERR;
-  }
-  if ((res = mp_sqr(&t,&t)) != MP_OKAY) {
-     goto ERR;
-  }
-
-  *ret = (mp_cmp_mag(&t,arg) == MP_EQ) ? MP_YES : MP_NO;
-ERR:mp_clear(&t);
-  return res;
-}
-#endif
-
-/* End: bn_mp_is_square.c */
-
-/* Start: bn_mp_jacobi.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_JACOBI_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* computes the jacobi c = (a | n) (or Legendre if n is prime)
- * HAC pp. 73 Algorithm 2.149
- */
-int mp_jacobi (mp_int * a, mp_int * p, int *c)
-{
-  mp_int  a1, p1;
-  int     k, s, r, res;
-  mp_digit residue;
-
-  /* if p <= 0 return MP_VAL */
-  if (mp_cmp_d(p, 0) != MP_GT) {
-     return MP_VAL;
-  }
-
-  /* step 1.  if a == 0, return 0 */
-  if (mp_iszero (a) == 1) {
-    *c = 0;
-    return MP_OKAY;
-  }
-
-  /* step 2.  if a == 1, return 1 */
-  if (mp_cmp_d (a, 1) == MP_EQ) {
-    *c = 1;
-    return MP_OKAY;
-  }
-
-  /* default */
-  s = 0;
-
-  /* step 3.  write a = a1 * 2**k  */
-  if ((res = mp_init_copy (&a1, a)) != MP_OKAY) {
-    return res;
-  }
-
-  if ((res = mp_init (&p1)) != MP_OKAY) {
-    goto __A1;
-  }
-
-  /* divide out larger power of two */
-  k = mp_cnt_lsb(&a1);
-  if ((res = mp_div_2d(&a1, k, &a1, NULL)) != MP_OKAY) {
-     goto __P1;
-  }
-
-  /* step 4.  if e is even set s=1 */
-  if ((k & 1) == 0) {
-    s = 1;
-  } else {
-    /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
-    residue = p->dp[0] & 7;
-
-    if (residue == 1 || residue == 7) {
-      s = 1;
-    } else if (residue == 3 || residue == 5) {
-      s = -1;
-    }
-  }
-
-  /* step 5.  if p == 3 (mod 4) *and* a1 == 3 (mod 4) then s = -s */
-  if ( ((p->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
-    s = -s;
-  }
-
-  /* if a1 == 1 we're done */
-  if (mp_cmp_d (&a1, 1) == MP_EQ) {
-    *c = s;
-  } else {
-    /* n1 = n mod a1 */
-    if ((res = mp_mod (p, &a1, &p1)) != MP_OKAY) {
-      goto __P1;
-    }
-    if ((res = mp_jacobi (&p1, &a1, &r)) != MP_OKAY) {
-      goto __P1;
-    }
-    *c = s * r;
-  }
-
-  /* done */
-  res = MP_OKAY;
-__P1:mp_clear (&p1);
-__A1:mp_clear (&a1);
-  return res;
-}
-#endif
-
-/* End: bn_mp_jacobi.c */
-
-/* Start: bn_mp_karatsuba_mul.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_KARATSUBA_MUL_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* c = |a| * |b| using Karatsuba Multiplication using 
- * three half size multiplications
- *
- * Let B represent the radix [e.g. 2**DIGIT_BIT] and 
- * let n represent half of the number of digits in 
- * the min(a,b)
- *
- * a = a1 * B**n + a0
- * b = b1 * B**n + b0
- *
- * Then, a * b => 
-   a1b1 * B**2n + ((a1 - a0)(b1 - b0) + a0b0 + a1b1) * B + a0b0
- *
- * Note that a1b1 and a0b0 are used twice and only need to be 
- * computed once.  So in total three half size (half # of 
- * digit) multiplications are performed, a0b0, a1b1 and 
- * (a1-b1)(a0-b0)
- *
- * Note that a multiplication of half the digits requires
- * 1/4th the number of single precision multiplications so in 
- * total after one call 25% of the single precision multiplications 
- * are saved.  Note also that the call to mp_mul can end up back 
- * in this function if the a0, a1, b0, or b1 are above the threshold.  
- * This is known as divide-and-conquer and leads to the famous 
- * O(N**lg(3)) or O(N**1.584) work which is asymptopically lower than 
- * the standard O(N**2) that the baseline/comba methods use.  
- * Generally though the overhead of this method doesn't pay off 
- * until a certain size (N ~ 80) is reached.
- */
-int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c)
-{
-  mp_int  x0, x1, y0, y1, t1, x0y0, x1y1;
-  int     B, err;
-
-  /* default the return code to an error */
-  err = MP_MEM;
-
-  /* min # of digits */
-  B = MIN (a->used, b->used);
-
-  /* now divide in two */
-  B = B >> 1;
-
-  /* init copy all the temps */
-  if (mp_init_size (&x0, B) != MP_OKAY)
-    goto ERR;
-  if (mp_init_size (&x1, a->used - B) != MP_OKAY)
-    goto X0;
-  if (mp_init_size (&y0, B) != MP_OKAY)
-    goto X1;
-  if (mp_init_size (&y1, b->used - B) != MP_OKAY)
-    goto Y0;
-
-  /* init temps */
-  if (mp_init_size (&t1, B * 2) != MP_OKAY)
-    goto Y1;
-  if (mp_init_size (&x0y0, B * 2) != MP_OKAY)
-    goto T1;
-  if (mp_init_size (&x1y1, B * 2) != MP_OKAY)
-    goto X0Y0;
-
-  /* now shift the digits */
-  x0.used = y0.used = B;
-  x1.used = a->used - B;
-  y1.used = b->used - B;
-
-  {
-    register int x;
-    register mp_digit *tmpa, *tmpb, *tmpx, *tmpy;
-
-    /* we copy the digits directly instead of using higher level functions
-     * since we also need to shift the digits
-     */
-    tmpa = a->dp;
-    tmpb = b->dp;
-
-    tmpx = x0.dp;
-    tmpy = y0.dp;
-    for (x = 0; x < B; x++) {
-      *tmpx++ = *tmpa++;
-      *tmpy++ = *tmpb++;
-    }
-
-    tmpx = x1.dp;
-    for (x = B; x < a->used; x++) {
-      *tmpx++ = *tmpa++;
-    }
-
-    tmpy = y1.dp;
-    for (x = B; x < b->used; x++) {
-      *tmpy++ = *tmpb++;
-    }
-  }
-
-  /* only need to clamp the lower words since by definition the 
-   * upper words x1/y1 must have a known number of digits
-   */
-  mp_clamp (&x0);
-  mp_clamp (&y0);
-
-  /* now calc the products x0y0 and x1y1 */
-  /* after this x0 is no longer required, free temp [x0==t2]! */
-  if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY)  
-    goto X1Y1;          /* x0y0 = x0*y0 */
-  if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY)
-    goto X1Y1;          /* x1y1 = x1*y1 */
-
-  /* now calc x1-x0 and y1-y0 */
-  if (mp_sub (&x1, &x0, &t1) != MP_OKAY)
-    goto X1Y1;          /* t1 = x1 - x0 */
-  if (mp_sub (&y1, &y0, &x0) != MP_OKAY)
-    goto X1Y1;          /* t2 = y1 - y0 */
-  if (mp_mul (&t1, &x0, &t1) != MP_OKAY)
-    goto X1Y1;          /* t1 = (x1 - x0) * (y1 - y0) */
-
-  /* add x0y0 */
-  if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY)
-    goto X1Y1;          /* t2 = x0y0 + x1y1 */
-  if (mp_sub (&x0, &t1, &t1) != MP_OKAY)
-    goto X1Y1;          /* t1 = x0y0 + x1y1 - (x1-x0)*(y1-y0) */
-
-  /* shift by B */
-  if (mp_lshd (&t1, B) != MP_OKAY)
-    goto X1Y1;          /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
-  if (mp_lshd (&x1y1, B * 2) != MP_OKAY)
-    goto X1Y1;          /* x1y1 = x1y1 << 2*B */
-
-  if (mp_add (&x0y0, &t1, &t1) != MP_OKAY)
-    goto X1Y1;          /* t1 = x0y0 + t1 */
-  if (mp_add (&t1, &x1y1, c) != MP_OKAY)
-    goto X1Y1;          /* t1 = x0y0 + t1 + x1y1 */
-
-  /* Algorithm succeeded set the return code to MP_OKAY */
-  err = MP_OKAY;
-
-X1Y1:mp_clear (&x1y1);
-X0Y0:mp_clear (&x0y0);
-T1:mp_clear (&t1);
-Y1:mp_clear (&y1);
-Y0:mp_clear (&y0);
-X1:mp_clear (&x1);
-X0:mp_clear (&x0);
-ERR:
-  return err;
-}
-#endif
-
-/* End: bn_mp_karatsuba_mul.c */
-
-/* Start: bn_mp_karatsuba_sqr.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_KARATSUBA_SQR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* Karatsuba squaring, computes b = a*a using three 
- * half size squarings
- *
- * See comments of karatsuba_mul for details.  It 
- * is essentially the same algorithm but merely 
- * tuned to perform recursive squarings.
- */
-int mp_karatsuba_sqr (mp_int * a, mp_int * b)
-{
-  mp_int  x0, x1, t1, t2, x0x0, x1x1;
-  int     B, err;
-
-  err = MP_MEM;
-
-  /* min # of digits */
-  B = a->used;
-
-  /* now divide in two */
-  B = B >> 1;
-
-  /* init copy all the temps */
-  if (mp_init_size (&x0, B) != MP_OKAY)
-    goto ERR;
-  if (mp_init_size (&x1, a->used - B) != MP_OKAY)
-    goto X0;
-
-  /* init temps */
-  if (mp_init_size (&t1, a->used * 2) != MP_OKAY)
-    goto X1;
-  if (mp_init_size (&t2, a->used * 2) != MP_OKAY)
-    goto T1;
-  if (mp_init_size (&x0x0, B * 2) != MP_OKAY)
-    goto T2;
-  if (mp_init_size (&x1x1, (a->used - B) * 2) != MP_OKAY)
-    goto X0X0;
-
-  {
-    register int x;
-    register mp_digit *dst, *src;
-
-    src = a->dp;
-
-    /* now shift the digits */
-    dst = x0.dp;
-    for (x = 0; x < B; x++) {
-      *dst++ = *src++;
-    }
-
-    dst = x1.dp;
-    for (x = B; x < a->used; x++) {
-      *dst++ = *src++;
-    }
-  }
-
-  x0.used = B;
-  x1.used = a->used - B;
-
-  mp_clamp (&x0);
-
-  /* now calc the products x0*x0 and x1*x1 */
-  if (mp_sqr (&x0, &x0x0) != MP_OKAY)
-    goto X1X1;           /* x0x0 = x0*x0 */
-  if (mp_sqr (&x1, &x1x1) != MP_OKAY)
-    goto X1X1;           /* x1x1 = x1*x1 */
-
-  /* now calc (x1-x0)**2 */
-  if (mp_sub (&x1, &x0, &t1) != MP_OKAY)
-    goto X1X1;           /* t1 = x1 - x0 */
-  if (mp_sqr (&t1, &t1) != MP_OKAY)
-    goto X1X1;           /* t1 = (x1 - x0) * (x1 - x0) */
-
-  /* add x0y0 */
-  if (s_mp_add (&x0x0, &x1x1, &t2) != MP_OKAY)
-    goto X1X1;           /* t2 = x0x0 + x1x1 */
-  if (mp_sub (&t2, &t1, &t1) != MP_OKAY)
-    goto X1X1;           /* t1 = x0x0 + x1x1 - (x1-x0)*(x1-x0) */
-
-  /* shift by B */
-  if (mp_lshd (&t1, B) != MP_OKAY)
-    goto X1X1;           /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */
-  if (mp_lshd (&x1x1, B * 2) != MP_OKAY)
-    goto X1X1;           /* x1x1 = x1x1 << 2*B */
-
-  if (mp_add (&x0x0, &t1, &t1) != MP_OKAY)
-    goto X1X1;           /* t1 = x0x0 + t1 */
-  if (mp_add (&t1, &x1x1, b) != MP_OKAY)
-    goto X1X1;           /* t1 = x0x0 + t1 + x1x1 */
-
-  err = MP_OKAY;
-
-X1X1:mp_clear (&x1x1);
-X0X0:mp_clear (&x0x0);
-T2:mp_clear (&t2);
-T1:mp_clear (&t1);
-X1:mp_clear (&x1);
-X0:mp_clear (&x0);
-ERR:
-  return err;
-}
-#endif
-
-/* End: bn_mp_karatsuba_sqr.c */
-
-/* Start: bn_mp_lcm.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_LCM_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* computes least common multiple as |a*b|/(a, b) */
-int mp_lcm (mp_int * a, mp_int * b, mp_int * c)
-{
-  int     res;
-  mp_int  t1, t2;
-
-
-  if ((res = mp_init_multi (&t1, &t2, NULL)) != MP_OKAY) {
-    return res;
-  }
-
-  /* t1 = get the GCD of the two inputs */
-  if ((res = mp_gcd (a, b, &t1)) != MP_OKAY) {
-    goto __T;
-  }
-
-  /* divide the smallest by the GCD */
-  if (mp_cmp_mag(a, b) == MP_LT) {
-     /* store quotient in t2 such that t2 * b is the LCM */
-     if ((res = mp_div(a, &t1, &t2, NULL)) != MP_OKAY) {
-        goto __T;
-     }
-     res = mp_mul(b, &t2, c);
-  } else {
-     /* store quotient in t2 such that t2 * a is the LCM */
-     if ((res = mp_div(b, &t1, &t2, NULL)) != MP_OKAY) {
-        goto __T;
-     }
-     res = mp_mul(a, &t2, c);
-  }
-
-  /* fix the sign to positive */
-  c->sign = MP_ZPOS;
-
-__T:
-  mp_clear_multi (&t1, &t2, NULL);
-  return res;
-}
-#endif
-
-/* End: bn_mp_lcm.c */
-
-/* Start: bn_mp_lshd.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_LSHD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* shift left a certain amount of digits */
-int mp_lshd (mp_int * a, int b)
-{
-  int     x, res;
-
-  /* if its less than zero return */
-  if (b <= 0) {
-    return MP_OKAY;
-  }
-
-  /* grow to fit the new digits */
-  if (a->alloc < a->used + b) {
-     if ((res = mp_grow (a, a->used + b)) != MP_OKAY) {
-       return res;
-     }
-  }
-
-  {
-    register mp_digit *top, *bottom;
-
-    /* increment the used by the shift amount then copy upwards */
-    a->used += b;
-
-    /* top */
-    top = a->dp + a->used - 1;
-
-    /* base */
-    bottom = a->dp + a->used - 1 - b;
-
-    /* much like mp_rshd this is implemented using a sliding window
-     * except the window goes the otherway around.  Copying from
-     * the bottom to the top.  see bn_mp_rshd.c for more info.
-     */
-    for (x = a->used - 1; x >= b; x--) {
-      *top-- = *bottom--;
-    }
-
-    /* zero the lower digits */
-    top = a->dp;
-    for (x = 0; x < b; x++) {
-      *top++ = 0;
-    }
-  }
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_lshd.c */
-
-/* Start: bn_mp_mod.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_MOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* c = a mod b, 0 <= c < b */
-int
-mp_mod (mp_int * a, mp_int * b, mp_int * c)
-{
-  mp_int  t;
-  int     res;
-
-  if ((res = mp_init (&t)) != MP_OKAY) {
-    return res;
-  }
-
-  if ((res = mp_div (a, b, NULL, &t)) != MP_OKAY) {
-    mp_clear (&t);
-    return res;
-  }
-
-  if (t.sign != b->sign) {
-    res = mp_add (b, &t, c);
-  } else {
-    res = MP_OKAY;
-    mp_exch (&t, c);
-  }
-
-  mp_clear (&t);
-  return res;
-}
-#endif
-
-/* End: bn_mp_mod.c */
-
-/* Start: bn_mp_mod_2d.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_MOD_2D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* calc a value mod 2**b */
-int
-mp_mod_2d (mp_int * a, int b, mp_int * c)
-{
-  int     x, res;
-
-  /* if b is <= 0 then zero the int */
-  if (b <= 0) {
-    mp_zero (c);
-    return MP_OKAY;
-  }
-
-  /* if the modulus is larger than the value than return */
-  if (b > (int) (a->used * DIGIT_BIT)) {
-    res = mp_copy (a, c);
-    return res;
-  }
-
-  /* copy */
-  if ((res = mp_copy (a, c)) != MP_OKAY) {
-    return res;
-  }
-
-  /* zero digits above the last digit of the modulus */
-  for (x = (b / DIGIT_BIT) + ((b % DIGIT_BIT) == 0 ? 0 : 1); x < c->used; x++) {
-    c->dp[x] = 0;
-  }
-  /* clear the digit that is not completely outside/inside the modulus */
-  c->dp[b / DIGIT_BIT] &=
-    (mp_digit) ((((mp_digit) 1) << (((mp_digit) b) % DIGIT_BIT)) - ((mp_digit) 1));
-  mp_clamp (c);
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_mod_2d.c */
-
-/* Start: bn_mp_mod_d.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_MOD_D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-int
-mp_mod_d (mp_int * a, mp_digit b, mp_digit * c)
-{
-  return mp_div_d(a, b, NULL, c);
-}
-#endif
-
-/* End: bn_mp_mod_d.c */
-
-/* Start: bn_mp_montgomery_calc_normalization.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/*
- * shifts with subtractions when the result is greater than b.
- *
- * The method is slightly modified to shift B unconditionally upto just under
- * the leading bit of b.  This saves alot of multiple precision shifting.
- */
-int mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
-{
-  int     x, bits, res;
-
-  /* how many bits of last digit does b use */
-  bits = mp_count_bits (b) % DIGIT_BIT;
-
-
-  if (b->used > 1) {
-     if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
-        return res;
-     }
-  } else {
-     mp_set(a, 1);
-     bits = 1;
-  }
-
-
-  /* now compute C = A * B mod b */
-  for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
-    if ((res = mp_mul_2 (a, a)) != MP_OKAY) {
-      return res;
-    }
-    if (mp_cmp_mag (a, b) != MP_LT) {
-      if ((res = s_mp_sub (a, b, a)) != MP_OKAY) {
-        return res;
-      }
-    }
-  }
-
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_montgomery_calc_normalization.c */
-
-/* Start: bn_mp_montgomery_reduce.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_MONTGOMERY_REDUCE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* computes xR**-1 == x (mod N) via Montgomery Reduction */
-int
-mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
-{
-  int     ix, res, digs;
-  mp_digit mu;
-
-  /* can the fast reduction [comba] method be used?
-   *
-   * Note that unlike in mul you're safely allowed *less*
-   * than the available columns [255 per default] since carries
-   * are fixed up in the inner loop.
-   */
-  digs = n->used * 2 + 1;
-  if ((digs < MP_WARRAY) &&
-      n->used <
-      (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
-    return fast_mp_montgomery_reduce (x, n, rho);
-  }
-
-  /* grow the input as required */
-  if (x->alloc < digs) {
-    if ((res = mp_grow (x, digs)) != MP_OKAY) {
-      return res;
-    }
-  }
-  x->used = digs;
-
-  for (ix = 0; ix < n->used; ix++) {
-    /* mu = ai * rho mod b
-     *
-     * The value of rho must be precalculated via
-     * montgomery_setup() such that
-     * it equals -1/n0 mod b this allows the
-     * following inner loop to reduce the
-     * input one digit at a time
-     */
-    mu = (mp_digit) (((mp_word)x->dp[ix]) * ((mp_word)rho) & MP_MASK);
-
-    /* a = a + mu * m * b**i */
-    {
-      register int iy;
-      register mp_digit *tmpn, *tmpx, u;
-      register mp_word r;
-
-      /* alias for digits of the modulus */
-      tmpn = n->dp;
-
-      /* alias for the digits of x [the input] */
-      tmpx = x->dp + ix;
-
-      /* set the carry to zero */
-      u = 0;
-
-      /* Multiply and add in place */
-      for (iy = 0; iy < n->used; iy++) {
-        /* compute product and sum */
-        r       = ((mp_word)mu) * ((mp_word)*tmpn++) +
-                  ((mp_word) u) + ((mp_word) * tmpx);
-
-        /* get carry */
-        u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
-
-        /* fix digit */
-        *tmpx++ = (mp_digit)(r & ((mp_word) MP_MASK));
-      }
-      /* At this point the ix'th digit of x should be zero */
-
-
-      /* propagate carries upwards as required*/
-      while (u) {
-        *tmpx   += u;
-        u        = *tmpx >> DIGIT_BIT;
-        *tmpx++ &= MP_MASK;
-      }
-    }
-  }
-
-  /* at this point the n.used'th least
-   * significant digits of x are all zero
-   * which means we can shift x to the
-   * right by n.used digits and the
-   * residue is unchanged.
-   */
-
-  /* x = x/b**n.used */
-  mp_clamp(x);
-  mp_rshd (x, n->used);
-
-  /* if x >= n then x = x - n */
-  if (mp_cmp_mag (x, n) != MP_LT) {
-    return s_mp_sub (x, n, x);
-  }
-
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_montgomery_reduce.c */
-
-/* Start: bn_mp_montgomery_setup.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_MONTGOMERY_SETUP_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* setups the montgomery reduction stuff */
-int
-mp_montgomery_setup (mp_int * n, mp_digit * rho)
-{
-  mp_digit x, b;
-
-/* fast inversion mod 2**k
- *
- * Based on the fact that
- *
- * XA = 1 (mod 2**n)  =>  (X(2-XA)) A = 1 (mod 2**2n)
- *                    =>  2*X*A - X*X*A*A = 1
- *                    =>  2*(1) - (1)     = 1
- */
-  b = n->dp[0];
-
-  if ((b & 1) == 0) {
-    return MP_VAL;
-  }
-
-  x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
-  x *= 2 - b * x;               /* here x*a==1 mod 2**8 */
-#if !defined(MP_8BIT)
-  x *= 2 - b * x;               /* here x*a==1 mod 2**16 */
-#endif
-#if defined(MP_64BIT) || !(defined(MP_8BIT) || defined(MP_16BIT))
-  x *= 2 - b * x;               /* here x*a==1 mod 2**32 */
-#endif
-#ifdef MP_64BIT
-  x *= 2 - b * x;               /* here x*a==1 mod 2**64 */
-#endif
-
-  /* rho = -1/m mod b */
-  *rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
-
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_montgomery_setup.c */
-
-/* Start: bn_mp_mul.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_MUL_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* high level multiplication (handles sign) */
-int mp_mul (mp_int * a, mp_int * b, mp_int * c)
-{
-  int     res, neg;
-  neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
-
-  /* use Toom-Cook? */
-#ifdef BN_MP_TOOM_MUL_C
-  if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) {
-    res = mp_toom_mul(a, b, c);
-  } else 
-#endif
-#ifdef BN_MP_KARATSUBA_MUL_C
-  /* use Karatsuba? */
-  if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
-    res = mp_karatsuba_mul (a, b, c);
-  } else 
-#endif
-  {
-    /* can we use the fast multiplier?
-     *
-     * The fast multiplier can be used if the output will 
-     * have less than MP_WARRAY digits and the number of 
-     * digits won't affect carry propagation
-     */
-    int     digs = a->used + b->used + 1;
-
-#ifdef BN_FAST_S_MP_MUL_DIGS_C
-    if ((digs < MP_WARRAY) &&
-        MIN(a->used, b->used) <= 
-        (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
-      res = fast_s_mp_mul_digs (a, b, c, digs);
-    } else 
-#endif
-#ifdef BN_S_MP_MUL_DIGS_C
-      res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
-#else
-      res = MP_VAL;
-#endif
-
-  }
-  c->sign = (c->used > 0) ? neg : MP_ZPOS;
-  return res;
-}
-#endif
-
-/* End: bn_mp_mul.c */
-
-/* Start: bn_mp_mul_2.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_MUL_2_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* b = a*2 */
-int mp_mul_2(mp_int * a, mp_int * b)
-{
-  int     x, res, oldused;
-
-  /* grow to accomodate result */
-  if (b->alloc < a->used + 1) {
-    if ((res = mp_grow (b, a->used + 1)) != MP_OKAY) {
-      return res;
-    }
-  }
-
-  oldused = b->used;
-  b->used = a->used;
-
-  {
-    register mp_digit r, rr, *tmpa, *tmpb;
-
-    /* alias for source */
-    tmpa = a->dp;
-    
-    /* alias for dest */
-    tmpb = b->dp;
-
-    /* carry */
-    r = 0;
-    for (x = 0; x < a->used; x++) {
-    
-      /* get what will be the *next* carry bit from the 
-       * MSB of the current digit 
-       */
-      rr = *tmpa >> ((mp_digit)(DIGIT_BIT - 1));
-      
-      /* now shift up this digit, add in the carry [from the previous] */
-      *tmpb++ = ((*tmpa++ << ((mp_digit)1)) | r) & MP_MASK;
-      
-      /* copy the carry that would be from the source 
-       * digit into the next iteration 
-       */
-      r = rr;
-    }
-
-    /* new leading digit? */
-    if (r != 0) {
-      /* add a MSB which is always 1 at this point */
-      *tmpb = 1;
-      ++(b->used);
-    }
-
-    /* now zero any excess digits on the destination 
-     * that we didn't write to 
-     */
-    tmpb = b->dp + b->used;
-    for (x = b->used; x < oldused; x++) {
-      *tmpb++ = 0;
-    }
-  }
-  b->sign = a->sign;
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_mul_2.c */
-
-/* Start: bn_mp_mul_2d.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_MUL_2D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* shift left by a certain bit count */
-int mp_mul_2d (mp_int * a, int b, mp_int * c)
-{
-  mp_digit d;
-  int      res;
-
-  /* copy */
-  if (a != c) {
-     if ((res = mp_copy (a, c)) != MP_OKAY) {
-       return res;
-     }
-  }
-
-  if (c->alloc < (int)(c->used + b/DIGIT_BIT + 1)) {
-     if ((res = mp_grow (c, c->used + b / DIGIT_BIT + 1)) != MP_OKAY) {
-       return res;
-     }
-  }
-
-  /* shift by as many digits in the bit count */
-  if (b >= (int)DIGIT_BIT) {
-    if ((res = mp_lshd (c, b / DIGIT_BIT)) != MP_OKAY) {
-      return res;
-    }
-  }
-
-  /* shift any bit count < DIGIT_BIT */
-  d = (mp_digit) (b % DIGIT_BIT);
-  if (d != 0) {
-    register mp_digit *tmpc, shift, mask, r, rr;
-    register int x;
-
-    /* bitmask for carries */
-    mask = (((mp_digit)1) << d) - 1;
-
-    /* shift for msbs */
-    shift = DIGIT_BIT - d;
-
-    /* alias */
-    tmpc = c->dp;
-
-    /* carry */
-    r    = 0;
-    for (x = 0; x < c->used; x++) {
-      /* get the higher bits of the current word */
-      rr = (*tmpc >> shift) & mask;
-
-      /* shift the current word and OR in the carry */
-      *tmpc = ((*tmpc << d) | r) & MP_MASK;
-      ++tmpc;
-
-      /* set the carry to the carry bits of the current word */
-      r = rr;
-    }
-    
-    /* set final carry */
-    if (r != 0) {
-       c->dp[(c->used)++] = r;
-    }
-  }
-  mp_clamp (c);
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_mul_2d.c */
-
-/* Start: bn_mp_mul_d.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_MUL_D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* multiply by a digit */
-int
-mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
-{
-  mp_digit u, *tmpa, *tmpc;
-  mp_word  r;
-  int      ix, res, olduse;
-
-  /* make sure c is big enough to hold a*b */
-  if (c->alloc < a->used + 1) {
-    if ((res = mp_grow (c, a->used + 1)) != MP_OKAY) {
-      return res;
-    }
-  }
-
-  /* get the original destinations used count */
-  olduse = c->used;
-
-  /* set the sign */
-  c->sign = a->sign;
-
-  /* alias for a->dp [source] */
-  tmpa = a->dp;
-
-  /* alias for c->dp [dest] */
-  tmpc = c->dp;
-
-  /* zero carry */
-  u = 0;
-
-  /* compute columns */
-  for (ix = 0; ix < a->used; ix++) {
-    /* compute product and carry sum for this term */
-    r       = ((mp_word) u) + ((mp_word)*tmpa++) * ((mp_word)b);
-
-    /* mask off higher bits to get a single digit */
-    *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
-
-    /* send carry into next iteration */
-    u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
-  }
-
-  /* store final carry [if any] */
-  *tmpc++ = u;
-
-  /* now zero digits above the top */
-  while (ix++ < olduse) {
-     *tmpc++ = 0;
-  }
-
-  /* set used count */
-  c->used = a->used + 1;
-  mp_clamp(c);
-
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_mul_d.c */
-
-/* Start: bn_mp_mulmod.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_MULMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* d = a * b (mod c) */
-int
-mp_mulmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
-{
-  int     res;
-  mp_int  t;
-
-  if ((res = mp_init (&t)) != MP_OKAY) {
-    return res;
-  }
-
-  if ((res = mp_mul (a, b, &t)) != MP_OKAY) {
-    mp_clear (&t);
-    return res;
-  }
-  res = mp_mod (&t, c, d);
-  mp_clear (&t);
-  return res;
-}
-#endif
-
-/* End: bn_mp_mulmod.c */
-
-/* Start: bn_mp_n_root.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_N_ROOT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* find the n'th root of an integer 
- *
- * Result found such that (c)**b <= a and (c+1)**b > a 
- *
- * This algorithm uses Newton's approximation 
- * x[i+1] = x[i] - f(x[i])/f'(x[i]) 
- * which will find the root in log(N) time where 
- * each step involves a fair bit.  This is not meant to 
- * find huge roots [square and cube, etc].
- */
-int mp_n_root (mp_int * a, mp_digit b, mp_int * c)
-{
-  mp_int  t1, t2, t3;
-  int     res, neg;
-
-  /* input must be positive if b is even */
-  if ((b & 1) == 0 && a->sign == MP_NEG) {
-    return MP_VAL;
-  }
-
-  if ((res = mp_init (&t1)) != MP_OKAY) {
-    return res;
-  }
-
-  if ((res = mp_init (&t2)) != MP_OKAY) {
-    goto __T1;
-  }
-
-  if ((res = mp_init (&t3)) != MP_OKAY) {
-    goto __T2;
-  }
-
-  /* if a is negative fudge the sign but keep track */
-  neg     = a->sign;
-  a->sign = MP_ZPOS;
-
-  /* t2 = 2 */
-  mp_set (&t2, 2);
-
-  do {
-    /* t1 = t2 */
-    if ((res = mp_copy (&t2, &t1)) != MP_OKAY) {
-      goto __T3;
-    }
-
-    /* t2 = t1 - ((t1**b - a) / (b * t1**(b-1))) */
-    
-    /* t3 = t1**(b-1) */
-    if ((res = mp_expt_d (&t1, b - 1, &t3)) != MP_OKAY) {   
-      goto __T3;
-    }
-
-    /* numerator */
-    /* t2 = t1**b */
-    if ((res = mp_mul (&t3, &t1, &t2)) != MP_OKAY) {    
-      goto __T3;
-    }
-
-    /* t2 = t1**b - a */
-    if ((res = mp_sub (&t2, a, &t2)) != MP_OKAY) {  
-      goto __T3;
-    }
-
-    /* denominator */
-    /* t3 = t1**(b-1) * b  */
-    if ((res = mp_mul_d (&t3, b, &t3)) != MP_OKAY) {    
-      goto __T3;
-    }
-
-    /* t3 = (t1**b - a)/(b * t1**(b-1)) */
-    if ((res = mp_div (&t2, &t3, &t3, NULL)) != MP_OKAY) {  
-      goto __T3;
-    }
-
-    if ((res = mp_sub (&t1, &t3, &t2)) != MP_OKAY) {
-      goto __T3;
-    }
-  }  while (mp_cmp (&t1, &t2) != MP_EQ);
-
-  /* result can be off by a few so check */
-  for (;;) {
-    if ((res = mp_expt_d (&t1, b, &t2)) != MP_OKAY) {
-      goto __T3;
-    }
-
-    if (mp_cmp (&t2, a) == MP_GT) {
-      if ((res = mp_sub_d (&t1, 1, &t1)) != MP_OKAY) {
-         goto __T3;
-      }
-    } else {
-      break;
-    }
-  }
-
-  /* reset the sign of a first */
-  a->sign = neg;
-
-  /* set the result */
-  mp_exch (&t1, c);
-
-  /* set the sign of the result */
-  c->sign = neg;
-
-  res = MP_OKAY;
-
-__T3:mp_clear (&t3);
-__T2:mp_clear (&t2);
-__T1:mp_clear (&t1);
-  return res;
-}
-#endif
-
-/* End: bn_mp_n_root.c */
-
-/* Start: bn_mp_neg.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_NEG_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* b = -a */
-int mp_neg (mp_int * a, mp_int * b)
-{
-  int     res;
-  if ((res = mp_copy (a, b)) != MP_OKAY) {
-    return res;
-  }
-  if (mp_iszero(b) != MP_YES) {
-     b->sign = (a->sign == MP_ZPOS) ? MP_NEG : MP_ZPOS;
-  }
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_neg.c */
-
-/* Start: bn_mp_or.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_OR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* OR two ints together */
-int mp_or (mp_int * a, mp_int * b, mp_int * c)
-{
-  int     res, ix, px;
-  mp_int  t, *x;
-
-  if (a->used > b->used) {
-    if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
-      return res;
-    }
-    px = b->used;
-    x = b;
-  } else {
-    if ((res = mp_init_copy (&t, b)) != MP_OKAY) {
-      return res;
-    }
-    px = a->used;
-    x = a;
-  }
-
-  for (ix = 0; ix < px; ix++) {
-    t.dp[ix] |= x->dp[ix];
-  }
-  mp_clamp (&t);
-  mp_exch (c, &t);
-  mp_clear (&t);
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_or.c */
-
-/* Start: bn_mp_prime_fermat.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_PRIME_FERMAT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* performs one Fermat test.
- * 
- * If "a" were prime then b**a == b (mod a) since the order of
- * the multiplicative sub-group would be phi(a) = a-1.  That means
- * it would be the same as b**(a mod (a-1)) == b**1 == b (mod a).
- *
- * Sets result to 1 if the congruence holds, or zero otherwise.
- */
-int mp_prime_fermat (mp_int * a, mp_int * b, int *result)
-{
-  mp_int  t;
-  int     err;
-
-  /* default to composite  */
-  *result = MP_NO;
-
-  /* ensure b > 1 */
-  if (mp_cmp_d(b, 1) != MP_GT) {
-     return MP_VAL;
-  }
-
-  /* init t */
-  if ((err = mp_init (&t)) != MP_OKAY) {
-    return err;
-  }
-
-  /* compute t = b**a mod a */
-  if ((err = mp_exptmod (b, a, a, &t)) != MP_OKAY) {
-    goto __T;
-  }
-
-  /* is it equal to b? */
-  if (mp_cmp (&t, b) == MP_EQ) {
-    *result = MP_YES;
-  }
-
-  err = MP_OKAY;
-__T:mp_clear (&t);
-  return err;
-}
-#endif
-
-/* End: bn_mp_prime_fermat.c */
-
-/* Start: bn_mp_prime_is_divisible.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_PRIME_IS_DIVISIBLE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* determines if an integers is divisible by one 
- * of the first PRIME_SIZE primes or not
- *
- * sets result to 0 if not, 1 if yes
- */
-int mp_prime_is_divisible (mp_int * a, int *result)
-{
-  int     err, ix;
-  mp_digit res;
-
-  /* default to not */
-  *result = MP_NO;
-
-  for (ix = 0; ix < PRIME_SIZE; ix++) {
-    /* what is a mod __prime_tab[ix] */
-    if ((err = mp_mod_d (a, __prime_tab[ix], &res)) != MP_OKAY) {
-      return err;
-    }
-
-    /* is the residue zero? */
-    if (res == 0) {
-      *result = MP_YES;
-      return MP_OKAY;
-    }
-  }
-
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_prime_is_divisible.c */
-
-/* Start: bn_mp_prime_is_prime.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_PRIME_IS_PRIME_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* performs a variable number of rounds of Miller-Rabin
- *
- * Probability of error after t rounds is no more than
-
- *
- * Sets result to 1 if probably prime, 0 otherwise
- */
-int mp_prime_is_prime (mp_int * a, int t, int *result)
-{
-  mp_int  b;
-  int     ix, err, res;
-
-  /* default to no */
-  *result = MP_NO;
-
-  /* valid value of t? */
-  if (t <= 0 || t > PRIME_SIZE) {
-    return MP_VAL;
-  }
-
-  /* is the input equal to one of the primes in the table? */
-  for (ix = 0; ix < PRIME_SIZE; ix++) {
-      if (mp_cmp_d(a, __prime_tab[ix]) == MP_EQ) {
-         *result = 1;
-         return MP_OKAY;
-      }
-  }
-
-  /* first perform trial division */
-  if ((err = mp_prime_is_divisible (a, &res)) != MP_OKAY) {
-    return err;
-  }
-
-  /* return if it was trivially divisible */
-  if (res == MP_YES) {
-    return MP_OKAY;
-  }
-
-  /* now perform the miller-rabin rounds */
-  if ((err = mp_init (&b)) != MP_OKAY) {
-    return err;
-  }
-
-  for (ix = 0; ix < t; ix++) {
-    /* set the prime */
-    mp_set (&b, __prime_tab[ix]);
-
-    if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) {
-      goto __B;
-    }
-
-    if (res == MP_NO) {
-      goto __B;
-    }
-  }
-
-  /* passed the test */
-  *result = MP_YES;
-__B:mp_clear (&b);
-  return err;
-}
-#endif
-
-/* End: bn_mp_prime_is_prime.c */
-
-/* Start: bn_mp_prime_miller_rabin.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_PRIME_MILLER_RABIN_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* Miller-Rabin test of "a" to the base of "b" as described in 
- * HAC pp. 139 Algorithm 4.24
- *
- * Sets result to 0 if definitely composite or 1 if probably prime.
- * Randomly the chance of error is no more than 1/4 and often 
- * very much lower.
- */
-int mp_prime_miller_rabin (mp_int * a, mp_int * b, int *result)
-{
-  mp_int  n1, y, r;
-  int     s, j, err;
-
-  /* default */
-  *result = MP_NO;
-
-  /* ensure b > 1 */
-  if (mp_cmp_d(b, 1) != MP_GT) {
-     return MP_VAL;
-  }     
-
-  /* get n1 = a - 1 */
-  if ((err = mp_init_copy (&n1, a)) != MP_OKAY) {
-    return err;
-  }
-  if ((err = mp_sub_d (&n1, 1, &n1)) != MP_OKAY) {
-    goto __N1;
-  }
-
-  /* set 2**s * r = n1 */
-  if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) {
-    goto __N1;
-  }
-
-  /* count the number of least significant bits
-   * which are zero
-   */
-  s = mp_cnt_lsb(&r);
-
-  /* now divide n - 1 by 2**s */
-  if ((err = mp_div_2d (&r, s, &r, NULL)) != MP_OKAY) {
-    goto __R;
-  }
-
-  /* compute y = b**r mod a */
-  if ((err = mp_init (&y)) != MP_OKAY) {
-    goto __R;
-  }
-  if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) {
-    goto __Y;
-  }
-
-  /* if y != 1 and y != n1 do */
-  if (mp_cmp_d (&y, 1) != MP_EQ && mp_cmp (&y, &n1) != MP_EQ) {
-    j = 1;
-    /* while j <= s-1 and y != n1 */
-    while ((j <= (s - 1)) && mp_cmp (&y, &n1) != MP_EQ) {
-      if ((err = mp_sqrmod (&y, a, &y)) != MP_OKAY) {
-         goto __Y;
-      }
-
-      /* if y == 1 then composite */
-      if (mp_cmp_d (&y, 1) == MP_EQ) {
-         goto __Y;
-      }
-
-      ++j;
-    }
-
-    /* if y != n1 then composite */
-    if (mp_cmp (&y, &n1) != MP_EQ) {
-      goto __Y;
-    }
-  }
-
-  /* probably prime now */
-  *result = MP_YES;
-__Y:mp_clear (&y);
-__R:mp_clear (&r);
-__N1:mp_clear (&n1);
-  return err;
-}
-#endif
-
-/* End: bn_mp_prime_miller_rabin.c */
-
-/* Start: bn_mp_prime_next_prime.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_PRIME_NEXT_PRIME_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* finds the next prime after the number "a" using "t" trials
- * of Miller-Rabin.
- *
- * bbs_style = 1 means the prime must be congruent to 3 mod 4
- */
-int mp_prime_next_prime(mp_int *a, int t, int bbs_style)
-{
-   int      err, res, x, y;
-   mp_digit res_tab[PRIME_SIZE], step, kstep;
-   mp_int   b;
-
-   /* ensure t is valid */
-   if (t <= 0 || t > PRIME_SIZE) {
-      return MP_VAL;
-   }
-
-   /* force positive */
-   a->sign = MP_ZPOS;
-
-   /* simple algo if a is less than the largest prime in the table */
-   if (mp_cmp_d(a, __prime_tab[PRIME_SIZE-1]) == MP_LT) {
-      /* find which prime it is bigger than */
-      for (x = PRIME_SIZE - 2; x >= 0; x--) {
-          if (mp_cmp_d(a, __prime_tab[x]) != MP_LT) {
-             if (bbs_style == 1) {
-                /* ok we found a prime smaller or
-                 * equal [so the next is larger]
-                 *
-                 * however, the prime must be
-                 * congruent to 3 mod 4
-                 */
-                if ((__prime_tab[x + 1] & 3) != 3) {
-                   /* scan upwards for a prime congruent to 3 mod 4 */
-                   for (y = x + 1; y < PRIME_SIZE; y++) {
-                       if ((__prime_tab[y] & 3) == 3) {
-                          mp_set(a, __prime_tab[y]);
-                          return MP_OKAY;
-                       }
-                   }
-                }
-             } else {
-                mp_set(a, __prime_tab[x + 1]);
-                return MP_OKAY;
-             }
-          }
-      }
-      /* at this point a maybe 1 */
-      if (mp_cmp_d(a, 1) == MP_EQ) {
-         mp_set(a, 2);
-         return MP_OKAY;
-      }
-      /* fall through to the sieve */
-   }
-
-   /* generate a prime congruent to 3 mod 4 or 1/3 mod 4? */
-   if (bbs_style == 1) {
-      kstep   = 4;
-   } else {
-      kstep   = 2;
-   }
-
-   /* at this point we will use a combination of a sieve and Miller-Rabin */
-
-   if (bbs_style == 1) {
-      /* if a mod 4 != 3 subtract the correct value to make it so */
-      if ((a->dp[0] & 3) != 3) {
-         if ((err = mp_sub_d(a, (a->dp[0] & 3) + 1, a)) != MP_OKAY) { return err; };
-      }
-   } else {
-      if (mp_iseven(a) == 1) {
-         /* force odd */
-         if ((err = mp_sub_d(a, 1, a)) != MP_OKAY) {
-            return err;
-         }
-      }
-   }
-
-   /* generate the restable */
-   for (x = 1; x < PRIME_SIZE; x++) {
-      if ((err = mp_mod_d(a, __prime_tab[x], res_tab + x)) != MP_OKAY) {
-         return err;
-      }
-   }
-
-   /* init temp used for Miller-Rabin Testing */
-   if ((err = mp_init(&b)) != MP_OKAY) {
-      return err;
-   }
-
-   for (;;) {
-      /* skip to the next non-trivially divisible candidate */
-      step = 0;
-      do {
-         /* y == 1 if any residue was zero [e.g. cannot be prime] */
-         y     =  0;
-
-         /* increase step to next candidate */
-         step += kstep;
-
-         /* compute the new residue without using division */
-         for (x = 1; x < PRIME_SIZE; x++) {
-             /* add the step to each residue */
-             res_tab[x] += kstep;
-
-             /* subtract the modulus [instead of using division] */
-             if (res_tab[x] >= __prime_tab[x]) {
-                res_tab[x]  -= __prime_tab[x];
-             }
-
-             /* set flag if zero */
-             if (res_tab[x] == 0) {
-                y = 1;
-             }
-         }
-      } while (y == 1 && step < ((((mp_digit)1)<<DIGIT_BIT) - kstep));
-
-      /* add the step */
-      if ((err = mp_add_d(a, step, a)) != MP_OKAY) {
-         goto __ERR;
-      }
-
-      /* if didn't pass sieve and step == MAX then skip test */
-      if (y == 1 && step >= ((((mp_digit)1)<<DIGIT_BIT) - kstep)) {
-         continue;
-      }
-
-      /* is this prime? */
-      for (x = 0; x < t; x++) {
-          mp_set(&b, __prime_tab[t]);
-          if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
-             goto __ERR;
-          }
-          if (res == MP_NO) {
-             break;
-          }
-      }
-
-      if (res == MP_YES) {
-         break;
-      }
-   }
-
-   err = MP_OKAY;
-__ERR:
-   mp_clear(&b);
-   return err;
-}
-
-#endif
-
-/* End: bn_mp_prime_next_prime.c */
-
-/* Start: bn_mp_prime_rabin_miller_trials.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-
-static const struct {
-   int k, t;
-} sizes[] = {
-{   128,    28 },
-{   256,    16 },
-{   384,    10 },
-{   512,     7 },
-{   640,     6 },
-{   768,     5 },
-{   896,     4 },
-{  1024,     4 }
-};
-
-/* returns # of RM trials required for a given bit size */
-int mp_prime_rabin_miller_trials(int size)
-{
-   int x;
-
-   for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) {
-       if (sizes[x].k == size) {
-          return sizes[x].t;
-       } else if (sizes[x].k > size) {
-          return (x == 0) ? sizes[0].t : sizes[x - 1].t;
-       }
-   }
-   return sizes[x-1].t + 1;
-}
-
-
-#endif
-
-/* End: bn_mp_prime_rabin_miller_trials.c */
-
-/* Start: bn_mp_prime_random_ex.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_PRIME_RANDOM_EX_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* makes a truly random prime of a given size (bits),
- *
- * Flags are as follows:
- * 
- *   LTM_PRIME_BBS      - make prime congruent to 3 mod 4
- *   LTM_PRIME_SAFE     - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
- *   LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero
- *   LTM_PRIME_2MSB_ON  - make the 2nd highest bit one
- *
- * You have to supply a callback which fills in a buffer with random bytes.  "dat" is a parameter you can
- * have passed to the callback (e.g. a state or something).  This function doesn't use "dat" itself
- * so it can be NULL
- *
- */
-
-/* This is possibly the mother of all prime generation functions, muahahahahaha! */
-int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat)
-{
-   unsigned char *tmp, maskAND, maskOR_msb, maskOR_lsb;
-   int res, err, bsize, maskOR_msb_offset;
-
-   /* sanity check the input */
-   if (size <= 1 || t <= 0) {
-      return MP_VAL;
-   }
-
-   /* LTM_PRIME_SAFE implies LTM_PRIME_BBS */
-   if (flags & LTM_PRIME_SAFE) {
-      flags |= LTM_PRIME_BBS;
-   }
-
-   /* calc the byte size */
-   bsize = (size>>3)+(size&7?1:0);
-
-   /* we need a buffer of bsize bytes */
-   tmp = OPT_CAST(unsigned char) XMALLOC(bsize);
-   if (tmp == NULL) {
-      return MP_MEM;
-   }
-
-   /* calc the maskAND value for the MSbyte*/
-   maskAND = 0xFF >> (8 - (size & 7));
-
-   /* calc the maskOR_msb */
-   maskOR_msb        = 0;
-   maskOR_msb_offset = (size - 2) >> 3;
-   if (flags & LTM_PRIME_2MSB_ON) {
-      maskOR_msb     |= 1 << ((size - 2) & 7);
-   } else if (flags & LTM_PRIME_2MSB_OFF) {
-      maskAND        &= ~(1 << ((size - 2) & 7));
-   }
-
-   /* get the maskOR_lsb */
-   maskOR_lsb         = 0;
-   if (flags & LTM_PRIME_BBS) {
-      maskOR_lsb     |= 3;
-   }
-
-   do {
-      /* read the bytes */
-      if (cb(tmp, bsize, dat) != bsize) {
-         err = MP_VAL;
-         goto error;
-      }
- 
-      /* work over the MSbyte */
-      tmp[0]    &= maskAND;
-      tmp[0]    |= 1 << ((size - 1) & 7);
-
-      /* mix in the maskORs */
-      tmp[maskOR_msb_offset]   |= maskOR_msb;
-      tmp[bsize-1]             |= maskOR_lsb;
-
-      /* read it in */
-      if ((err = mp_read_unsigned_bin(a, tmp, bsize)) != MP_OKAY)     { goto error; }
-
-      /* is it prime? */
-      if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY)           { goto error; }
-      if (res == MP_NO) {  
-         continue;
-      }
-
-      if (flags & LTM_PRIME_SAFE) {
-         /* see if (a-1)/2 is prime */
-         if ((err = mp_sub_d(a, 1, a)) != MP_OKAY)                    { goto error; }
-         if ((err = mp_div_2(a, a)) != MP_OKAY)                       { goto error; }
- 
-         /* is it prime? */
-         if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY)        { goto error; }
-      }
-   } while (res == MP_NO);
-
-   if (flags & LTM_PRIME_SAFE) {
-      /* restore a to the original value */
-      if ((err = mp_mul_2(a, a)) != MP_OKAY)                          { goto error; }
-      if ((err = mp_add_d(a, 1, a)) != MP_OKAY)                       { goto error; }
-   }
-
-   err = MP_OKAY;
-error:
-   XFREE(tmp);
-   return err;
-}
-
-
-#endif
-
-/* End: bn_mp_prime_random_ex.c */
-
-/* Start: bn_mp_radix_size.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_RADIX_SIZE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* returns size of ASCII reprensentation */
-int mp_radix_size (mp_int * a, int radix, int *size)
-{
-  int     res, digs;
-  mp_int  t;
-  mp_digit d;
-
-  *size = 0;
-
-  /* special case for binary */
-  if (radix == 2) {
-    *size = mp_count_bits (a) + (a->sign == MP_NEG ? 1 : 0) + 1;
-    return MP_OKAY;
-  }
-
-  /* make sure the radix is in range */
-  if (radix < 2 || radix > 64) {
-    return MP_VAL;
-  }
-
-  /* init a copy of the input */
-  if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
-    return res;
-  }
-
-  /* digs is the digit count */
-  digs = 0;
-
-  /* if it's negative add one for the sign */
-  if (t.sign == MP_NEG) {
-    ++digs;
-    t.sign = MP_ZPOS;
-  }
-
-  /* fetch out all of the digits */
-  while (mp_iszero (&t) == 0) {
-    if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
-      mp_clear (&t);
-      return res;
-    }
-    ++digs;
-  }
-  mp_clear (&t);
-
-  /* return digs + 1, the 1 is for the NULL byte that would be required. */
-  *size = digs + 1;
-  return MP_OKAY;
-}
-
-#endif
-
-/* End: bn_mp_radix_size.c */
-
-/* Start: bn_mp_radix_smap.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_RADIX_SMAP_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* chars used in radix conversions */
-const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
-#endif
-
-/* End: bn_mp_radix_smap.c */
-
-/* Start: bn_mp_rand.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_RAND_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* makes a pseudo-random int of a given size */
-int
-mp_rand (mp_int * a, int digits)
-{
-  int     res;
-  mp_digit d;
-
-  mp_zero (a);
-  if (digits <= 0) {
-    return MP_OKAY;
-  }
-
-  /* first place a random non-zero digit */
-  do {
-    d = ((mp_digit) abs (rand ()));
-  } while (d == 0);
-
-  if ((res = mp_add_d (a, d, a)) != MP_OKAY) {
-    return res;
-  }
-
-  while (digits-- > 0) {
-    if ((res = mp_lshd (a, 1)) != MP_OKAY) {
-      return res;
-    }
-
-    if ((res = mp_add_d (a, ((mp_digit) abs (rand ())), a)) != MP_OKAY) {
-      return res;
-    }
-  }
-
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_rand.c */
-
-/* Start: bn_mp_read_radix.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_READ_RADIX_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* read a string [ASCII] in a given radix */
-int mp_read_radix (mp_int * a, char *str, int radix)
-{
-  int     y, res, neg;
-  char    ch;
-
-  /* make sure the radix is ok */
-  if (radix < 2 || radix > 64) {
-    return MP_VAL;
-  }
-
-  /* if the leading digit is a 
-   * minus set the sign to negative. 
-   */
-  if (*str == '-') {
-    ++str;
-    neg = MP_NEG;
-  } else {
-    neg = MP_ZPOS;
-  }
-
-  /* set the integer to the default of zero */
-  mp_zero (a);
-  
-  /* process each digit of the string */
-  while (*str) {
-    /* if the radix < 36 the conversion is case insensitive
-     * this allows numbers like 1AB and 1ab to represent the same  value
-     * [e.g. in hex]
-     */
-    ch = (char) ((radix < 36) ? toupper (*str) : *str);
-    for (y = 0; y < 64; y++) {
-      if (ch == mp_s_rmap[y]) {
-         break;
-      }
-    }
-
-    /* if the char was found in the map 
-     * and is less than the given radix add it
-     * to the number, otherwise exit the loop. 
-     */
-    if (y < radix) {
-      if ((res = mp_mul_d (a, (mp_digit) radix, a)) != MP_OKAY) {
-         return res;
-      }
-      if ((res = mp_add_d (a, (mp_digit) y, a)) != MP_OKAY) {
-         return res;
-      }
-    } else {
-      break;
-    }
-    ++str;
-  }
-  
-  /* set the sign only if a != 0 */
-  if (mp_iszero(a) != 1) {
-     a->sign = neg;
-  }
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_read_radix.c */
-
-/* Start: bn_mp_read_signed_bin.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_READ_SIGNED_BIN_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* read signed bin, big endian, first byte is 0==positive or 1==negative */
-int
-mp_read_signed_bin (mp_int * a, unsigned char *b, int c)
-{
-  int     res;
-
-  /* read magnitude */
-  if ((res = mp_read_unsigned_bin (a, b + 1, c - 1)) != MP_OKAY) {
-    return res;
-  }
-
-  /* first byte is 0 for positive, non-zero for negative */
-  if (b[0] == 0) {
-     a->sign = MP_ZPOS;
-  } else {
-     a->sign = MP_NEG;
-  }
-
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_read_signed_bin.c */
-
-/* Start: bn_mp_read_unsigned_bin.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_READ_UNSIGNED_BIN_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* reads a unsigned char array, assumes the msb is stored first [big endian] */
-int
-mp_read_unsigned_bin (mp_int * a, unsigned char *b, int c)
-{
-  int     res;
-
-  /* make sure there are at least two digits */
-  if (a->alloc < 2) {
-     if ((res = mp_grow(a, 2)) != MP_OKAY) {
-        return res;
-     }
-  }
-
-  /* zero the int */
-  mp_zero (a);
-
-  /* read the bytes in */
-  while (c-- > 0) {
-    if ((res = mp_mul_2d (a, 8, a)) != MP_OKAY) {
-      return res;
-    }
-
-#ifndef MP_8BIT
-      a->dp[0] |= *b++;
-      a->used += 1;
-#else
-      a->dp[0] = (*b & MP_MASK);
-      a->dp[1] |= ((*b++ >> 7U) & 1);
-      a->used += 2;
-#endif
-  }
-  mp_clamp (a);
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_read_unsigned_bin.c */
-
-/* Start: bn_mp_reduce.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_REDUCE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* reduces x mod m, assumes 0 < x < m**2, mu is 
- * precomputed via mp_reduce_setup.
- * From HAC pp.604 Algorithm 14.42
- */
-int
-mp_reduce (mp_int * x, mp_int * m, mp_int * mu)
-{
-  mp_int  q;
-  int     res, um = m->used;
-
-  /* q = x */
-  if ((res = mp_init_copy (&q, x)) != MP_OKAY) {
-    return res;
-  }
-
-  /* q1 = x / b**(k-1)  */
-  mp_rshd (&q, um - 1);         
-
-  /* according to HAC this optimization is ok */
-  if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
-    if ((res = mp_mul (&q, mu, &q)) != MP_OKAY) {
-      goto CLEANUP;
-    }
-  } else {
-#ifdef BN_S_MP_MUL_HIGH_DIGS_C
-    if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) {
-      goto CLEANUP;
-    }
-#elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C)
-    if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) {
-      goto CLEANUP;
-    }
-#else 
-    { 
-      res = MP_VAL;
-      goto CLEANUP;
-    }
-#endif
-  }
-
-  /* q3 = q2 / b**(k+1) */
-  mp_rshd (&q, um + 1);         
-
-  /* x = x mod b**(k+1), quick (no division) */
-  if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
-    goto CLEANUP;
-  }
-
-  /* q = q * m mod b**(k+1), quick (no division) */
-  if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) {
-    goto CLEANUP;
-  }
-
-  /* x = x - q */
-  if ((res = mp_sub (x, &q, x)) != MP_OKAY) {
-    goto CLEANUP;
-  }
-
-  /* If x < 0, add b**(k+1) to it */
-  if (mp_cmp_d (x, 0) == MP_LT) {
-    mp_set (&q, 1);
-    if ((res = mp_lshd (&q, um + 1)) != MP_OKAY)
-      goto CLEANUP;
-    if ((res = mp_add (x, &q, x)) != MP_OKAY)
-      goto CLEANUP;
-  }
-
-  /* Back off if it's too big */
-  while (mp_cmp (x, m) != MP_LT) {
-    if ((res = s_mp_sub (x, m, x)) != MP_OKAY) {
-      goto CLEANUP;
-    }
-  }
-  
-CLEANUP:
-  mp_clear (&q);
-
-  return res;
-}
-#endif
-
-/* End: bn_mp_reduce.c */
-
-/* Start: bn_mp_reduce_2k.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_REDUCE_2K_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* reduces a modulo n where n is of the form 2**p - d */
-int
-mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d)
-{
-   mp_int q;
-   int    p, res;
-   
-   if ((res = mp_init(&q)) != MP_OKAY) {
-      return res;
-   }
-   
-   p = mp_count_bits(n);    
-top:
-   /* q = a/2**p, a = a mod 2**p */
-   if ((res = mp_div_2d(a, p, &q, a)) != MP_OKAY) {
-      goto ERR;
-   }
-   
-   if (d != 1) {
-      /* q = q * d */
-      if ((res = mp_mul_d(&q, d, &q)) != MP_OKAY) { 
-         goto ERR;
-      }
-   }
-   
-   /* a = a + q */
-   if ((res = s_mp_add(a, &q, a)) != MP_OKAY) {
-      goto ERR;
-   }
-   
-   if (mp_cmp_mag(a, n) != MP_LT) {
-      s_mp_sub(a, n, a);
-      goto top;
-   }
-   
-ERR:
-   mp_clear(&q);
-   return res;
-}
-
-#endif
-
-/* End: bn_mp_reduce_2k.c */
-
-/* Start: bn_mp_reduce_2k_setup.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_REDUCE_2K_SETUP_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* determines the setup value */
-int 
-mp_reduce_2k_setup(mp_int *a, mp_digit *d)
-{
-   int res, p;
-   mp_int tmp;
-   
-   if ((res = mp_init(&tmp)) != MP_OKAY) {
-      return res;
-   }
-   
-   p = mp_count_bits(a);
-   if ((res = mp_2expt(&tmp, p)) != MP_OKAY) {
-      mp_clear(&tmp);
-      return res;
-   }
-   
-   if ((res = s_mp_sub(&tmp, a, &tmp)) != MP_OKAY) {
-      mp_clear(&tmp);
-      return res;
-   }
-   
-   *d = tmp.dp[0];
-   mp_clear(&tmp);
-   return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_reduce_2k_setup.c */
-
-/* Start: bn_mp_reduce_is_2k.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_REDUCE_IS_2K_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* determines if mp_reduce_2k can be used */
-int mp_reduce_is_2k(mp_int *a)
-{
-   int ix, iy, iw;
-   mp_digit iz;
-   
-   if (a->used == 0) {
-      return 0;
-   } else if (a->used == 1) {
-      return 1;
-   } else if (a->used > 1) {
-      iy = mp_count_bits(a);
-      iz = 1;
-      iw = 1;
-    
-      /* Test every bit from the second digit up, must be 1 */
-      for (ix = DIGIT_BIT; ix < iy; ix++) {
-          if ((a->dp[iw] & iz) == 0) {
-             return 0;
-          }
-          iz <<= 1;
-          if (iz > (mp_digit)MP_MASK) {
-             ++iw;
-             iz = 1;
-          }
-      }
-   }
-   return 1;
-}
-
-#endif
-
-/* End: bn_mp_reduce_is_2k.c */
-
-/* Start: bn_mp_reduce_setup.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_REDUCE_SETUP_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* pre-calculate the value required for Barrett reduction
- * For a given modulus "b" it calulates the value required in "a"
- */
-int mp_reduce_setup (mp_int * a, mp_int * b)
-{
-  int     res;
-  
-  if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
-    return res;
-  }
-  return mp_div (a, b, a, NULL);
-}
-#endif
-
-/* End: bn_mp_reduce_setup.c */
-
-/* Start: bn_mp_rshd.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_RSHD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* shift right a certain amount of digits */
-void mp_rshd (mp_int * a, int b)
-{
-  int     x;
-
-  /* if b <= 0 then ignore it */
-  if (b <= 0) {
-    return;
-  }
-
-  /* if b > used then simply zero it and return */
-  if (a->used <= b) {
-    mp_zero (a);
-    return;
-  }
-
-  {
-    register mp_digit *bottom, *top;
-
-    /* shift the digits down */
-
-    /* bottom */
-    bottom = a->dp;
-
-    /* top [offset into digits] */
-    top = a->dp + b;
-
-    /* this is implemented as a sliding window where 
-     * the window is b-digits long and digits from 
-     * the top of the window are copied to the bottom
-     *
-     * e.g.
-
-     b-2 | b-1 | b0 | b1 | b2 | ... | bb |   ---->
-                 /\                   |      ---->
-                  \-------------------/      ---->
-     */
-    for (x = 0; x < (a->used - b); x++) {
-      *bottom++ = *top++;
-    }
-
-    /* zero the top digits */
-    for (; x < a->used; x++) {
-      *bottom++ = 0;
-    }
-  }
-  
-  /* remove excess digits */
-  a->used -= b;
-}
-#endif
-
-/* End: bn_mp_rshd.c */
-
-/* Start: bn_mp_set.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_SET_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* set to a digit */
-void mp_set (mp_int * a, mp_digit b)
-{
-  mp_zero (a);
-  a->dp[0] = b & MP_MASK;
-  a->used  = (a->dp[0] != 0) ? 1 : 0;
-}
-#endif
-
-/* End: bn_mp_set.c */
-
-/* Start: bn_mp_set_int.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_SET_INT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* set a 32-bit const */
-int mp_set_int (mp_int * a, unsigned long b)
-{
-  int     x, res;
-
-  mp_zero (a);
-  
-  /* set four bits at a time */
-  for (x = 0; x < 8; x++) {
-    /* shift the number up four bits */
-    if ((res = mp_mul_2d (a, 4, a)) != MP_OKAY) {
-      return res;
-    }
-
-    /* OR in the top four bits of the source */
-    a->dp[0] |= (b >> 28) & 15;
-
-    /* shift the source up to the next four bits */
-    b <<= 4;
-
-    /* ensure that digits are not clamped off */
-    a->used += 1;
-  }
-  mp_clamp (a);
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_set_int.c */
-
-/* Start: bn_mp_shrink.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_SHRINK_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* shrink a bignum */
-int mp_shrink (mp_int * a)
-{
-  mp_digit *tmp;
-  if (a->alloc != a->used && a->used > 0) {
-    if ((tmp = OPT_CAST(mp_digit) XREALLOC (a->dp, sizeof (mp_digit) * a->used)) == NULL) {
-      return MP_MEM;
-    }
-    a->dp    = tmp;
-    a->alloc = a->used;
-  }
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_shrink.c */
-
-/* Start: bn_mp_signed_bin_size.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_SIGNED_BIN_SIZE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* get the size for an signed equivalent */
-int mp_signed_bin_size (mp_int * a)
-{
-  return 1 + mp_unsigned_bin_size (a);
-}
-#endif
-
-/* End: bn_mp_signed_bin_size.c */
-
-/* Start: bn_mp_sqr.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_SQR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* computes b = a*a */
-int
-mp_sqr (mp_int * a, mp_int * b)
-{
-  int     res;
-
-#ifdef BN_MP_TOOM_SQR_C
-  /* use Toom-Cook? */
-  if (a->used >= TOOM_SQR_CUTOFF) {
-    res = mp_toom_sqr(a, b);
-  /* Karatsuba? */
-  } else 
-#endif
-#ifdef BN_MP_KARATSUBA_SQR_C
-if (a->used >= KARATSUBA_SQR_CUTOFF) {
-    res = mp_karatsuba_sqr (a, b);
-  } else 
-#endif
-  {
-#ifdef BN_FAST_S_MP_SQR_C
-    /* can we use the fast comba multiplier? */
-    if ((a->used * 2 + 1) < MP_WARRAY && 
-         a->used < 
-         (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
-      res = fast_s_mp_sqr (a, b);
-    } else
-#endif
-#ifdef BN_S_MP_SQR_C
-      res = s_mp_sqr (a, b);
-#else
-      res = MP_VAL;
-#endif
-  }
-  b->sign = MP_ZPOS;
-  return res;
-}
-#endif
-
-/* End: bn_mp_sqr.c */
-
-/* Start: bn_mp_sqrmod.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_SQRMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* c = a * a (mod b) */
-int
-mp_sqrmod (mp_int * a, mp_int * b, mp_int * c)
-{
-  int     res;
-  mp_int  t;
-
-  if ((res = mp_init (&t)) != MP_OKAY) {
-    return res;
-  }
-
-  if ((res = mp_sqr (a, &t)) != MP_OKAY) {
-    mp_clear (&t);
-    return res;
-  }
-  res = mp_mod (&t, b, c);
-  mp_clear (&t);
-  return res;
-}
-#endif
-
-/* End: bn_mp_sqrmod.c */
-
-/* Start: bn_mp_sqrt.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_SQRT_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* this function is less generic than mp_n_root, simpler and faster */
-int mp_sqrt(mp_int *arg, mp_int *ret) 
-{
-  int res;
-  mp_int t1,t2;
-
-  /* must be positive */
-  if (arg->sign == MP_NEG) {
-    return MP_VAL;
-  }
-
-  /* easy out */
-  if (mp_iszero(arg) == MP_YES) {
-    mp_zero(ret);
-    return MP_OKAY;
-  }
-
-  if ((res = mp_init_copy(&t1, arg)) != MP_OKAY) {
-    return res;
-  }
-
-  if ((res = mp_init(&t2)) != MP_OKAY) {
-    goto E2;
-  }
-
-  /* First approx. (not very bad for large arg) */
-  mp_rshd (&t1,t1.used/2);
-
-  /* t1 > 0  */ 
-  if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
-    goto E1;
-  }
-  if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
-    goto E1;
-  }
-  if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
-    goto E1;
-  }
-  /* And now t1 > sqrt(arg) */
-  do { 
-    if ((res = mp_div(arg,&t1,&t2,NULL)) != MP_OKAY) {
-      goto E1;
-    }
-    if ((res = mp_add(&t1,&t2,&t1)) != MP_OKAY) {
-      goto E1;
-    }
-    if ((res = mp_div_2(&t1,&t1)) != MP_OKAY) {
-      goto E1;
-    }
-    /* t1 >= sqrt(arg) >= t2 at this point */
-  } while (mp_cmp_mag(&t1,&t2) == MP_GT);
-
-  mp_exch(&t1,ret);
-
-E1: mp_clear(&t2);
-E2: mp_clear(&t1);
-  return res;
-}
-
-#endif
-
-/* End: bn_mp_sqrt.c */
-
-/* Start: bn_mp_sub.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_SUB_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* high level subtraction (handles signs) */
-int
-mp_sub (mp_int * a, mp_int * b, mp_int * c)
-{
-  int     sa, sb, res;
-
-  sa = a->sign;
-  sb = b->sign;
-
-  if (sa != sb) {
-    /* subtract a negative from a positive, OR */
-    /* subtract a positive from a negative. */
-    /* In either case, ADD their magnitudes, */
-    /* and use the sign of the first number. */
-    c->sign = sa;
-    res = s_mp_add (a, b, c);
-  } else {
-    /* subtract a positive from a positive, OR */
-    /* subtract a negative from a negative. */
-    /* First, take the difference between their */
-    /* magnitudes, then... */
-    if (mp_cmp_mag (a, b) != MP_LT) {
-      /* Copy the sign from the first */
-      c->sign = sa;
-      /* The first has a larger or equal magnitude */
-      res = s_mp_sub (a, b, c);
-    } else {
-      /* The result has the *opposite* sign from */
-      /* the first number. */
-      c->sign = (sa == MP_ZPOS) ? MP_NEG : MP_ZPOS;
-      /* The second has a larger magnitude */
-      res = s_mp_sub (b, a, c);
-    }
-  }
-  return res;
-}
-
-#endif
-
-/* End: bn_mp_sub.c */
-
-/* Start: bn_mp_sub_d.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_SUB_D_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* single digit subtraction */
-int
-mp_sub_d (mp_int * a, mp_digit b, mp_int * c)
-{
-  mp_digit *tmpa, *tmpc, mu;
-  int       res, ix, oldused;
-
-  /* grow c as required */
-  if (c->alloc < a->used + 1) {
-     if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
-        return res;
-     }
-  }
-
-  /* if a is negative just do an unsigned
-   * addition [with fudged signs]
-   */
-  if (a->sign == MP_NEG) {
-     a->sign = MP_ZPOS;
-     res     = mp_add_d(a, b, c);
-     a->sign = c->sign = MP_NEG;
-     return res;
-  }
-
-  /* setup regs */
-  oldused = c->used;
-  tmpa    = a->dp;
-  tmpc    = c->dp;
-
-  /* if a <= b simply fix the single digit */
-  if ((a->used == 1 && a->dp[0] <= b) || a->used == 0) {
-     if (a->used == 1) {
-        *tmpc++ = b - *tmpa;
-     } else {
-        *tmpc++ = b;
-     }
-     ix      = 1;
-
-     /* negative/1digit */
-     c->sign = MP_NEG;
-     c->used = 1;
-  } else {
-     /* positive/size */
-     c->sign = MP_ZPOS;
-     c->used = a->used;
-
-     /* subtract first digit */
-     *tmpc    = *tmpa++ - b;
-     mu       = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
-     *tmpc++ &= MP_MASK;
-
-     /* handle rest of the digits */
-     for (ix = 1; ix < a->used; ix++) {
-        *tmpc    = *tmpa++ - mu;
-        mu       = *tmpc >> (sizeof(mp_digit) * CHAR_BIT - 1);
-        *tmpc++ &= MP_MASK;
-     }
-  }
-
-  /* zero excess digits */
-  while (ix++ < oldused) {
-     *tmpc++ = 0;
-  }
-  mp_clamp(c);
-  return MP_OKAY;
-}
-
-#endif
-
-/* End: bn_mp_sub_d.c */
-
-/* Start: bn_mp_submod.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_SUBMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* d = a - b (mod c) */
-int
-mp_submod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
-{
-  int     res;
-  mp_int  t;
-
-
-  if ((res = mp_init (&t)) != MP_OKAY) {
-    return res;
-  }
-
-  if ((res = mp_sub (a, b, &t)) != MP_OKAY) {
-    mp_clear (&t);
-    return res;
-  }
-  res = mp_mod (&t, c, d);
-  mp_clear (&t);
-  return res;
-}
-#endif
-
-/* End: bn_mp_submod.c */
-
-/* Start: bn_mp_to_signed_bin.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_TO_SIGNED_BIN_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* store in signed [big endian] format */
-int
-mp_to_signed_bin (mp_int * a, unsigned char *b)
-{
-  int     res;
-
-  if ((res = mp_to_unsigned_bin (a, b + 1)) != MP_OKAY) {
-    return res;
-  }
-  b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1);
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_to_signed_bin.c */
-
-/* Start: bn_mp_to_unsigned_bin.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_TO_UNSIGNED_BIN_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* store in unsigned [big endian] format */
-int
-mp_to_unsigned_bin (mp_int * a, unsigned char *b)
-{
-  int     x, res;
-  mp_int  t;
-
-  if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
-    return res;
-  }
-
-  x = 0;
-  while (mp_iszero (&t) == 0) {
-#ifndef MP_8BIT
-      b[x++] = (unsigned char) (t.dp[0] & 255);
-#else
-      b[x++] = (unsigned char) (t.dp[0] | ((t.dp[1] & 0x01) << 7));
-#endif
-    if ((res = mp_div_2d (&t, 8, &t, NULL)) != MP_OKAY) {
-      mp_clear (&t);
-      return res;
-    }
-  }
-  bn_reverse (b, x);
-  mp_clear (&t);
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_to_unsigned_bin.c */
-
-/* Start: bn_mp_toom_mul.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_TOOM_MUL_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* multiplication using the Toom-Cook 3-way algorithm 
- *
- * Much more complicated than Karatsuba but has a lower asymptotic running time of 
- * O(N**1.464).  This algorithm is only particularly useful on VERY large
- * inputs (we're talking 1000s of digits here...).
-*/
-int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c)
-{
-    mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2;
-    int res, B;
-        
-    /* init temps */
-    if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, 
-                             &a0, &a1, &a2, &b0, &b1, 
-                             &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) {
-       return res;
-    }
-    
-    /* B */
-    B = MIN(a->used, b->used) / 3;
-    
-    /* a = a2 * B**2 + a1 * B + a0 */
-    if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    if ((res = mp_copy(a, &a1)) != MP_OKAY) {
-       goto ERR;
-    }
-    mp_rshd(&a1, B);
-    mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
-
-    if ((res = mp_copy(a, &a2)) != MP_OKAY) {
-       goto ERR;
-    }
-    mp_rshd(&a2, B*2);
-    
-    /* b = b2 * B**2 + b1 * B + b0 */
-    if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    if ((res = mp_copy(b, &b1)) != MP_OKAY) {
-       goto ERR;
-    }
-    mp_rshd(&b1, B);
-    mp_mod_2d(&b1, DIGIT_BIT * B, &b1);
-
-    if ((res = mp_copy(b, &b2)) != MP_OKAY) {
-       goto ERR;
-    }
-    mp_rshd(&b2, B*2);
-    
-    /* w0 = a0*b0 */
-    if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) {
-       goto ERR;
-    }
-    
-    /* w4 = a2 * b2 */
-    if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) {
-       goto ERR;
-    }
-    
-    /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
-    if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    
-    if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
-       goto ERR;
-    }
-    
-    if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) {
-       goto ERR;
-    }
-    
-    /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
-    if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    
-    if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
-       goto ERR;
-    }
-    
-    if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) {
-       goto ERR;
-    }
-    
-
-    /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
-    if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) {
-       goto ERR;
-    }
-    
-    /* now solve the matrix 
-    
-       0  0  0  0  1
-       1  2  4  8  16
-       1  1  1  1  1
-       16 8  4  2  1
-       1  0  0  0  0
-       
-       using 12 subtractions, 4 shifts, 
-              2 small divisions and 1 small multiplication 
-     */
-     
-     /* r1 - r4 */
-     if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3 - r0 */
-     if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r1/2 */
-     if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3/2 */
-     if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r2 - r0 - r4 */
-     if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r1 - r2 */
-     if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3 - r2 */
-     if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r1 - 8r0 */
-     if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3 - 8r4 */
-     if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* 3r2 - r1 - r3 */
-     if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r1 - r2 */
-     if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3 - r2 */
-     if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r1/3 */
-     if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3/3 */
-     if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
-        goto ERR;
-     }
-     
-     /* at this point shift W[n] by B*n */
-     if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
-        goto ERR;
-     }     
-     
-     if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) {
-        goto ERR;
-     }     
-     
-ERR:
-     mp_clear_multi(&w0, &w1, &w2, &w3, &w4, 
-                    &a0, &a1, &a2, &b0, &b1, 
-                    &b2, &tmp1, &tmp2, NULL);
-     return res;
-}     
-     
-#endif
-
-/* End: bn_mp_toom_mul.c */
-
-/* Start: bn_mp_toom_sqr.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_TOOM_SQR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* squaring using Toom-Cook 3-way algorithm */
-int
-mp_toom_sqr(mp_int *a, mp_int *b)
-{
-    mp_int w0, w1, w2, w3, w4, tmp1, a0, a1, a2;
-    int res, B;
-
-    /* init temps */
-    if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL)) != MP_OKAY) {
-       return res;
-    }
-
-    /* B */
-    B = a->used / 3;
-
-    /* a = a2 * B**2 + a1 * B + a0 */
-    if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    if ((res = mp_copy(a, &a1)) != MP_OKAY) {
-       goto ERR;
-    }
-    mp_rshd(&a1, B);
-    mp_mod_2d(&a1, DIGIT_BIT * B, &a1);
-
-    if ((res = mp_copy(a, &a2)) != MP_OKAY) {
-       goto ERR;
-    }
-    mp_rshd(&a2, B*2);
-
-    /* w0 = a0*a0 */
-    if ((res = mp_sqr(&a0, &w0)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    /* w4 = a2 * a2 */
-    if ((res = mp_sqr(&a2, &w4)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    /* w1 = (a2 + 2(a1 + 2a0))**2 */
-    if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    if ((res = mp_sqr(&tmp1, &w1)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    /* w3 = (a0 + 2(a1 + 2a2))**2 */
-    if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    if ((res = mp_sqr(&tmp1, &w3)) != MP_OKAY) {
-       goto ERR;
-    }
-
-
-    /* w2 = (a2 + a1 + a0)**2 */
-    if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
-       goto ERR;
-    }
-    if ((res = mp_sqr(&tmp1, &w2)) != MP_OKAY) {
-       goto ERR;
-    }
-
-    /* now solve the matrix
-
-       0  0  0  0  1
-       1  2  4  8  16
-       1  1  1  1  1
-       16 8  4  2  1
-       1  0  0  0  0
-
-       using 12 subtractions, 4 shifts, 2 small divisions and 1 small multiplication.
-     */
-
-     /* r1 - r4 */
-     if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3 - r0 */
-     if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r1/2 */
-     if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3/2 */
-     if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r2 - r0 - r4 */
-     if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r1 - r2 */
-     if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3 - r2 */
-     if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r1 - 8r0 */
-     if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3 - 8r4 */
-     if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* 3r2 - r1 - r3 */
-     if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r1 - r2 */
-     if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3 - r2 */
-     if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r1/3 */
-     if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) {
-        goto ERR;
-     }
-     /* r3/3 */
-     if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) {
-        goto ERR;
-     }
-
-     /* at this point shift W[n] by B*n */
-     if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) {
-        goto ERR;
-     }
-
-     if ((res = mp_add(&w0, &w1, b)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
-        goto ERR;
-     }
-     if ((res = mp_add(&tmp1, b, b)) != MP_OKAY) {
-        goto ERR;
-     }
-
-ERR:
-     mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL);
-     return res;
-}
-
-#endif
-
-/* End: bn_mp_toom_sqr.c */
-
-/* Start: bn_mp_toradix.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_TORADIX_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* stores a bignum as a ASCII string in a given radix (2..64) */
-int mp_toradix (mp_int * a, char *str, int radix)
-{
-  int     res, digs;
-  mp_int  t;
-  mp_digit d;
-  char   *_s = str;
-
-  /* check range of the radix */
-  if (radix < 2 || radix > 64) {
-    return MP_VAL;
-  }
-
-  /* quick out if its zero */
-  if (mp_iszero(a) == 1) {
-     *str++ = '0';
-     *str = '\0';
-     return MP_OKAY;
-  }
-
-  if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
-    return res;
-  }
-
-  /* if it is negative output a - */
-  if (t.sign == MP_NEG) {
-    ++_s;
-    *str++ = '-';
-    t.sign = MP_ZPOS;
-  }
-
-  digs = 0;
-  while (mp_iszero (&t) == 0) {
-    if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
-      mp_clear (&t);
-      return res;
-    }
-    *str++ = mp_s_rmap[d];
-    ++digs;
-  }
-
-  /* reverse the digits of the string.  In this case _s points
-   * to the first digit [exluding the sign] of the number]
-   */
-  bn_reverse ((unsigned char *)_s, digs);
-
-  /* append a NULL so the string is properly terminated */
-  *str = '\0';
-
-  mp_clear (&t);
-  return MP_OKAY;
-}
-
-#endif
-
-/* End: bn_mp_toradix.c */
-
-/* Start: bn_mp_toradix_n.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_TORADIX_N_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* stores a bignum as a ASCII string in a given radix (2..64) 
- *
- * Stores upto maxlen-1 chars and always a NULL byte 
- */
-int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen)
-{
-  int     res, digs;
-  mp_int  t;
-  mp_digit d;
-  char   *_s = str;
-
-  /* check range of the maxlen, radix */
-  if (maxlen < 3 || radix < 2 || radix > 64) {
-    return MP_VAL;
-  }
-
-  /* quick out if its zero */
-  if (mp_iszero(a) == 1) {
-     *str++ = '0';
-     *str = '\0';
-     return MP_OKAY;
-  }
-
-  if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
-    return res;
-  }
-
-  /* if it is negative output a - */
-  if (t.sign == MP_NEG) {
-    /* we have to reverse our digits later... but not the - sign!! */
-    ++_s;
-
-    /* store the flag and mark the number as positive */
-    *str++ = '-';
-    t.sign = MP_ZPOS;
- 
-    /* subtract a char */
-    --maxlen;
-  }
-
-  digs = 0;
-  while (mp_iszero (&t) == 0) {
-    if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
-      mp_clear (&t);
-      return res;
-    }
-    *str++ = mp_s_rmap[d];
-    ++digs;
-
-    if (--maxlen == 1) {
-       /* no more room */
-       break;
-    }
-  }
-
-  /* reverse the digits of the string.  In this case _s points
-   * to the first digit [exluding the sign] of the number]
-   */
-  bn_reverse ((unsigned char *)_s, digs);
-
-  /* append a NULL so the string is properly terminated */
-  *str = '\0';
-
-  mp_clear (&t);
-  return MP_OKAY;
-}
-
-#endif
-
-/* End: bn_mp_toradix_n.c */
-
-/* Start: bn_mp_unsigned_bin_size.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_UNSIGNED_BIN_SIZE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* get the size for an unsigned equivalent */
-int
-mp_unsigned_bin_size (mp_int * a)
-{
-  int     size = mp_count_bits (a);
-  return (size / 8 + ((size & 7) != 0 ? 1 : 0));
-}
-#endif
-
-/* End: bn_mp_unsigned_bin_size.c */
-
-/* Start: bn_mp_xor.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_XOR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* XOR two ints together */
-int
-mp_xor (mp_int * a, mp_int * b, mp_int * c)
-{
-  int     res, ix, px;
-  mp_int  t, *x;
-
-  if (a->used > b->used) {
-    if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
-      return res;
-    }
-    px = b->used;
-    x = b;
-  } else {
-    if ((res = mp_init_copy (&t, b)) != MP_OKAY) {
-      return res;
-    }
-    px = a->used;
-    x = a;
-  }
-
-  for (ix = 0; ix < px; ix++) {
-
-  }
-  mp_clamp (&t);
-  mp_exch (c, &t);
-  mp_clear (&t);
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_mp_xor.c */
-
-/* Start: bn_mp_zero.c */
-#include <ltc_tommath.h>
-#ifdef BN_MP_ZERO_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* set to zero */
-void
-mp_zero (mp_int * a)
-{
-  a->sign = MP_ZPOS;
-  a->used = 0;
-  memset (a->dp, 0, sizeof (mp_digit) * a->alloc);
-}
-#endif
-
-/* End: bn_mp_zero.c */
-
-/* Start: bn_prime_tab.c */
-#include <ltc_tommath.h>
-#ifdef BN_PRIME_TAB_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-const mp_digit __prime_tab[] = {
-  0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013,
-  0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035,
-  0x003B, 0x003D, 0x0043, 0x0047, 0x0049, 0x004F, 0x0053, 0x0059,
-  0x0061, 0x0065, 0x0067, 0x006B, 0x006D, 0x0071, 0x007F,
-#ifndef MP_8BIT
-  0x0083,
-  0x0089, 0x008B, 0x0095, 0x0097, 0x009D, 0x00A3, 0x00A7, 0x00AD,
-  0x00B3, 0x00B5, 0x00BF, 0x00C1, 0x00C5, 0x00C7, 0x00D3, 0x00DF,
-  0x00E3, 0x00E5, 0x00E9, 0x00EF, 0x00F1, 0x00FB, 0x0101, 0x0107,
-  0x010D, 0x010F, 0x0115, 0x0119, 0x011B, 0x0125, 0x0133, 0x0137,
-
-  0x0139, 0x013D, 0x014B, 0x0151, 0x015B, 0x015D, 0x0161, 0x0167,
-  0x016F, 0x0175, 0x017B, 0x017F, 0x0185, 0x018D, 0x0191, 0x0199,
-  0x01A3, 0x01A5, 0x01AF, 0x01B1, 0x01B7, 0x01BB, 0x01C1, 0x01C9,
-  0x01CD, 0x01CF, 0x01D3, 0x01DF, 0x01E7, 0x01EB, 0x01F3, 0x01F7,
-  0x01FD, 0x0209, 0x020B, 0x021D, 0x0223, 0x022D, 0x0233, 0x0239,
-  0x023B, 0x0241, 0x024B, 0x0251, 0x0257, 0x0259, 0x025F, 0x0265,
-  0x0269, 0x026B, 0x0277, 0x0281, 0x0283, 0x0287, 0x028D, 0x0293,
-  0x0295, 0x02A1, 0x02A5, 0x02AB, 0x02B3, 0x02BD, 0x02C5, 0x02CF,
-
-  0x02D7, 0x02DD, 0x02E3, 0x02E7, 0x02EF, 0x02F5, 0x02F9, 0x0301,
-  0x0305, 0x0313, 0x031D, 0x0329, 0x032B, 0x0335, 0x0337, 0x033B,
-  0x033D, 0x0347, 0x0355, 0x0359, 0x035B, 0x035F, 0x036D, 0x0371,
-  0x0373, 0x0377, 0x038B, 0x038F, 0x0397, 0x03A1, 0x03A9, 0x03AD,
-  0x03B3, 0x03B9, 0x03C7, 0x03CB, 0x03D1, 0x03D7, 0x03DF, 0x03E5,
-  0x03F1, 0x03F5, 0x03FB, 0x03FD, 0x0407, 0x0409, 0x040F, 0x0419,
-  0x041B, 0x0425, 0x0427, 0x042D, 0x043F, 0x0443, 0x0445, 0x0449,
-  0x044F, 0x0455, 0x045D, 0x0463, 0x0469, 0x047F, 0x0481, 0x048B,
-
-  0x0493, 0x049D, 0x04A3, 0x04A9, 0x04B1, 0x04BD, 0x04C1, 0x04C7,
-  0x04CD, 0x04CF, 0x04D5, 0x04E1, 0x04EB, 0x04FD, 0x04FF, 0x0503,
-  0x0509, 0x050B, 0x0511, 0x0515, 0x0517, 0x051B, 0x0527, 0x0529,
-  0x052F, 0x0551, 0x0557, 0x055D, 0x0565, 0x0577, 0x0581, 0x058F,
-  0x0593, 0x0595, 0x0599, 0x059F, 0x05A7, 0x05AB, 0x05AD, 0x05B3,
-  0x05BF, 0x05C9, 0x05CB, 0x05CF, 0x05D1, 0x05D5, 0x05DB, 0x05E7,
-  0x05F3, 0x05FB, 0x0607, 0x060D, 0x0611, 0x0617, 0x061F, 0x0623,
-  0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653
-#endif
-};
-#endif
-
-/* End: bn_prime_tab.c */
-
-/* Start: bn_reverse.c */
-#include <ltc_tommath.h>
-#ifdef BN_REVERSE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* reverse an array, used for radix code */
-void
-bn_reverse (unsigned char *s, int len)
-{
-  int     ix, iy;
-  unsigned char t;
-
-  ix = 0;
-  iy = len - 1;
-  while (ix < iy) {
-    t     = s[ix];
-    s[ix] = s[iy];
-    s[iy] = t;
-    ++ix;
-    --iy;
-  }
-}
-#endif
-
-/* End: bn_reverse.c */
-
-/* Start: bn_s_mp_add.c */
-#include <ltc_tommath.h>
-#ifdef BN_S_MP_ADD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* low level addition, based on HAC pp.594, Algorithm 14.7 */
-int
-s_mp_add (mp_int * a, mp_int * b, mp_int * c)
-{
-  mp_int *x;
-  int     olduse, res, min, max;
-
-  /* find sizes, we let |a| <= |b| which means we have to sort
-   * them.  "x" will point to the input with the most digits
-   */
-  if (a->used > b->used) {
-    min = b->used;
-    max = a->used;
-    x = a;
-  } else {
-    min = a->used;
-    max = b->used;
-    x = b;
-  }
-
-  /* init result */
-  if (c->alloc < max + 1) {
-    if ((res = mp_grow (c, max + 1)) != MP_OKAY) {
-      return res;
-    }
-  }
-
-  /* get old used digit count and set new one */
-  olduse = c->used;
-  c->used = max + 1;
-
-  {
-    register mp_digit u, *tmpa, *tmpb, *tmpc;
-    register int i;
-
-    /* alias for digit pointers */
-
-    /* first input */
-    tmpa = a->dp;
-
-    /* second input */
-    tmpb = b->dp;
-
-    /* destination */
-    tmpc = c->dp;
-
-    /* zero the carry */
-    u = 0;
-    for (i = 0; i < min; i++) {
-      /* Compute the sum at one digit, T[i] = A[i] + B[i] + U */
-      *tmpc = *tmpa++ + *tmpb++ + u;
-
-      /* U = carry bit of T[i] */
-      u = *tmpc >> ((mp_digit)DIGIT_BIT);
-
-      /* take away carry bit from T[i] */
-      *tmpc++ &= MP_MASK;
-    }
-
-    /* now copy higher words if any, that is in A+B 
-     * if A or B has more digits add those in 
-     */
-    if (min != max) {
-      for (; i < max; i++) {
-        /* T[i] = X[i] + U */
-        *tmpc = x->dp[i] + u;
-
-        /* U = carry bit of T[i] */
-        u = *tmpc >> ((mp_digit)DIGIT_BIT);
-
-        /* take away carry bit from T[i] */
-        *tmpc++ &= MP_MASK;
-      }
-    }
-
-    /* add carry */
-    *tmpc++ = u;
-
-    /* clear digits above oldused */
-    for (i = c->used; i < olduse; i++) {
-      *tmpc++ = 0;
-    }
-  }
-
-  mp_clamp (c);
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_s_mp_add.c */
-
-/* Start: bn_s_mp_exptmod.c */
-#include <ltc_tommath.h>
-#ifdef BN_S_MP_EXPTMOD_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-#ifdef MP_LOW_MEM
-   #define TAB_SIZE 32
-#else
-   #define TAB_SIZE 256
-#endif
-
-int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y)
-{
-  mp_int  M[TAB_SIZE], res, mu;
-  mp_digit buf;
-  int     err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
-
-  /* find window size */
-  x = mp_count_bits (X);
-  if (x <= 7) {
-    winsize = 2;
-  } else if (x <= 36) {
-    winsize = 3;
-  } else if (x <= 140) {
-    winsize = 4;
-  } else if (x <= 450) {
-    winsize = 5;
-  } else if (x <= 1303) {
-    winsize = 6;
-  } else if (x <= 3529) {
-    winsize = 7;
-  } else {
-    winsize = 8;
-  }
-
-#ifdef MP_LOW_MEM
-    if (winsize > 5) {
-       winsize = 5;
-    }
-#endif
-
-  /* init M array */
-  /* init first cell */
-  if ((err = mp_init(&M[1])) != MP_OKAY) {
-     return err; 
-  }
-
-  /* now init the second half of the array */
-  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
-    if ((err = mp_init(&M[x])) != MP_OKAY) {
-      for (y = 1<<(winsize-1); y < x; y++) {
-        mp_clear (&M[y]);
-      }
-      mp_clear(&M[1]);
-      return err;
-    }
-  }
-
-  /* create mu, used for Barrett reduction */
-  if ((err = mp_init (&mu)) != MP_OKAY) {
-    goto __M;
-  }
-  if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
-    goto __MU;
-  }
-
-  /* create M table
-   *
-   * The M table contains powers of the base, 
-   * e.g. M[x] = G**x mod P
-   *
-   * The first half of the table is not 
-   * computed though accept for M[0] and M[1]
-   */
-  if ((err = mp_mod (G, P, &M[1])) != MP_OKAY) {
-    goto __MU;
-  }
-
-  /* compute the value at M[1<<(winsize-1)] by squaring 
-   * M[1] (winsize-1) times 
-   */
-  if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
-    goto __MU;
-  }
-
-  for (x = 0; x < (winsize - 1); x++) {
-    if ((err = mp_sqr (&M[1 << (winsize - 1)], 
-                       &M[1 << (winsize - 1)])) != MP_OKAY) {
-      goto __MU;
-    }
-    if ((err = mp_reduce (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
-      goto __MU;
-    }
-  }
-
-  /* create upper table, that is M[x] = M[x-1] * M[1] (mod P)
-   * for x = (2**(winsize - 1) + 1) to (2**winsize - 1)
-   */
-  for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
-    if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
-      goto __MU;
-    }
-    if ((err = mp_reduce (&M[x], P, &mu)) != MP_OKAY) {
-      goto __MU;
-    }
-  }
-
-  /* setup result */
-  if ((err = mp_init (&res)) != MP_OKAY) {
-    goto __MU;
-  }
-  mp_set (&res, 1);
-
-  /* set initial mode and bit cnt */
-  mode   = 0;
-  bitcnt = 1;
-  buf    = 0;
-  digidx = X->used - 1;
-  bitcpy = 0;
-  bitbuf = 0;
-
-  for (;;) {
-    /* grab next digit as required */
-    if (--bitcnt == 0) {
-      /* if digidx == -1 we are out of digits */
-      if (digidx == -1) {
-        break;
-      }
-      /* read next digit and reset the bitcnt */
-      buf    = X->dp[digidx--];
-      bitcnt = (int) DIGIT_BIT;
-    }
-
-    /* grab the next msb from the exponent */
-    y     = (buf >> (mp_digit)(DIGIT_BIT - 1)) & 1;
-    buf <<= (mp_digit)1;
-
-    /* if the bit is zero and mode == 0 then we ignore it
-     * These represent the leading zero bits before the first 1 bit
-     * in the exponent.  Technically this opt is not required but it
-     * does lower the # of trivial squaring/reductions used
-     */
-    if (mode == 0 && y == 0) {
-      continue;
-    }
-
-    /* if the bit is zero and mode == 1 then we square */
-    if (mode == 1 && y == 0) {
-      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
-        goto __RES;
-      }
-      if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
-        goto __RES;
-      }
-      continue;
-    }
-
-    /* else we add it to the window */
-    bitbuf |= (y << (winsize - ++bitcpy));
-    mode    = 2;
-
-    if (bitcpy == winsize) {
-      /* ok window is filled so square as required and multiply  */
-      /* square first */
-      for (x = 0; x < winsize; x++) {
-        if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
-          goto __RES;
-        }
-        if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
-          goto __RES;
-        }
-      }
-
-      /* then multiply */
-      if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
-        goto __RES;
-      }
-      if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
-        goto __RES;
-      }
-
-      /* empty window and reset */
-      bitcpy = 0;
-      bitbuf = 0;
-      mode   = 1;
-    }
-  }
-
-  /* if bits remain then square/multiply */
-  if (mode == 2 && bitcpy > 0) {
-    /* square then multiply if the bit is set */
-    for (x = 0; x < bitcpy; x++) {
-      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
-        goto __RES;
-      }
-      if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
-        goto __RES;
-      }
-
-      bitbuf <<= 1;
-      if ((bitbuf & (1 << winsize)) != 0) {
-        /* then multiply */
-        if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
-          goto __RES;
-        }
-        if ((err = mp_reduce (&res, P, &mu)) != MP_OKAY) {
-          goto __RES;
-        }
-      }
-    }
-  }
-
-  mp_exch (&res, Y);
-  err = MP_OKAY;
-__RES:mp_clear (&res);
-__MU:mp_clear (&mu);
-__M:
-  mp_clear(&M[1]);
-  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
-    mp_clear (&M[x]);
-  }
-  return err;
-}
-#endif
-
-/* End: bn_s_mp_exptmod.c */
-
-/* Start: bn_s_mp_mul_digs.c */
-#include <ltc_tommath.h>
-#ifdef BN_S_MP_MUL_DIGS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* multiplies |a| * |b| and only computes upto digs digits of result
- * HAC pp. 595, Algorithm 14.12  Modified so you can control how 
- * many digits of output are created.
- */
-int
-s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
-{
-  mp_int  t;
-  int     res, pa, pb, ix, iy;
-  mp_digit u;
-  mp_word r;
-  mp_digit tmpx, *tmpt, *tmpy;
-
-  /* can we use the fast multiplier? */
-  if (((digs) < MP_WARRAY) &&
-      MIN (a->used, b->used) < 
-          (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
-    return fast_s_mp_mul_digs (a, b, c, digs);
-  }
-
-  if ((res = mp_init_size (&t, digs)) != MP_OKAY) {
-    return res;
-  }
-  t.used = digs;
-
-  /* compute the digits of the product directly */
-  pa = a->used;
-  for (ix = 0; ix < pa; ix++) {
-    /* set the carry to zero */
-    u = 0;
-
-    /* limit ourselves to making digs digits of output */
-    pb = MIN (b->used, digs - ix);
-
-    /* setup some aliases */
-    /* copy of the digit from a used within the nested loop */
-    tmpx = a->dp[ix];
-    
-    /* an alias for the destination shifted ix places */
-    tmpt = t.dp + ix;
-    
-    /* an alias for the digits of b */
-    tmpy = b->dp;
-
-    /* compute the columns of the output and propagate the carry */
-    for (iy = 0; iy < pb; iy++) {
-      /* compute the column as a mp_word */
-      r       = ((mp_word)*tmpt) +
-                ((mp_word)tmpx) * ((mp_word)*tmpy++) +
-                ((mp_word) u);
-
-      /* the new column is the lower part of the result */
-      *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
-
-      /* get the carry word from the result */
-      u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
-    }
-    /* set carry if it is placed below digs */
-    if (ix + iy < digs) {
-      *tmpt = u;
-    }
-  }
-
-  mp_clamp (&t);
-  mp_exch (&t, c);
-
-  mp_clear (&t);
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_s_mp_mul_digs.c */
-
-/* Start: bn_s_mp_mul_high_digs.c */
-#include <ltc_tommath.h>
-#ifdef BN_S_MP_MUL_HIGH_DIGS_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* multiplies |a| * |b| and does not compute the lower digs digits
- * [meant to get the higher part of the product]
- */
-int
-s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
-{
-  mp_int  t;
-  int     res, pa, pb, ix, iy;
-  mp_digit u;
-  mp_word r;
-  mp_digit tmpx, *tmpt, *tmpy;
-
-  /* can we use the fast multiplier? */
-#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C
-  if (((a->used + b->used + 1) < MP_WARRAY)
-      && MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
-    return fast_s_mp_mul_high_digs (a, b, c, digs);
-  }
-#endif
-
-  if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) {
-    return res;
-  }
-  t.used = a->used + b->used + 1;
-
-  pa = a->used;
-  pb = b->used;
-  for (ix = 0; ix < pa; ix++) {
-    /* clear the carry */
-    u = 0;
-
-    /* left hand side of A[ix] * B[iy] */
-    tmpx = a->dp[ix];
-
-    /* alias to the address of where the digits will be stored */
-    tmpt = &(t.dp[digs]);
-
-    /* alias for where to read the right hand side from */
-    tmpy = b->dp + (digs - ix);
-
-    for (iy = digs - ix; iy < pb; iy++) {
-      /* calculate the double precision result */
-      r       = ((mp_word)*tmpt) +
-                ((mp_word)tmpx) * ((mp_word)*tmpy++) +
-                ((mp_word) u);
-
-      /* get the lower part */
-      *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
-
-      /* carry the carry */
-      u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
-    }
-    *tmpt = u;
-  }
-  mp_clamp (&t);
-  mp_exch (&t, c);
-  mp_clear (&t);
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_s_mp_mul_high_digs.c */
-
-/* Start: bn_s_mp_sqr.c */
-#include <ltc_tommath.h>
-#ifdef BN_S_MP_SQR_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
-int
-s_mp_sqr (mp_int * a, mp_int * b)
-{
-  mp_int  t;
-  int     res, ix, iy, pa;
-  mp_word r;
-  mp_digit u, tmpx, *tmpt;
-
-  pa = a->used;
-  if ((res = mp_init_size (&t, 2*pa + 1)) != MP_OKAY) {
-    return res;
-  }
-
-  /* default used is maximum possible size */
-  t.used = 2*pa + 1;
-
-  for (ix = 0; ix < pa; ix++) {
-    /* first calculate the digit at 2*ix */
-    /* calculate double precision result */
-    r = ((mp_word) t.dp[2*ix]) +
-        ((mp_word)a->dp[ix])*((mp_word)a->dp[ix]);
-
-    /* store lower part in result */
-    t.dp[ix+ix] = (mp_digit) (r & ((mp_word) MP_MASK));
-
-    /* get the carry */
-    u           = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
-
-    /* left hand side of A[ix] * A[iy] */
-    tmpx        = a->dp[ix];
-
-    /* alias for where to store the results */
-    tmpt        = t.dp + (2*ix + 1);
-    
-    for (iy = ix + 1; iy < pa; iy++) {
-      /* first calculate the product */
-      r       = ((mp_word)tmpx) * ((mp_word)a->dp[iy]);
-
-      /* now calculate the double precision result, note we use
-       * addition instead of *2 since it's easier to optimize
-       */
-      r       = ((mp_word) *tmpt) + r + r + ((mp_word) u);
-
-      /* store lower part */
-      *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
-
-      /* get carry */
-      u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
-    }
-    /* propagate upwards */
-    while (u != ((mp_digit) 0)) {
-      r       = ((mp_word) *tmpt) + ((mp_word) u);
-      *tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
-      u       = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
-    }
-  }
-
-  mp_clamp (&t);
-  mp_exch (&t, b);
-  mp_clear (&t);
-  return MP_OKAY;
-}
-#endif
-
-/* End: bn_s_mp_sqr.c */
-
-/* Start: bn_s_mp_sub.c */
-#include <ltc_tommath.h>
-#ifdef BN_S_MP_SUB_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
-int
-s_mp_sub (mp_int * a, mp_int * b, mp_int * c)
-{
-  int     olduse, res, min, max;
-
-  /* find sizes */
-  min = b->used;
-  max = a->used;
-
-  /* init result */
-  if (c->alloc < max) {
-    if ((res = mp_grow (c, max)) != MP_OKAY) {
-      return res;
-    }
-  }
-  olduse = c->used;
-  c->used = max;
-
-  {
-    register mp_digit u, *tmpa, *tmpb, *tmpc;
-    register int i;
-
-    /* alias for digit pointers */
-    tmpa = a->dp;
-    tmpb = b->dp;
-    tmpc = c->dp;
-
-    /* set carry to zero */
-    u = 0;
-    for (i = 0; i < min; i++) {
-      /* T[i] = A[i] - B[i] - U */
-      *tmpc = *tmpa++ - *tmpb++ - u;
-
-      /* U = carry bit of T[i]
-       * Note this saves performing an AND operation since
-       * if a carry does occur it will propagate all the way to the
-       * MSB.  As a result a single shift is enough to get the carry
-       */
-      u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
-
-      /* Clear carry from T[i] */
-      *tmpc++ &= MP_MASK;
-    }
-
-    /* now copy higher words if any, e.g. if A has more digits than B  */
-    for (; i < max; i++) {
-      /* T[i] = A[i] - U */
-      *tmpc = *tmpa++ - u;
-
-      /* U = carry bit of T[i] */
-      u = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof (mp_digit) - 1));
-
-      /* Clear carry from T[i] */
-      *tmpc++ &= MP_MASK;
-    }
-
-    /* clear digits above used (since we may not have grown result above) */
-    for (i = c->used; i < olduse; i++) {
-      *tmpc++ = 0;
-    }
-  }
-
-  mp_clamp (c);
-  return MP_OKAY;
-}
-
-#endif
-
-/* End: bn_s_mp_sub.c */
-
-/* Start: bncore.c */
-#include <ltc_tommath.h>
-#ifdef BNCORE_C
-/* LibTomMath, multiple-precision integer library -- Tom St Denis
- *
- * LibTomMath is a library that provides multiple-precision
- * integer arithmetic as well as number theoretic functionality.
- *
- * The library was designed directly after the MPI library by
- * Michael Fromberger but has been written from scratch with
- * additional optimizations in place.
- *
- * The library is free for all purposes without any express
- * guarantee it works.
- *
- * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
- */
-
-/* Known optimal configurations
-
- CPU                    /Compiler     /MUL CUTOFF/SQR CUTOFF
--------------------------------------------------------------
- Intel P4 Northwood     /GCC v3.4.1   /        88/       128/LTM 0.32 ;-)
- 
-*/
-
-int     KARATSUBA_MUL_CUTOFF = 88,      /* Min. number of digits before Karatsuba multiplication is used. */
-        KARATSUBA_SQR_CUTOFF = 128,     /* Min. number of digits before Karatsuba squaring is used. */
-        
-        TOOM_MUL_CUTOFF      = 350,      /* no optimal values of these are known yet so set em high */
-        TOOM_SQR_CUTOFF      = 400; 
-#endif
-
-/* End: bncore.c */
-
-
-/* EOF */