Update netpgpverify package to 20140712

+ bring the bignum implementation up to the latest version

	+ radix conversion routines added
	+ bitwise operations added
	+ whitespace cleanups

3 files changed, 4335 insertions, 4292 deletions

diff --git a/security/netpgpverify/Makefile b/security/netpgpverify/Makefile
index 70428eede59..a5a1b610aec 100644
--- a/security/netpgpverify/Makefile
+++ b/security/netpgpverify/Makefile
@@ -1,6 +1,6 @@
-# $NetBSD: Makefile,v 1.7 2014/03/05 04:51:37 agc Exp $
+# $NetBSD: Makefile,v 1.8 2014/07/12 15:45:52 agc Exp $
 
-DISTNAME=		netpgpverify-20140304
+DISTNAME=		netpgpverify-20140712
 CATEGORIES=		security
 MASTER_SITES=		# empty
 DISTFILES=		# empty
diff --git a/security/netpgpverify/files/bignum.c b/security/netpgpverify/files/bignum.c
index c825b30c501..f02b512d0fe 100644
--- a/security/netpgpverify/files/bignum.c
+++ b/security/netpgpverify/files/bignum.c
@@ -39,26 +39,20 @@
 #include "config.h"
 
 #include <sys/types.h>
-#include <sys/stat.h>
 #include <sys/param.h>
 
 #ifdef _KERNEL
 # include <sys/kmem.h>
 #else
 # include <arpa/inet.h>
-# include <ctype.h>
-# include <inttypes.h>
 # include <stdarg.h>
 # include <stdio.h>
 # include <stdlib.h>
 # include <string.h>
-# include <time.h>
 # include <unistd.h>
 #endif
 
-#include "misc.h"
 #include "bn.h"
-#include "digest.h"
 
 /**************************************************************************/
 
@@ -94,116 +88,108 @@
 #define	__arraycount(__x)	(sizeof(__x) / sizeof(__x[0]))
 #endif
 
-#define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
-
-#define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
+#define MP_ISZERO(a) (((a)->used == 0) ? MP_YES : MP_NO)
 
 typedef int           mp_err;
 
-static int mp_mul(mp_int * a, mp_int * b, mp_int * c);
-static int mp_sqr(mp_int * a, mp_int * b);
+static int signed_multiply(mp_int * a, mp_int * b, mp_int * c);
+static int square(mp_int * a, mp_int * b);
 
-static int mp_sub_d(mp_int *a, mp_digit b, mp_int *c);
+static int signed_subtract_word(mp_int *a, mp_digit b, mp_int *c);
 
-/* set to zero */
-static void
-mp_zero(mp_int *a)
+static inline void *
+allocate(size_t n, size_t m)
 {
-  int       n;
-  mp_digit *tmp;
+	return calloc(n, m);
+}
 
-  a->sign = MP_ZPOS;
-  a->used = 0;
+static inline void
+deallocate(void *v, size_t sz)
+{
+	USE_ARG(sz);
+	free(v);
+}
 
-  tmp = a->dp;
-  /* XXX - memset */
-  for (n = 0; n < a->alloc; n++) {
-     *tmp++ = 0;
-  }
+/* set to zero */
+static inline void
+mp_zero(mp_int *a)
+{
+	a->sign = MP_ZPOS;
+	a->used = 0;
+	memset(a->dp, 0x0, a->alloc * sizeof(*a->dp));
 }
 
 /* grow as required */
 static 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 = realloc(a->dp, sizeof(*tmp) * 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;
+	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 = realloc(a->dp, sizeof(*tmp) * 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 */
+		memset(&a->dp[a->alloc], 0x0, (size - a->alloc) * sizeof(*a->dp));
+		a->alloc = size;
+	}
+	return MP_OKAY;
 }
 
 /* shift left a certain amount of digits */
 static int
-mp_lshd (mp_int * a, int b)
+lshift_digits(mp_int * a, int b)
 {
-  int     x, res;
+	mp_digit *top, *bottom;
+	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;
-     }
-  }
+	/* if its less than zero return */
+	if (b <= 0) {
+		return MP_OKAY;
+	}
 
-  {
-    mp_digit *top, *bottom;
+	/* grow to fit the new digits */
+	if (a->alloc < a->used + b) {
+		if ((res = mp_grow(a, a->used + b)) != MP_OKAY) {
+			return res;
+		}
+	}
 
-    /* increment the used by the shift amount then copy upwards */
-    a->used += b;
+	/* increment the used by the shift amount then copy upwards */
+	a->used += b;
 
-    /* top */
-    top = a->dp + a->used - 1;
+	/* top */
+	top = a->dp + a->used - 1;
 
-    /* base */
-    bottom = a->dp + a->used - 1 - b;
+	/* 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--;
-    }
+	/* much like rshift_digits this is implemented using a sliding window
+	* except the window goes the otherway around.  Copying from
+	* the bottom to the top.
+	*/
+	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;
+	/* zero the lower digits */
+	memset(a->dp, 0x0, b * sizeof(*a->dp));
+	return MP_OKAY;
 }
 
 /* trim unused digits 
@@ -214,710 +200,646 @@ mp_lshd (mp_int * a, int b)
  * are no more leading digits
  */
 static void
-mp_clamp (mp_int * a)
+trim_unused_digits(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;
-  }
+	/* decrease used while the most significant digit is
+	* zero.
+	*/
+	while (a->used > 0 && a->dp[a->used - 1] == 0) {
+		a->used -= 1;
+	}
+	/* reset the sign flag if used == 0 */
+	if (a->used == 0) {
+		a->sign = MP_ZPOS;
+	}
 }
 
 /* copy, b = a */
 static int
 mp_copy(BIGNUM *a, BIGNUM *b)
 {
-  int     res, n;
+	int	res;
 
-  /* if dst == src do nothing */
-  if (a == b) {
-    return MP_OKAY;
-  }
-  if (a == NULL || b == NULL) {
-	return MP_VAL;
-  }
+	/* if dst == src do nothing */
+	if (a == b) {
+		return MP_OKAY;
+	}
+	if (a == NULL || b == NULL) {
+		return MP_VAL;
+	}
 
-  /* grow dest */
-  if (b->alloc < a->used) {
-     if ((res = mp_grow (b, a->used)) != MP_OKAY) {
-        return res;
-     }
-  }
+	/* 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 */
-  {
-    mp_digit *tmpa, *tmpb;
+	memcpy(b->dp, a->dp, a->used * sizeof(*b->dp));
+	if (b->used > a->used) {
+		memset(&b->dp[a->used], 0x0, (b->used - a->used) * sizeof(*b->dp));
+	}
 
-    /* pointer aliases */
+	/* copy used count and sign */
+	b->used = a->used;
+	b->sign = a->sign;
+	return MP_OKAY;
+}
 
-    /* source */
-    tmpa = a->dp;
+/* shift left by a certain bit count */
+static int
+lshift_bits(mp_int *a, int b, mp_int *c)
+{
+	mp_digit d;
+	int      res;
 
-    /* destination */
-    tmpb = b->dp;
+	/* copy */
+	if (a != c) {
+		if ((res = mp_copy(a, c)) != MP_OKAY) {
+			return res;
+		}
+	}
 
-    /* copy all the digits */
-    for (n = 0; n < a->used; n++) {
-      *tmpb++ = *tmpa++;
-    }
+	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;
+		}
+	}
 
-    /* clear high digits */
-    for (; n < b->used; n++) {
-      *tmpb++ = 0;
-    }
-  }
+	/* shift by as many digits in the bit count */
+	if (b >= (int)DIGIT_BIT) {
+		if ((res = lshift_digits(c, b / DIGIT_BIT)) != MP_OKAY) {
+			return res;
+		}
+	}
 
-  /* copy used count and sign */
-  b->used = a->used;
-  b->sign = a->sign;
-  return MP_OKAY;
-}
+	/* shift any bit count < DIGIT_BIT */
+	d = (mp_digit) (b % DIGIT_BIT);
+	if (d != 0) {
+		mp_digit *tmpc, shift, mask, carry, rr;
+		int x;
 
-/* shift left by a certain bit count */
-static 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) {
-    mp_digit *tmpc, shift, mask, r, rr;
-    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;
+		/* bitmask for carries */
+		mask = (((mp_digit)1) << d) - 1;
+
+		/* shift for msbs */
+		shift = DIGIT_BIT - d;
+
+		/* alias */
+		tmpc = c->dp;
+
+		/* carry */
+		carry = 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) | carry) & MP_MASK;
+			++tmpc;
+
+			/* set the carry to the carry bits of the current word */
+			carry = rr;
+		}
+
+		/* set final carry */
+		if (carry != 0) {
+			c->dp[c->used++] = carry;
+		}
+	}
+	trim_unused_digits(c);
+	return MP_OKAY;
 }
 
 /* reads a unsigned char array, assumes the msb is stored first [big endian] */
 static int
 mp_read_unsigned_bin(mp_int *a, const uint8_t *b, int c)
 {
-  int     res;
+	int     res;
 
-  /* make sure there are at least two digits */
-  if (a->alloc < 2) {
-     if ((res = mp_grow(a, 2)) != MP_OKAY) {
-        return 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);
+	/* 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;
-    }
+	/* read the bytes in */
+	while (c-- > 0) {
+		if ((res = lshift_bits(a, 8, a)) != MP_OKAY) {
+			return res;
+		}
 
-      a->dp[0] |= *b++;
-      a->used += 1;
-  }
-  mp_clamp (a);
-  return MP_OKAY;
+		a->dp[0] |= *b++;
+		a->used += 1;
+	}
+	trim_unused_digits(a);
+	return MP_OKAY;
 }
 
-/* returns the number of bits in an int */
+/* returns the number of bits in an mpi */
 static int
 mp_count_bits(const mp_int *a)
 {
-  int     r;
-  mp_digit q;
+	int     r;
+	mp_digit q;
+
+	/* shortcut */
+	if (a->used == 0) {
+		return 0;
+	}
 
-  /* shortcut */
-  if (a->used == 0) {
-    return 0;
-  }
+	/* get number of digits and add that */
+	r = (a->used - 1) * DIGIT_BIT;
 
-  /* 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;
+	/* take the last digit and count the bits in it */
+	for (q = a->dp[a->used - 1]; q > ((mp_digit) 0) ; r++) {
+		q >>= ((mp_digit) 1);
+	}
+	return r;
 }
 
 /* compare maginitude of two ints (unsigned) */
 static int
-mp_cmp_mag (mp_int * a, mp_int * b)
+compare_magnitude(mp_int * a, mp_int * b)
 {
-  int     n;
-  mp_digit *tmpa, *tmpb;
+	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;
-  }
+	/* compare based on # of non-zero digits */
+	if (a->used > b->used) {
+		return MP_GT;
+	}
 
-  /* alias for a */
-  tmpa = a->dp + (a->used - 1);
+	if (a->used < b->used) {
+		return MP_LT;
+	}
 
-  /* alias for b */
-  tmpb = b->dp + (a->used - 1);
+	/* alias for a */
+	tmpa = a->dp + (a->used - 1);
 
-  /* compare based on digits  */
-  for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
-    if (*tmpa > *tmpb) {
-      return MP_GT;
-    }
+	/* alias for b */
+	tmpb = b->dp + (a->used - 1);
 
-    if (*tmpa < *tmpb) {
-      return MP_LT;
-    }
-  }
-  return MP_EQ;
+	/* 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;
 }
 
 /* compare two ints (signed)*/
 static 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);
-  }
+signed_compare(mp_int * a, mp_int * b)
+{
+	/* compare based on sign */
+	if (a->sign != b->sign) {
+		return (a->sign == MP_NEG) ? MP_LT : MP_GT;
+	}
+	return (a->sign == MP_NEG) ? compare_magnitude(b, a) : compare_magnitude(a, b);
 }
 
 /* get the size for an unsigned equivalent */
 static int
-mp_unsigned_bin_size (mp_int * a)
+mp_unsigned_bin_size(mp_int * a)
 {
-  int     size = mp_count_bits (a);
-  return (size / 8 + ((size & 7) != 0 ? 1 : 0));
+	int     size = mp_count_bits(a);
+
+	return (size / 8 + ((size & 7) != 0 ? 1 : 0));
 }
 
 /* init a new mp_int */
 static int
-mp_init (mp_int * a)
+mp_init(mp_int * a)
 {
-  int i;
-
-  /* allocate memory required and clear it */
-  a->dp = netpgp_allocate(1, sizeof (*a->dp) * MP_PREC);
-  if (a->dp == NULL) {
-    return MP_MEM;
-  }
+	/* allocate memory required and clear it */
+	a->dp = allocate(1, sizeof(*a->dp) * 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 digits to zero */
+	memset(a->dp, 0x0, MP_PREC * sizeof(*a->dp));
 
-  /* 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;
+	/* 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;
+	return MP_OKAY;
 }
 
 /* clear one (frees)  */
 static void
-mp_clear (mp_int * a)
+mp_clear(mp_int * a)
 {
-  int i;
+	/* only do anything if a hasn't been freed previously */
+	if (a->dp != NULL) {
+		memset(a->dp, 0x0, a->used * sizeof(*a->dp));
 
-  /* 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 */
+		deallocate(a->dp, (size_t)a->alloc);
 
-    /* free ram */
-    netpgp_deallocate(a->dp, (size_t)a->alloc);
-
-    /* reset members to make debugging easier */
-    a->dp    = NULL;
-    a->alloc = a->used = 0;
-    a->sign  = MP_ZPOS;
-  }
+		/* reset members to make debugging easier */
+		a->dp = NULL;
+		a->alloc = a->used = 0;
+		a->sign  = MP_ZPOS;
+	}
 }
 
 static 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. */
+	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. */
 }
 
 /* init an mp_init for a given size */
 static int
-mp_init_size (mp_int * a, int size)
+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);	
 
-  /* pad size so there are always extra digits */
-  size += (MP_PREC * 2) - (size % MP_PREC);	
-  
-  /* alloc mem */
-  a->dp = netpgp_allocate (1, sizeof (*a->dp) * size);
-  if (a->dp == NULL) {
-    return MP_MEM;
-  }
-
-  /* set the members */
-  a->used  = 0;
-  a->alloc = size;
-  a->sign  = MP_ZPOS;
+	/* alloc mem */
+	a->dp = allocate(1, sizeof(*a->dp) * size);
+	if (a->dp == NULL) {
+		return MP_MEM;
+	}
 
-  /* zero the digits */
-  for (x = 0; x < size; x++) {
-      a->dp[x] = 0;
-  }
+	/* set the members */
+	a->used  = 0;
+	a->alloc = size;
+	a->sign  = MP_ZPOS;
 
-  return MP_OKAY;
+	/* zero the digits */
+	memset(a->dp, 0x0, size * sizeof(*a->dp));
+	return MP_OKAY;
 }
 
 /* creates "a" then copies b into it */
-static int mp_init_copy (mp_int * a, mp_int * b)
+static int
+mp_init_copy(mp_int * a, mp_int * b)
 {
-  int     res;
+	int     res;
 
-  if ((res = mp_init (a)) != MP_OKAY) {
-    return res;
-  }
-  return mp_copy (b, a);
+	if ((res = mp_init(a)) != MP_OKAY) {
+		return res;
+	}
+	return mp_copy(b, a);
 }
 
 /* low level addition, based on HAC pp.594, Algorithm 14.7 */
 static 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;
-
-  {
-    mp_digit u, *tmpa, *tmpb, *tmpc;
-    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;
+basic_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;
+
+	{
+		mp_digit carry, *tmpa, *tmpb, *tmpc;
+		int i;
+
+		/* alias for digit pointers */
+
+		/* first input */
+		tmpa = a->dp;
+
+		/* second input */
+		tmpb = b->dp;
+
+		/* destination */
+		tmpc = c->dp;
+
+		/* zero the carry */
+		carry = 0;
+		for (i = 0; i < min; i++) {
+			/* Compute the sum at one digit, T[i] = A[i] + B[i] + U */
+			*tmpc = *tmpa++ + *tmpb++ + carry;
+
+			/* U = carry bit of T[i] */
+			carry = *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] + carry;
+
+				/* U = carry bit of T[i] */
+				carry = *tmpc >> ((mp_digit)DIGIT_BIT);
+
+				/* take away carry bit from T[i] */
+				*tmpc++ &= MP_MASK;
+			}
+		}
+
+		/* add carry */
+		*tmpc++ = carry;
+
+		/* clear digits above oldused */
+		if (olduse > c->used) {
+			memset(tmpc, 0x0, (olduse - c->used) * sizeof(*c->dp));
+		}
+	}
+
+	trim_unused_digits(c);
+	return MP_OKAY;
 }
 
 /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */
 static 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;
-
-  {
-    mp_digit u, *tmpa, *tmpb, *tmpc;
-    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;
-}
+basic_subtract(mp_int * a, mp_int * b, mp_int * c)
+{
+	int     olduse, res, min, max;
 
-/* high level subtraction (handles signs) */
-static 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;
-}
+	/* find sizes */
+	min = b->used;
+	max = a->used;
 
-/* shift right a certain amount of digits */
-static int mp_rshd (mp_int * a, int b)
-{
-  int     x;
+	/* init result */
+	if (c->alloc < max) {
+		if ((res = mp_grow(c, max)) != MP_OKAY) {
+			return res;
+		}
+	}
+	olduse = c->used;
+	c->used = max;
+
+	{
+		mp_digit carry, *tmpa, *tmpb, *tmpc;
+		int i;
+
+		/* alias for digit pointers */
+		tmpa = a->dp;
+		tmpb = b->dp;
+		tmpc = c->dp;
+
+		/* set carry to zero */
+		carry = 0;
+		for (i = 0; i < min; i++) {
+			/* T[i] = A[i] - B[i] - U */
+			*tmpc = *tmpa++ - *tmpb++ - carry;
+
+			/* 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
+			*/
+			carry = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof(mp_digit) - 1));
+
+			/* Clear carry from T[i] */
+			*tmpc++ &= MP_MASK;
+		}
 
-  /* if b <= 0 then ignore it */
-  if (b <= 0) {
-    return 0;
-  }
+		/* 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++ - carry;
 
-  /* if b > used then simply zero it and return */
-  if (a->used <= b) {
-    mp_zero (a);
-    return 0;
-  }
+			/* U = carry bit of T[i] */
+			carry = *tmpc >> ((mp_digit)(CHAR_BIT * sizeof(mp_digit) - 1));
 
-  {
-    mp_digit *bottom, *top;
+			/* Clear carry from T[i] */
+			*tmpc++ &= MP_MASK;
+		}
 
-    /* shift the digits down */
+		/* clear digits above used (since we may not have grown result above) */
+		if (olduse > c->used) {
+			memset(tmpc, 0x0, (olduse - c->used) * sizeof(*a->dp));
+		}
+	}
 
-    /* bottom */
-    bottom = a->dp;
+	trim_unused_digits(c);
+	return MP_OKAY;
+}
 
-    /* top [offset into digits] */
-    top = a->dp + b;
+/* high level subtraction (handles signs) */
+static int
+signed_subtract(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 = basic_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 (compare_magnitude(a, b) != MP_LT) {
+			/* Copy the sign from the first */
+			c->sign = sa;
+			/* The first has a larger or equal magnitude */
+			res = basic_subtract(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 = basic_subtract(b, a, c);
+		}
+	}
+	return res;
+}
 
-    /* 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.
+/* shift right a certain amount of digits */
+static int
+rshift_digits(mp_int * a, int b)
+{
+	/* if b <= 0 then ignore it */
+	if (b <= 0) {
+		return 0;
+	}
 
-     b-2 | b-1 | b0 | b1 | b2 | ... | bb |   ---->
-                 /\                   |      ---->
-                  \-------------------/      ---->
-     */
-    for (x = 0; x < (a->used - b); x++) {
-      *bottom++ = *top++;
-    }
+	/* if b > used then simply zero it and return */
+	if (a->used <= b) {
+		mp_zero(a);
+		return 0;
+	}
 
-    /* zero the top digits */
-    for (; x < a->used; x++) {
-      *bottom++ = 0;
-    }
-  }
-  
-  /* remove excess digits */
-  a->used -= b;
-  return 1;
+	/* 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 |   ---->
+		 /\                   |      ---->
+		  \-------------------/      ---->
+	*/
+	memmove(a->dp, &a->dp[b], (a->used - b) * sizeof(*a->dp));
+	memset(&a->dp[a->used - b], 0x0, b * sizeof(*a->dp));
+
+	/* remove excess digits */
+	a->used -= b;
+	return 1;
 }
 
 /* multiply by a digit */
 static int
-mp_mul_d (mp_int * a, mp_digit b, mp_int * c)
+multiply_digit(mp_int * a, mp_digit b, mp_int * c)
 {
-  mp_digit u, *tmpa, *tmpc;
-  mp_word  r;
-  int      ix, res, olduse;
+	mp_digit carry, *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;
+	/* 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;
+		}
+	}
 
-  /* set the sign */
-  c->sign = a->sign;
+	/* get the original destinations used count */
+	olduse = c->used;
 
-  /* alias for a->dp [source] */
-  tmpa = a->dp;
+	/* set the sign */
+	c->sign = a->sign;
 
-  /* alias for c->dp [dest] */
-  tmpc = c->dp;
+	/* alias for a->dp [source] */
+	tmpa = a->dp;
 
-  /* zero carry */
-  u = 0;
+	/* alias for c->dp [dest] */
+	tmpc = c->dp;
 
-  /* 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);
+	/* zero carry */
+	carry = 0;
 
-    /* mask off higher bits to get a single digit */
-    *tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
+	/* compute columns */
+	for (ix = 0; ix < a->used; ix++) {
+		/* compute product and carry sum for this term */
+		r = ((mp_word) carry) + ((mp_word)*tmpa++) * ((mp_word)b);
 
-    /* send carry into next iteration */
-    u       = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
-  }
+		/* mask off higher bits to get a single digit */
+		*tmpc++ = (mp_digit) (r & ((mp_word) MP_MASK));
 
-  /* store final carry [if any] and increment ix offset  */
-  *tmpc++ = u;
-  ++ix;
+		/* send carry into next iteration */
+		carry = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
+	}
 
-  /* now zero digits above the top */
-  while (ix++ < olduse) {
-     *tmpc++ = 0;
-  }
+	/* store final carry [if any] and increment ix offset  */
+	*tmpc++ = carry;
+	++ix;
+	if (olduse > ix) {
+		memset(tmpc, 0x0, (olduse - ix) * sizeof(*tmpc));
+	}
 
-  /* set used count */
-  c->used = a->used + 1;
-  mp_clamp(c);
+	/* set used count */
+	c->used = a->used + 1;
+	trim_unused_digits(c);
 
-  return MP_OKAY;
+	return MP_OKAY;
 }
 
 /* high level addition (handles signs) */
-static 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;
+static int
+signed_add(mp_int * a, mp_int * b, mp_int * c)
+{
+	int     asign, bsign, res;
+
+	/* get sign of both inputs */
+	asign = a->sign;
+	bsign = b->sign;
+
+	/* handle two cases, not four */
+	if (asign == bsign) {
+		/* both positive or both negative */
+		/* add their magnitudes, copy the sign */
+		c->sign = asign;
+		res = basic_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 (compare_magnitude(a, b) == MP_LT) {
+			c->sign = bsign;
+			res = basic_subtract(b, a, c);
+		} else {
+			c->sign = asign;
+			res = basic_subtract(a, b, c);
+		}
+	}
+	return res;
 }
 
 /* swap the elements of two integers, for cases where you can't simply swap the 
@@ -926,121 +848,122 @@ static int mp_add (mp_int * a, mp_int * b, mp_int * c)
 static void
 mp_exch(mp_int *a, mp_int *b)
 {
-  mp_int  t;
+	mp_int  t;
 
-  t  = *a;
-  *a = *b;
-  *b = t;
+	t  = *a;
+	*a = *b;
+	*b = t;
 }
 
 /* calc a value mod 2**b */
 static 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;
+modulo_2_to_power(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));
+	trim_unused_digits(c);
+	return MP_OKAY;
 }
 
 /* shift right by a certain bit count (store quotient in c, optional remainder in d) */
-static 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) {
-    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;
+static int
+rshift_bits(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 = modulo_2_to_power(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) {
+		rshift_digits(c, b / DIGIT_BIT);
+	}
+
+	/* shift any bit count < DIGIT_BIT */
+	D = (mp_digit) (b % DIGIT_BIT);
+	if (D != 0) {
+		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;
+		}
+	}
+	trim_unused_digits(c);
+	if (d != NULL) {
+		mp_exch(&t, d);
+	}
+	mp_clear(&t);
+	return MP_OKAY;
 }
 
 /* integer signed division. 
@@ -1057,304 +980,314 @@ static int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d)
  * 14.20 from HAC but fixed to treat these cases.
 */
 static int
-mp_div(mp_int *c, mp_int *d, mp_int *a, mp_int *b)
-{
-  mp_int  q, x, y, t1, t2;
-  int     res, n, t, i, norm, neg;
-
-  /* is divisor zero ? */
-  if (BN_is_zero (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 LBL_Q;
-  }
-
-  if ((res = mp_init (&t2)) != MP_OKAY) {
-    goto LBL_T1;
-  }
-
-  if ((res = mp_init_copy (&x, a)) != MP_OKAY) {
-    goto LBL_T2;
-  }
-
-  if ((res = mp_init_copy (&y, b)) != MP_OKAY) {
-    goto LBL_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 LBL_Y;
-     }
-     if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) {
-       goto LBL_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 LBL_Y;
-  }
-
-  while (mp_cmp (&x, &y) != MP_LT) {
-    ++(q.dp[n - t]);
-    if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) {
-      goto LBL_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 LBL_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 LBL_Y;
-    }
-
-    if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
-      goto LBL_Y;
-    }
-
-    if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) {
-      goto LBL_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 LBL_Y;
-      }
-      if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) {
-        goto LBL_Y;
-      }
-      if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) {
-        goto LBL_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;
-
-LBL_Y:mp_clear (&y);
-LBL_X:mp_clear (&x);
-LBL_T2:mp_clear (&t2);
-LBL_T1:mp_clear (&t1);
-LBL_Q:mp_clear (&q);
-  return res;
+signed_divide(mp_int *c, mp_int *d, mp_int *a, mp_int *b)
+{
+	mp_int  q, x, y, t1, t2;
+	int     res, n, t, i, norm, neg;
+
+	/* is divisor zero ? */
+	if (MP_ISZERO(b) == MP_YES) {
+		return MP_VAL;
+	}
+
+	/* if a < b then q=0, r = a */
+	if (compare_magnitude(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 LBL_Q;
+	}
+
+	if ((res = mp_init(&t2)) != MP_OKAY) {
+		goto LBL_T1;
+	}
+
+	if ((res = mp_init_copy(&x, a)) != MP_OKAY) {
+		goto LBL_T2;
+	}
+
+	if ((res = mp_init_copy(&y, b)) != MP_OKAY) {
+		goto LBL_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 = lshift_bits(&x, norm, &x)) != MP_OKAY) {
+			goto LBL_Y;
+		}
+		if ((res = lshift_bits(&y, norm, &y)) != MP_OKAY) {
+			goto LBL_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 = lshift_digits(&y, n - t)) != MP_OKAY) { /* y = y*b**{n-t} */
+		goto LBL_Y;
+	}
+
+	while (signed_compare(&x, &y) != MP_LT) {
+		++(q.dp[n - t]);
+		if ((res = signed_subtract(&x, &y, &x)) != MP_OKAY) {
+			goto LBL_Y;
+		}
+	}
+
+	/* reset y by shifting it back down */
+	rshift_digits(&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 = multiply_digit(&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) {
+				goto LBL_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 (compare_magnitude(&t1, &t2) == MP_GT);
+
+		/* step 3.3 x = x - q{i-t-1} * y * b**{i-t-1} */
+		if ((res = multiply_digit(&y, q.dp[i - t - 1], &t1)) != MP_OKAY) {
+			goto LBL_Y;
+		}
+
+		if ((res = lshift_digits(&t1, i - t - 1)) != MP_OKAY) {
+			goto LBL_Y;
+		}
+
+		if ((res = signed_subtract(&x, &t1, &x)) != MP_OKAY) {
+			goto LBL_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 LBL_Y;
+			}
+			if ((res = lshift_digits(&t1, i - t - 1)) != MP_OKAY) {
+				goto LBL_Y;
+			}
+			if ((res = signed_add(&x, &t1, &x)) != MP_OKAY) {
+				goto LBL_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) {
+		trim_unused_digits(&q);
+		mp_exch(&q, c);
+		c->sign = neg;
+	}
+
+	if (d != NULL) {
+		rshift_bits(&x, norm, &x, NULL);
+		mp_exch(&x, d);
+	}
+
+	res = MP_OKAY;
+
+LBL_Y:
+	mp_clear(&y);
+LBL_X:
+	mp_clear(&x);
+LBL_T2:
+	mp_clear(&t2);
+LBL_T1:
+	mp_clear(&t1);
+LBL_Q:
+	mp_clear(&q);
+	return res;
 }
 
 /* c = a mod b, 0 <= c < b */
 static int
-mp_mod (mp_int * a, mp_int * b, mp_int * c)
+modulo(mp_int * a, mp_int * b, mp_int * c)
 {
-  mp_int  t;
-  int     res;
+	mp_int  t;
+	int     res;
 
-  if ((res = mp_init (&t)) != MP_OKAY) {
-    return res;
-  }
+	if ((res = mp_init(&t)) != MP_OKAY) {
+		return res;
+	}
 
-  if ((res = mp_div (NULL, &t, a, b)) != MP_OKAY) {
-    mp_clear (&t);
-    return res;
-  }
+	if ((res = signed_divide(NULL, &t, a, b)) != 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);
-  }
+	if (t.sign != b->sign) {
+		res = signed_add(b, &t, c);
+	} else {
+		res = MP_OKAY;
+		mp_exch(&t, c);
+	}
 
-  mp_clear (&t);
-  return res;
+	mp_clear(&t);
+	return res;
 }
 
 /* set to a digit */
-static void mp_set (mp_int * a, mp_digit b)
+static void
+set_word(mp_int * a, mp_digit b)
 {
-  mp_zero (a);
-  a->dp[0] = b & MP_MASK;
-  a->used  = (a->dp[0] != 0) ? 1 : 0;
+	mp_zero(a);
+	a->dp[0] = b & MP_MASK;
+	a->used = (a->dp[0] != 0) ? 1 : 0;
 }
 
 /* b = a/2 */
-static int mp_div_2(mp_int * a, mp_int * b)
+static int
+half(mp_int * a, mp_int * b)
 {
-  int     x, res, oldused;
+	int     x, res, oldused;
 
-  /* copy */
-  if (b->alloc < a->used) {
-    if ((res = mp_grow (b, a->used)) != MP_OKAY) {
-      return res;
-    }
-  }
+	/* copy */
+	if (b->alloc < a->used) {
+		if ((res = mp_grow(b, a->used)) != MP_OKAY) {
+			return res;
+		}
+	}
 
-  oldused = b->used;
-  b->used = a->used;
-  {
-    mp_digit r, rr, *tmpa, *tmpb;
+	oldused = b->used;
+	b->used = a->used;
+	{
+		mp_digit r, rr, *tmpa, *tmpb;
 
-    /* source alias */
-    tmpa = a->dp + b->used - 1;
+		/* source alias */
+		tmpa = a->dp + b->used - 1;
 
-    /* dest alias */
-    tmpb = b->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;
+		/* 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));
+			/* shift the current digit, add in carry and store */
+			*tmpb-- = (*tmpa-- >> 1) | (r << (DIGIT_BIT - 1));
 
-      /* forward carry to next iteration */
-      r = rr;
-    }
+			/* 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;
+		/* zero excess digits */
+		tmpb = b->dp + b->used;
+		for (x = b->used; x < oldused; x++) {
+			*tmpb++ = 0;
+		}
+	}
+	b->sign = a->sign;
+	trim_unused_digits(b);
+	return MP_OKAY;
 }
 
 /* compare a digit */
-static int mp_cmp_d(mp_int * a, mp_digit b)
+static int
+compare_digit(mp_int * a, mp_digit b)
 {
-  /* compare based on sign */
-  if (a->sign == MP_NEG) {
-    return MP_LT;
-  }
+	/* compare based on sign */
+	if (a->sign == MP_NEG) {
+		return MP_LT;
+	}
 
-  /* compare based on magnitude */
-  if (a->used > 1) {
-    return MP_GT;
-  }
+	/* 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;
-  }
+	/* 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;
+	}
 }
 
-static void mp_clear_multi(mp_int *mp, ...) 
+static 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);
+	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);
 }
 
 /* computes the modular inverse via binary extended euclidean algorithm, 
@@ -1364,299 +1297,297 @@ static void mp_clear_multi(mp_int *mp, ...)
  * odd as per HAC Note 14.64 on pp. 610
  */
 static 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 (BN_is_even (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 LBL_ERR;
-  }
-
-  /* we need y = |a| */
-  if ((res = mp_mod (a, b, &y)) != MP_OKAY) {
-    goto LBL_ERR;
-  }
-
-  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
-  if ((res = mp_copy (&x, &u)) != MP_OKAY) {
-    goto LBL_ERR;
-  }
-  if ((res = mp_copy (&y, &v)) != MP_OKAY) {
-    goto LBL_ERR;
-  }
-  mp_set (&D, 1);
+fast_modular_inverse(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_ISZERO(b) == MP_YES) {
+		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 LBL_ERR;
+	}
+
+	/* we need y = |a| */
+	if ((res = modulo(a, b, &y)) != MP_OKAY) {
+		goto LBL_ERR;
+	}
+
+	/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
+	if ((res = mp_copy(&x, &u)) != MP_OKAY) {
+		goto LBL_ERR;
+	}
+	if ((res = mp_copy(&y, &v)) != MP_OKAY) {
+		goto LBL_ERR;
+	}
+	set_word(&D, 1);
 
 top:
-  /* 4.  while u is even do */
-  while (BN_is_even (&u) == 1) {
-    /* 4.1 u = u/2 */
-    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-    /* 4.2 if B is odd then */
-    if (BN_is_odd (&B) == 1) {
-      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
-        goto LBL_ERR;
-      }
-    }
-    /* B = B/2 */
-    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-  }
-
-  /* 5.  while v is even do */
-  while (BN_is_even (&v) == 1) {
-    /* 5.1 v = v/2 */
-    if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-    /* 5.2 if D is odd then */
-    if (BN_is_odd (&D) == 1) {
-      /* D = (D-x)/2 */
-      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
-        goto LBL_ERR;
-      }
-    }
-    /* D = D/2 */
-    if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
-      goto LBL_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 LBL_ERR;
-    }
-
-    if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-  } else {
-    /* v - v - u, D = D - B */
-    if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-
-    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-  }
-
-  /* if not zero goto step 4 */
-  if (BN_is_zero (&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 LBL_ERR;
-  }
-
-  /* b is now the inverse */
-  neg = a->sign;
-  while (D.sign == MP_NEG) {
-    if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-  }
-  mp_exch (&D, c);
-  c->sign = neg;
-  res = MP_OKAY;
-
-LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
-  return res;
+	/* 4.  while u is even do */
+	while (BN_is_even(&u) == 1) {
+		/* 4.1 u = u/2 */
+		if ((res = half(&u, &u)) != MP_OKAY) {
+			goto LBL_ERR;
+		}
+		/* 4.2 if B is odd then */
+		if (BN_is_odd(&B) == 1) {
+			if ((res = signed_subtract(&B, &x, &B)) != MP_OKAY) {
+				goto LBL_ERR;
+			}
+		}
+		/* B = B/2 */
+		if ((res = half(&B, &B)) != MP_OKAY) {
+			goto LBL_ERR;
+		}
+	}
+
+	/* 5.  while v is even do */
+	while (BN_is_even(&v) == 1) {
+		/* 5.1 v = v/2 */
+		if ((res = half(&v, &v)) != MP_OKAY) {
+			goto LBL_ERR;
+		}
+		/* 5.2 if D is odd then */
+		if (BN_is_odd(&D) == 1) {
+			/* D = (D-x)/2 */
+			if ((res = signed_subtract(&D, &x, &D)) != MP_OKAY) {
+				goto LBL_ERR;
+			}
+		}
+		/* D = D/2 */
+		if ((res = half(&D, &D)) != MP_OKAY) {
+			goto LBL_ERR;
+		}
+	}
+
+	/* 6.  if u >= v then */
+	if (signed_compare(&u, &v) != MP_LT) {
+		/* u = u - v, B = B - D */
+		if ((res = signed_subtract(&u, &v, &u)) != MP_OKAY) {
+			goto LBL_ERR;
+		}
+
+		if ((res = signed_subtract(&B, &D, &B)) != MP_OKAY) {
+			goto LBL_ERR;
+		}
+	} else {
+		/* v - v - u, D = D - B */
+		if ((res = signed_subtract(&v, &u, &v)) != MP_OKAY) {
+			goto LBL_ERR;
+		}
+
+		if ((res = signed_subtract(&D, &B, &D)) != MP_OKAY) {
+			goto LBL_ERR;
+		}
+	}
+
+	/* if not zero goto step 4 */
+	if (MP_ISZERO(&u) == MP_NO) {
+		goto top;
+	}
+
+	/* now a = C, b = D, gcd == g*v */
+
+	/* if v != 1 then there is no inverse */
+	if (compare_digit(&v, 1) != MP_EQ) {
+		res = MP_VAL;
+		goto LBL_ERR;
+	}
+
+	/* b is now the inverse */
+	neg = a->sign;
+	while (D.sign == MP_NEG) {
+		if ((res = signed_add(&D, b, &D)) != MP_OKAY) {
+			goto LBL_ERR;
+		}
+	}
+	mp_exch(&D, c);
+	c->sign = neg;
+	res = MP_OKAY;
+
+LBL_ERR:
+	mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
+	return res;
 }
 
 /* hac 14.61, pp608 */
 static 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 || BN_is_zero(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_mod(a, b, &x)) != MP_OKAY) {
-      goto LBL_ERR;
-  }
-  if ((res = mp_copy (b, &y)) != MP_OKAY) {
-    goto LBL_ERR;
-  }
-
-  /* 2. [modified] if x,y are both even then return an error! */
-  if (BN_is_even (&x) == 1 && BN_is_even (&y) == 1) {
-    res = MP_VAL;
-    goto LBL_ERR;
-  }
-
-  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
-  if ((res = mp_copy (&x, &u)) != MP_OKAY) {
-    goto LBL_ERR;
-  }
-  if ((res = mp_copy (&y, &v)) != MP_OKAY) {
-    goto LBL_ERR;
-  }
-  mp_set (&A, 1);
-  mp_set (&D, 1);
+slow_modular_inverse(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) == MP_YES) {
+		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 = modulo(a, b, &x)) != MP_OKAY) {
+		goto LBL_ERR;
+	}
+	if ((res = mp_copy(b, &y)) != MP_OKAY) {
+		goto LBL_ERR;
+	}
+
+	/* 2. [modified] if x,y are both even then return an error! */
+	if (BN_is_even(&x) == 1 && BN_is_even(&y) == 1) {
+		res = MP_VAL;
+		goto LBL_ERR;
+	}
+
+	/* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
+	if ((res = mp_copy(&x, &u)) != MP_OKAY) {
+		goto LBL_ERR;
+	}
+	if ((res = mp_copy(&y, &v)) != MP_OKAY) {
+		goto LBL_ERR;
+	}
+	set_word(&A, 1);
+	set_word(&D, 1);
 
 top:
-  /* 4.  while u is even do */
-  while (BN_is_even (&u) == 1) {
-    /* 4.1 u = u/2 */
-    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-    /* 4.2 if A or B is odd then */
-    if (BN_is_odd (&A) == 1 || BN_is_odd (&B) == 1) {
-      /* A = (A+y)/2, B = (B-x)/2 */
-      if ((res = mp_add (&A, &y, &A)) != MP_OKAY) {
-         goto LBL_ERR;
-      }
-      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
-         goto LBL_ERR;
-      }
-    }
-    /* A = A/2, B = B/2 */
-    if ((res = mp_div_2 (&A, &A)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-  }
-
-  /* 5.  while v is even do */
-  while (BN_is_even (&v) == 1) {
-    /* 5.1 v = v/2 */
-    if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-    /* 5.2 if C or D is odd then */
-    if (BN_is_odd (&C) == 1 || BN_is_odd (&D) == 1) {
-      /* C = (C+y)/2, D = (D-x)/2 */
-      if ((res = mp_add (&C, &y, &C)) != MP_OKAY) {
-         goto LBL_ERR;
-      }
-      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
-         goto LBL_ERR;
-      }
-    }
-    /* C = C/2, D = D/2 */
-    if ((res = mp_div_2 (&C, &C)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-    if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
-      goto LBL_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 LBL_ERR;
-    }
-
-    if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-
-    if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-  } else {
-    /* v - v - u, C = C - A, D = D - B */
-    if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-
-    if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-
-    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
-      goto LBL_ERR;
-    }
-  }
-
-  /* if not zero goto step 4 */
-  if (BN_is_zero (&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 LBL_ERR;
-  }
-
-  /* if its too low */
-  while (mp_cmp_d(&C, 0) == MP_LT) {
-      if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
-         goto LBL_ERR;
-      }
-  }
-  
-  /* too big */
-  while (mp_cmp_mag(&C, b) != MP_LT) {
-      if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
-         goto LBL_ERR;
-      }
-  }
-  
-  /* C is now the inverse */
-  mp_exch (&C, c);
-  res = MP_OKAY;
-LBL_ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL);
-  return res;
+	/* 4.  while u is even do */
+	while (BN_is_even(&u) == 1) {
+		/* 4.1 u = u/2 */
+		if ((res = half(&u, &u)) != MP_OKAY) {
+			goto LBL_ERR;
+		}
+		/* 4.2 if A or B is odd then */
+		if (BN_is_odd(&A) == 1 || BN_is_odd(&B) == 1) {
+			/* A = (A+y)/2, B = (B-x)/2 */
+			if ((res = signed_add(&A, &y, &A)) != MP_OKAY) {
+				 goto LBL_ERR;
+			}
+			if ((res = signed_subtract(&B, &x, &B)) != MP_OKAY) {
+				 goto LBL_ERR;
+			}
+		}
+		/* A = A/2, B = B/2 */
+		if ((res = half(&A, &A)) != MP_OKAY) {
+			goto LBL_ERR;
+		}
+		if ((res = half(&B, &B)) != MP_OKAY) {
+			goto LBL_ERR;
+		}
+	}
+
+	/* 5.  while v is even do */
+	while (BN_is_even(&v) == 1) {
+		/* 5.1 v = v/2 */
+		if ((res = half(&v, &v)) != MP_OKAY) {
+			goto LBL_ERR;
+		}
+		/* 5.2 if C or D is odd then */
+		if (BN_is_odd(&C) == 1 || BN_is_odd(&D) == 1) {
+			/* C = (C+y)/2, D = (D-x)/2 */
+			if ((res = signed_add(&C, &y, &C)) != MP_OKAY) {
+				 goto LBL_ERR;
+			}
+			if ((res = signed_subtract(&D, &x, &D)) != MP_OKAY) {
+				 goto LBL_ERR;
+			}
+		}
+		/* C = C/2, D = D/2 */
+		if ((res = half(&C, &C)) != MP_OKAY) {
+			goto LBL_ERR;
+		}
+		if ((res = half(&D, &D)) != MP_OKAY) {
+			goto LBL_ERR;
+		}
+	}
+
+	/* 6.  if u >= v then */
+	if (signed_compare(&u, &v) != MP_LT) {
+		/* u = u - v, A = A - C, B = B - D */
+		if ((res = signed_subtract(&u, &v, &u)) != MP_OKAY) {
+			goto LBL_ERR;
+		}
+
+		if ((res = signed_subtract(&A, &C, &A)) != MP_OKAY) {
+			goto LBL_ERR;
+		}
+
+		if ((res = signed_subtract(&B, &D, &B)) != MP_OKAY) {
+			goto LBL_ERR;
+		}
+	} else {
+		/* v - v - u, C = C - A, D = D - B */
+		if ((res = signed_subtract(&v, &u, &v)) != MP_OKAY) {
+			goto LBL_ERR;
+		}
+
+		if ((res = signed_subtract(&C, &A, &C)) != MP_OKAY) {
+			goto LBL_ERR;
+		}
+
+		if ((res = signed_subtract(&D, &B, &D)) != MP_OKAY) {
+			goto LBL_ERR;
+		}
+	}
+
+	/* if not zero goto step 4 */
+	if (BN_is_zero(&u) == 0) {
+		goto top;
+	}
+	/* now a = C, b = D, gcd == g*v */
+
+	/* if v != 1 then there is no inverse */
+	if (compare_digit(&v, 1) != MP_EQ) {
+		res = MP_VAL;
+		goto LBL_ERR;
+	}
+
+	/* if its too low */
+	while (compare_digit(&C, 0) == MP_LT) {
+		if ((res = signed_add(&C, b, &C)) != MP_OKAY) {
+			 goto LBL_ERR;
+		}
+	}
+
+	/* too big */
+	while (compare_magnitude(&C, b) != MP_LT) {
+		if ((res = signed_subtract(&C, b, &C)) != MP_OKAY) {
+			 goto LBL_ERR;
+		}
+	}
+
+	/* C is now the inverse */
+	mp_exch(&C, c);
+	res = MP_OKAY;
+LBL_ERR:
+	mp_clear_multi(&x, &y, &u, &v, &A, &B, &C, &D, NULL);
+	return res;
 }
 
 static int
-mp_invmod(mp_int *c, mp_int *a, mp_int *b)
+modular_inverse(mp_int *c, mp_int *a, mp_int *b)
 {
-  /* b cannot be negative */
-  if (b->sign == MP_NEG || BN_is_zero(b) == 1) {
-    return MP_VAL;
-  }
-
-  /* if the modulus is odd we can use a faster routine instead */
-  if (BN_is_odd (b) == 1) {
-    return fast_mp_invmod(a, b, c);
-  }
-
-  return mp_invmod_slow(a, b, c);
+	/* b cannot be negative */
+	if (b->sign == MP_NEG || MP_ISZERO(b) == MP_YES) {
+		return MP_VAL;
+	}
 
-  /*NOTREACHED*/
-  return MP_VAL;
+	/* if the modulus is odd we can use a faster routine instead */
+	if (BN_is_odd(b) == 1) {
+		return fast_modular_inverse(a, b, c);
+	}
+	return slow_modular_inverse(a, b, c);
 }
 
 /* b = |a| 
@@ -1664,43 +1595,44 @@ mp_invmod(mp_int *c, mp_int *a, mp_int *b)
  * Simple function copies the input and fixes the sign to positive
  */
 static int
-mp_abs (mp_int * a, mp_int * b)
+absolute(mp_int * a, mp_int * b)
 {
-  int     res;
+	int     res;
 
-  /* copy a to b */
-  if (a != b) {
-     if ((res = mp_copy (a, b)) != MP_OKAY) {
-       return 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;
+	/* force the sign of b to positive */
+	b->sign = MP_ZPOS;
 
-  return MP_OKAY;
+	return MP_OKAY;
 }
 
 /* determines if reduce_2k_l can be used */
-static int mp_reduce_is_2k_l(mp_int *a)
-{
-   int ix, iy;
-   
-   if (a->used == 0) {
-      return MP_NO;
-   } else if (a->used == 1) {
-      return MP_YES;
-   } else if (a->used > 1) {
-      /* if more than half of the digits are -1 we're sold */
-      for (iy = ix = 0; ix < a->used; ix++) {
-          if (a->dp[ix] == MP_MASK) {
-              ++iy;
-          }
-      }
-      return (iy >= (a->used/2)) ? MP_YES : MP_NO;
-      
-   }
-   return MP_NO;
+static int
+mp_reduce_is_2k_l(mp_int *a)
+{
+	int ix, iy;
+
+	if (a->used == 0) {
+		return MP_NO;
+	} else if (a->used == 1) {
+		return MP_YES;
+	} else if (a->used > 1) {
+		/* if more than half of the digits are -1 we're sold */
+		for (iy = ix = 0; ix < a->used; ix++) {
+			if (a->dp[ix] == MP_MASK) {
+				++iy;
+			}
+		}
+		return (iy >= (a->used/2)) ? MP_YES : MP_NO;
+
+	}
+	return MP_NO;
 }
 
 /* computes a = 2**b 
@@ -1709,156 +1641,158 @@ static int mp_reduce_is_2k_l(mp_int *a)
  * as required.
  */
 static int
-mp_2expt (mp_int * a, int b)
+mp_2expt(mp_int * a, int b)
 {
-  int     res;
+	int     res;
 
-  /* zero a as per default */
-  mp_zero (a);
+	/* 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;
-  }
+	/* 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;
+	/* 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);
+	/* put the single bit in its place */
+	a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT);
 
-  return MP_OKAY;
+	return MP_OKAY;
 }
 
 /* pre-calculate the value required for Barrett reduction
  * For a given modulus "b" it calulates the value required in "a"
  */
-static int mp_reduce_setup (mp_int * a, mp_int * b)
+static 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, NULL, a, b);
+	int     res;
+
+	if ((res = mp_2expt(a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) {
+		return res;
+	}
+	return signed_divide(a, NULL, a, b);
 }
 
 /* b = a*2 */
-static 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;
-
-  {
-    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;
+static int
+doubled(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;
+
+	{
+		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;
 }
 
 /* divide by three (based on routine from MPI and the GMP manual) */
 static 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;
+third(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) {
+		trim_unused_digits(&q);
+		mp_exch(&q, c);
+	}
+	mp_clear(&q);
+
+	return res;
 }
 
 /* multiplication using the Toom-Cook 3-way algorithm 
@@ -1868,259 +1802,260 @@ mp_div_3 (mp_int * a, mp_int *c, mp_digit * d)
  * only particularly useful on VERY large inputs 
  * (we're talking 1000s of digits here...).
 */
-static 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;
-     }     
-     
+static int
+toom_cook_multiply(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 = modulo_2_to_power(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	if ((res = mp_copy(a, &a1)) != MP_OKAY) {
+		goto ERR;
+	}
+	rshift_digits(&a1, B);
+	modulo_2_to_power(&a1, DIGIT_BIT * B, &a1);
+
+	if ((res = mp_copy(a, &a2)) != MP_OKAY) {
+		goto ERR;
+	}
+	rshift_digits(&a2, B*2);
+
+	/* b = b2 * B**2 + b1 * B + b0 */
+	if ((res = modulo_2_to_power(b, DIGIT_BIT * B, &b0)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	if ((res = mp_copy(b, &b1)) != MP_OKAY) {
+		goto ERR;
+	}
+	rshift_digits(&b1, B);
+	modulo_2_to_power(&b1, DIGIT_BIT * B, &b1);
+
+	if ((res = mp_copy(b, &b2)) != MP_OKAY) {
+		goto ERR;
+	}
+	rshift_digits(&b2, B*2);
+
+	/* w0 = a0*b0 */
+	if ((res = signed_multiply(&a0, &b0, &w0)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	/* w4 = a2 * b2 */
+	if ((res = signed_multiply(&a2, &b2, &w4)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	/* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */
+	if ((res = doubled(&a0, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = doubled(&tmp1, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	if ((res = doubled(&b0, &tmp2)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = doubled(&tmp2, &tmp2)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_add(&tmp2, &b2, &tmp2)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	if ((res = signed_multiply(&tmp1, &tmp2, &w1)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	/* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */
+	if ((res = doubled(&a2, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = doubled(&tmp1, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	if ((res = doubled(&b2, &tmp2)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_add(&tmp2, &b1, &tmp2)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = doubled(&tmp2, &tmp2)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	if ((res = signed_multiply(&tmp1, &tmp2, &w3)) != MP_OKAY) {
+		goto ERR;
+	}
+
+
+	/* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */
+	if ((res = signed_add(&a2, &a1, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_add(&b2, &b1, &tmp2)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_add(&tmp2, &b0, &tmp2)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_multiply(&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 = signed_subtract(&w1, &w4, &w1)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r3 - r0 */
+	if ((res = signed_subtract(&w3, &w0, &w3)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r1/2 */
+	if ((res = half(&w1, &w1)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r3/2 */
+	if ((res = half(&w3, &w3)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r2 - r0 - r4 */
+	if ((res = signed_subtract(&w2, &w0, &w2)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_subtract(&w2, &w4, &w2)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r1 - r2 */
+	if ((res = signed_subtract(&w1, &w2, &w1)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r3 - r2 */
+	if ((res = signed_subtract(&w3, &w2, &w3)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r1 - 8r0 */
+	if ((res = lshift_bits(&w0, 3, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_subtract(&w1, &tmp1, &w1)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r3 - 8r4 */
+	if ((res = lshift_bits(&w4, 3, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_subtract(&w3, &tmp1, &w3)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* 3r2 - r1 - r3 */
+	if ((res = multiply_digit(&w2, 3, &w2)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_subtract(&w2, &w1, &w2)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_subtract(&w2, &w3, &w2)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r1 - r2 */
+	if ((res = signed_subtract(&w1, &w2, &w1)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r3 - r2 */
+	if ((res = signed_subtract(&w3, &w2, &w3)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r1/3 */
+	if ((res = third(&w1, &w1, NULL)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r3/3 */
+	if ((res = third(&w3, &w3, NULL)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	/* at this point shift W[n] by B*n */
+	if ((res = lshift_digits(&w1, 1*B)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = lshift_digits(&w2, 2*B)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = lshift_digits(&w3, 3*B)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = lshift_digits(&w4, 4*B)) != MP_OKAY) {
+		goto ERR;
+	}     
+
+	if ((res = signed_add(&w0, &w1, c)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_add(&w2, &w3, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_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;
+	mp_clear_multi(&w0, &w1, &w2, &w3, &w4, 
+		&a0, &a1, &a2, &b0, &b1, 
+		&b2, &tmp1, &tmp2, NULL);
+	return res;
 }     
      
 #define TOOM_MUL_CUTOFF	350
@@ -2147,7 +2082,7 @@ ERR:
  * 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 
+ * are saved.  Note also that the call to signed_multiply 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 
@@ -2155,122 +2090,141 @@ ERR:
  * Generally though the overhead of this method doesn't pay off 
  * until a certain size (N ~ 80) is reached.
  */
-static int mp_karatsuba_mul (mp_int * a, mp_int * b, mp_int * c)
-{
-  mp_int  x0, x1, y0, y1, t1, x0y0, x1y1;
-  int     B;
-  int     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 = (int)((unsigned)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;
-
-  {
-    int x;
-    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 (s_mp_add (&x1, &x0, &t1) != MP_OKAY)
-    goto X1Y1;          /* t1 = x1 - x0 */
-  if (s_mp_add (&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 (s_mp_sub (&t1, &x0, &t1) != MP_OKAY)
-    goto X1Y1;          /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */
-
-  /* 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);
+static int
+karatsuba_multiply(mp_int * a, mp_int * b, mp_int * c)
+{
+	mp_int  x0, x1, y0, y1, t1, x0y0, x1y1;
+	int     B;
+	int     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 = (int)((unsigned)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;
+
+	{
+		int x;
+		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
+	*/
+	trim_unused_digits(&x0);
+	trim_unused_digits(&y0);
+
+	/* now calc the products x0y0 and x1y1 */
+	/* after this x0 is no longer required, free temp [x0==t2]! */
+	if (signed_multiply(&x0, &y0, &x0y0) != MP_OKAY)  {
+		goto X1Y1;          /* x0y0 = x0*y0 */
+	}
+	if (signed_multiply(&x1, &y1, &x1y1) != MP_OKAY) {
+		goto X1Y1;          /* x1y1 = x1*y1 */
+	}
+	/* now calc x1+x0 and y1+y0 */
+	if (basic_add(&x1, &x0, &t1) != MP_OKAY) {
+		goto X1Y1;          /* t1 = x1 - x0 */
+	}
+	if (basic_add(&y1, &y0, &x0) != MP_OKAY) {
+		goto X1Y1;          /* t2 = y1 - y0 */
+	}
+	if (signed_multiply(&t1, &x0, &t1) != MP_OKAY) {
+		goto X1Y1;          /* t1 = (x1 + x0) * (y1 + y0) */
+	}
+	/* add x0y0 */
+	if (signed_add(&x0y0, &x1y1, &x0) != MP_OKAY) {
+		goto X1Y1;          /* t2 = x0y0 + x1y1 */
+	}
+	if (basic_subtract(&t1, &x0, &t1) != MP_OKAY) {
+		goto X1Y1;          /* t1 = (x1+x0)*(y1+y0) - (x1y1 + x0y0) */
+	}
+	/* shift by B */
+	if (lshift_digits(&t1, B) != MP_OKAY) {
+		goto X1Y1;          /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */
+	}
+	if (lshift_digits(&x1y1, B * 2) != MP_OKAY) {
+		goto X1Y1;          /* x1y1 = x1y1 << 2*B */
+	}
+	if (signed_add(&x0y0, &t1, &t1) != MP_OKAY) {
+		goto X1Y1;          /* t1 = x0y0 + t1 */
+	}
+	if (signed_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;
+	return err;
 }
 
 /* Fast (comba) multiplier
@@ -2289,75 +2243,89 @@ ERR:
  * Based on Algorithm 14.12 on pp.595 of HAC.
  *
  */
-static int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
-{
-  int     olduse, res, pa, ix, iz;
-  /*LINTED*/
-  mp_digit W[MP_WARRAY];
-  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 
-         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;
-
-  {
-    mp_digit *tmpc;
-    tmpc = c->dp;
-    for (ix = 0; ix < pa+1; 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;
+static int
+fast_col_array_multiply(mp_int * a, mp_int * b, mp_int * c, int digs)
+{
+	int     olduse, res, pa, ix, iz;
+	/*LINTED*/
+	mp_digit W[MP_WARRAY];
+	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 
+		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;
+
+	{
+		mp_digit *tmpc;
+		tmpc = c->dp;
+		for (ix = 0; ix < pa+1; 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;
+		}
+	}
+	trim_unused_digits(c);
+	return MP_OKAY;
+}
+
+/* return 1 if we can use fast column array multiply */
+/*
+* 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
+*/
+static inline int
+can_use_fast_column_array(int ndigits, int used)
+{
+	return (((unsigned)ndigits < MP_WARRAY) &&
+		used < (1 << (unsigned)((CHAR_BIT * sizeof(mp_word)) - (2 * DIGIT_BIT))));
 }
 
 /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_fast_s_mp_mul_digs.c,v $ */
@@ -2369,69 +2337,68 @@ static int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
  * HAC pp. 595, Algorithm 14.12  Modified so you can control how 
  * many digits of output are created.
  */
-static 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 (((unsigned)(digs) < MP_WARRAY) &&
-      MIN (a->used, b->used) < 
-          (1 << (unsigned)((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;
+static int
+basic_multiply_partial_lower(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 (can_use_fast_column_array(digs, MIN(a->used, b->used))) {
+		return fast_col_array_multiply(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;
+		}
+	}
+
+	trim_unused_digits(&t);
+	mp_exch(&t, c);
+
+	mp_clear(&t);
+	return MP_OKAY;
 }
 
 /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_s_mp_mul_digs.c,v $ */
@@ -2440,38 +2407,29 @@ static int s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
 
 /* high level multiplication (handles sign) */
 static 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? */
-  if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) {
-    res = mp_toom_mul(a, b, c);
-  } else 
-  /* use Karatsuba? */
-  if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
-    res = mp_karatsuba_mul (a, b, c);
-  } else 
-  {
-    /* 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;
-
-    if (((unsigned)digs < MP_WARRAY) &&
-        MIN(a->used, b->used) <= 
-        (1 << (unsigned)((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
-      res = fast_s_mp_mul_digs (a, b, c, digs);
-    } else 
-      res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */
-
-  }
-  c->sign = (c->used > 0) ? neg : MP_ZPOS;
-  return res;
+signed_multiply(mp_int * a, mp_int * b, mp_int * c)
+{
+	int     res, neg;
+
+	neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG;
+	/* use Toom-Cook? */
+	if (MIN(a->used, b->used) >= TOOM_MUL_CUTOFF) {
+		res = toom_cook_multiply(a, b, c);
+	} else if (MIN(a->used, b->used) >= KARATSUBA_MUL_CUTOFF) {
+		/* use Karatsuba? */
+		res = karatsuba_multiply(a, b, c);
+	} else {
+		/* can we use the fast multiplier? */
+		int     digs = a->used + b->used + 1;
+
+		if (can_use_fast_column_array(digs, MIN(a->used, b->used))) {
+			res = fast_col_array_multiply(a, b, c, digs);
+		} else  {
+			res = basic_multiply_partial_lower(a, b, c, (a)->used + (b)->used + 1);
+		}
+	}
+	c->sign = (c->used > 0) ? neg : MP_ZPOS;
+	return res;
 }
 
 /* this is a modified version of fast_s_mul_digs that only produces
@@ -2484,72 +2442,72 @@ mp_mul(mp_int * a, mp_int * b, mp_int * c)
  * Based on Algorithm 14.12 on pp.595 of HAC.
  */
 static 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;
-
-  {
-    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;
+fast_basic_multiply_partial_upper(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;
+
+	{
+		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;
+		}
+	}
+	trim_unused_digits(c);
+	return MP_OKAY;
 }
 
 /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_fast_s_mp_mul_high_digs.c,v $ */
@@ -2560,58 +2518,57 @@ fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
  * [meant to get the higher part of the product]
  */
 static 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? */
-  if (((unsigned)(a->used + b->used + 1) < MP_WARRAY)
-      && MIN (a->used, b->used) < (1 << (unsigned)((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
-    return fast_s_mp_mul_high_digs (a, b, c, digs);
-  }
-
-  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;
+basic_multiply_partial_upper(mp_int * a, mp_int * b, mp_int * c, int digs)
+{
+	mp_int  t;
+	int     res, pa, pb, ix, iy;
+	mp_digit carry;
+	mp_word r;
+	mp_digit tmpx, *tmpt, *tmpy;
+
+	/* can we use the fast multiplier? */
+	if (can_use_fast_column_array(a->used + b->used + 1, MIN(a->used, b->used))) {
+		return fast_basic_multiply_partial_upper(a, b, c, digs);
+	}
+
+	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 */
+		carry = 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) carry);
+
+			/* get the lower part */
+			*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
+
+			/* carry the carry */
+			carry = (mp_digit) (r >> ((mp_word) DIGIT_BIT));
+		}
+		*tmpt = carry;
+	}
+	trim_unused_digits(&t);
+	mp_exch(&t, c);
+	mp_clear(&t);
+	return MP_OKAY;
 }
 
 /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_s_mp_mul_high_digs.c,v $ */
@@ -2623,91 +2580,94 @@ s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
  * From HAC pp.604 Algorithm 14.42
  */
 static 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 {
-    if ((res = s_mp_mul_high_digs (&q, mu, &q, um)) != MP_OKAY) {
-      goto CLEANUP;
-    }
-  }
-
-  /* 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;
-    }
-  }
-  
+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)  */
+	rshift_digits(&q, um - 1);         
+
+	/* according to HAC this optimization is ok */
+	if (((unsigned long) um) > (((mp_digit)1) << (DIGIT_BIT - 1))) {
+		if ((res = signed_multiply(&q, mu, &q)) != MP_OKAY) {
+			goto CLEANUP;
+		}
+	} else {
+		if ((res = basic_multiply_partial_upper(&q, mu, &q, um)) != MP_OKAY) {
+			goto CLEANUP;
+		}
+	}
+
+	/* q3 = q2 / b**(k+1) */
+	rshift_digits(&q, um + 1);         
+
+	/* x = x mod b**(k+1), quick (no division) */
+	if ((res = modulo_2_to_power(x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) {
+		goto CLEANUP;
+	}
+
+	/* q = q * m mod b**(k+1), quick (no division) */
+	if ((res = basic_multiply_partial_lower(&q, m, &q, um + 1)) != MP_OKAY) {
+		goto CLEANUP;
+	}
+
+	/* x = x - q */
+	if ((res = signed_subtract(x, &q, x)) != MP_OKAY) {
+		goto CLEANUP;
+	}
+
+	/* If x < 0, add b**(k+1) to it */
+	if (compare_digit(x, 0) == MP_LT) {
+		set_word(&q, 1);
+		if ((res = lshift_digits(&q, um + 1)) != MP_OKAY) {
+			goto CLEANUP;
+		}
+		if ((res = signed_add(x, &q, x)) != MP_OKAY) {
+			goto CLEANUP;
+		}
+	}
+
+	/* Back off if it's too big */
+	while (signed_compare(x, m) != MP_LT) {
+		if ((res = basic_subtract(x, m, x)) != MP_OKAY) {
+			goto CLEANUP;
+		}
+	}
+
 CLEANUP:
-  mp_clear (&q);
+	mp_clear(&q);
 
-  return res;
+	return res;
 }
 
 /* determines the setup value */
-static int mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
-{
-   int    res;
-   mp_int tmp;
-   
-   if ((res = mp_init(&tmp)) != MP_OKAY) {
-      return res;
-   }
-   
-   if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) {
-      goto ERR;
-   }
-   
-   if ((res = s_mp_sub(&tmp, a, d)) != MP_OKAY) {
-      goto ERR;
-   }
-   
+static int
+mp_reduce_2k_setup_l(mp_int *a, mp_int *d)
+{
+	int    res;
+	mp_int tmp;
+
+	if ((res = mp_init(&tmp)) != MP_OKAY) {
+		return res;
+	}
+
+	if ((res = mp_2expt(&tmp, mp_count_bits(a))) != MP_OKAY) {
+		goto ERR;
+	}
+
+	if ((res = basic_subtract(&tmp, a, d)) != MP_OKAY) {
+		goto ERR;
+	}
+
 ERR:
-   mp_clear(&tmp);
-   return res;
+	mp_clear(&tmp);
+	return res;
 }
 
 /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_reduce_2k_setup_l.c,v $ */
@@ -2721,38 +2681,38 @@ ERR:
 static int
 mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d)
 {
-   mp_int q;
-   int    p, res;
-   
-   if ((res = mp_init(&q)) != MP_OKAY) {
-      return res;
-   }
-   
-   p = mp_count_bits(n);    
+	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;
-   }
-   
-   /* q = q * d */
-   if ((res = mp_mul(&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;
-   }
-   
+	/* q = a/2**p, a = a mod 2**p */
+	if ((res = rshift_bits(a, p, &q, a)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	/* q = q * d */
+	if ((res = signed_multiply(&q, d, &q)) != MP_OKAY) { 
+		goto ERR;
+	}
+
+	/* a = a + q */
+	if ((res = basic_add(a, &q, a)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	if (compare_magnitude(a, n) != MP_LT) {
+		basic_subtract(a, n, a);
+		goto top;
+	}
+
 ERR:
-   mp_clear(&q);
-   return res;
+	mp_clear(&q);
+	return res;
 }
 
 /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_reduce_2k_l.c,v $ */
@@ -2761,206 +2721,206 @@ ERR:
 
 /* squaring using Toom-Cook 3-way algorithm */
 static 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;
-     }
+toom_cook_square(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 = modulo_2_to_power(a, DIGIT_BIT * B, &a0)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	if ((res = mp_copy(a, &a1)) != MP_OKAY) {
+		goto ERR;
+	}
+	rshift_digits(&a1, B);
+	modulo_2_to_power(&a1, DIGIT_BIT * B, &a1);
+
+	if ((res = mp_copy(a, &a2)) != MP_OKAY) {
+		goto ERR;
+	}
+	rshift_digits(&a2, B*2);
+
+	/* w0 = a0*a0 */
+	if ((res = square(&a0, &w0)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	/* w4 = a2 * a2 */
+	if ((res = square(&a2, &w4)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	/* w1 = (a2 + 2(a1 + 2a0))**2 */
+	if ((res = doubled(&a0, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = doubled(&tmp1, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_add(&tmp1, &a2, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	if ((res = square(&tmp1, &w1)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	/* w3 = (a0 + 2(a1 + 2a2))**2 */
+	if ((res = doubled(&a2, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_add(&tmp1, &a1, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = doubled(&tmp1, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	if ((res = square(&tmp1, &w3)) != MP_OKAY) {
+		goto ERR;
+	}
+
+
+	/* w2 = (a2 + a1 + a0)**2 */
+	if ((res = signed_add(&a2, &a1, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_add(&tmp1, &a0, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = square(&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 = signed_subtract(&w1, &w4, &w1)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r3 - r0 */
+	if ((res = signed_subtract(&w3, &w0, &w3)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r1/2 */
+	if ((res = half(&w1, &w1)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r3/2 */
+	if ((res = half(&w3, &w3)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r2 - r0 - r4 */
+	if ((res = signed_subtract(&w2, &w0, &w2)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_subtract(&w2, &w4, &w2)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r1 - r2 */
+	if ((res = signed_subtract(&w1, &w2, &w1)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r3 - r2 */
+	if ((res = signed_subtract(&w3, &w2, &w3)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r1 - 8r0 */
+	if ((res = lshift_bits(&w0, 3, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_subtract(&w1, &tmp1, &w1)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r3 - 8r4 */
+	if ((res = lshift_bits(&w4, 3, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_subtract(&w3, &tmp1, &w3)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* 3r2 - r1 - r3 */
+	if ((res = multiply_digit(&w2, 3, &w2)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_subtract(&w2, &w1, &w2)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_subtract(&w2, &w3, &w2)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r1 - r2 */
+	if ((res = signed_subtract(&w1, &w2, &w1)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r3 - r2 */
+	if ((res = signed_subtract(&w3, &w2, &w3)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r1/3 */
+	if ((res = third(&w1, &w1, NULL)) != MP_OKAY) {
+		goto ERR;
+	}
+	/* r3/3 */
+	if ((res = third(&w3, &w3, NULL)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	/* at this point shift W[n] by B*n */
+	if ((res = lshift_digits(&w1, 1*B)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = lshift_digits(&w2, 2*B)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = lshift_digits(&w3, 3*B)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = lshift_digits(&w4, 4*B)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	if ((res = signed_add(&w0, &w1, b)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_add(&w2, &w3, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_add(&w4, &tmp1, &tmp1)) != MP_OKAY) {
+		goto ERR;
+	}
+	if ((res = signed_add(&tmp1, b, b)) != MP_OKAY) {
+		goto ERR;
+	}
 
 ERR:
-     mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL);
-     return res;
+	mp_clear_multi(&w0, &w1, &w2, &w3, &w4, &a0, &a1, &a2, &tmp1, NULL);
+	return res;
 }
 
 
@@ -2975,97 +2935,99 @@ ERR:
  * is essentially the same algorithm but merely 
  * tuned to perform recursive squarings.
  */
-static 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 = (unsigned)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;
-
-  {
-    int x;
-    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 (s_mp_add (&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 (s_mp_sub (&t1, &t2, &t1) != MP_OKAY)
-    goto X1X1;           /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */
-
-  /* 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);
+static int
+karatsuba_square(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 = (unsigned)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;
+	}
+
+	memcpy(x0.dp, a->dp, B * sizeof(*x0.dp));
+	memcpy(x1.dp, &a->dp[B], (a->used - B) * sizeof(*x1.dp));
+
+	x0.used = B;
+	x1.used = a->used - B;
+
+	trim_unused_digits(&x0);
+
+	/* now calc the products x0*x0 and x1*x1 */
+	if (square(&x0, &x0x0) != MP_OKAY) {
+		goto X1X1;           /* x0x0 = x0*x0 */
+	}
+	if (square(&x1, &x1x1) != MP_OKAY) {
+		goto X1X1;           /* x1x1 = x1*x1 */
+	}
+	/* now calc (x1+x0)**2 */
+	if (basic_add(&x1, &x0, &t1) != MP_OKAY) {
+		goto X1X1;           /* t1 = x1 - x0 */
+	}
+	if (square(&t1, &t1) != MP_OKAY) {
+		goto X1X1;           /* t1 = (x1 - x0) * (x1 - x0) */
+	}
+	/* add x0y0 */
+	if (basic_add(&x0x0, &x1x1, &t2) != MP_OKAY) {
+		goto X1X1;           /* t2 = x0x0 + x1x1 */
+	}
+	if (basic_subtract(&t1, &t2, &t1) != MP_OKAY) {
+		goto X1X1;           /* t1 = (x1+x0)**2 - (x0x0 + x1x1) */
+	}
+	/* shift by B */
+	if (lshift_digits(&t1, B) != MP_OKAY) {
+		goto X1X1;           /* t1 = (x0x0 + x1x1 - (x1-x0)*(x1-x0))<<B */
+	}
+	if (lshift_digits(&x1x1, B * 2) != MP_OKAY) {
+		goto X1X1;           /* x1x1 = x1x1 << 2*B */
+	}
+	if (signed_add(&x0x0, &t1, &t1) != MP_OKAY) {
+		goto X1X1;           /* t1 = x0x0 + t1 */
+	}
+	if (signed_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;
+	return err;
 }
 
 /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_karatsuba_sqr.c,v $ */
@@ -3082,87 +3044,88 @@ ERR:
 After that loop you do the squares and add them in.
 */
 
-static 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
-         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, (int)((unsigned)(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[(unsigned)ix>>1])*((mp_word)a->dp[(unsigned)ix>>1]);
-      }
-
-      /* store it */
-      W[ix] = (mp_digit)(_W & MP_MASK);
-
-      /* 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;
+static int
+fast_basic_square(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
+		 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, (int)((unsigned)(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[(unsigned)ix>>1])*((mp_word)a->dp[(unsigned)ix>>1]);
+		}
+
+		/* store it */
+		W[ix] = (mp_digit)(_W & MP_MASK);
+
+		/* 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;
+		}
+	}
+	trim_unused_digits(b);
+	return MP_OKAY;
 }
 
 /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_fast_s_mp_sqr.c,v $ */
@@ -3171,66 +3134,66 @@ static int fast_s_mp_sqr (mp_int * a, mp_int * b)
 
 /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */
 static 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;
+basic_square(mp_int * a, mp_int * b)
+{
+	mp_int  t;
+	int     res, ix, iy, pa;
+	mp_word r;
+	mp_digit carry, 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 */
+		carry = (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) carry);
+
+			/* store lower part */
+			*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
+
+			/* get carry */
+			carry = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+		}
+		/* propagate upwards */
+		while (carry != ((mp_digit) 0)) {
+			r = ((mp_word) *tmpt) + ((mp_word) carry);
+			*tmpt++ = (mp_digit) (r & ((mp_word) MP_MASK));
+			carry = (mp_digit)(r >> ((mp_word) DIGIT_BIT));
+		}
+	}
+
+	trim_unused_digits(&t);
+	mp_exch(&t, b);
+	mp_clear(&t);
+	return MP_OKAY;
 }
 
 /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_s_mp_sqr.c,v $ */
@@ -3242,29 +3205,36 @@ s_mp_sqr (mp_int * a, mp_int * b)
 
 /* computes b = a*a */
 static int
-mp_sqr (mp_int * a, mp_int * b)
-{
-  int     res;
-
-  /* use Toom-Cook? */
-  if (a->used >= TOOM_SQR_CUTOFF) {
-    res = mp_toom_sqr(a, b);
-  /* Karatsuba? */
-  } else 
-if (a->used >= KARATSUBA_SQR_CUTOFF) {
-    res = mp_karatsuba_sqr (a, b);
-  } else 
-  {
-    /* can we use the fast comba multiplier? */
-    if (((unsigned)a->used * 2 + 1) < MP_WARRAY && 
-         a->used < 
-         (1 << (unsigned)(sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) {
-      res = fast_s_mp_sqr (a, b);
-    } else
-      res = s_mp_sqr (a, b);
-  }
-  b->sign = MP_ZPOS;
-  return res;
+square(mp_int * a, mp_int * b)
+{
+	int     res;
+
+	/* use Toom-Cook? */
+	if (a->used >= TOOM_SQR_CUTOFF) {
+		res = toom_cook_square(a, b);
+		/* Karatsuba? */
+	} else if (a->used >= KARATSUBA_SQR_CUTOFF) {
+		res = karatsuba_square(a, b);
+	} else {
+		/* can we use the fast comba multiplier? */
+		if (can_use_fast_column_array(a->used + a->used + 1, a->used)) {
+			res = fast_basic_square(a, b);
+		} else {
+			res = basic_square(a, b);
+		}
+	}
+	b->sign = MP_ZPOS;
+	return res;
+}
+
+/* find window size */
+static inline int
+find_window_size(mp_int *X)
+{
+	int	x;
+
+	x = mp_count_bits(X);
+	return (x <= 7) ? 2 : (x <= 36) ? 3 : (x <= 140) ? 4 : (x <= 450) ? 5 : (x <= 1303) ? 6 : (x <= 3529) ? 7 : 8;
 }
 
 /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_sqr.c,v $ */
@@ -3273,246 +3243,233 @@ if (a->used >= KARATSUBA_SQR_CUTOFF) {
 
 #define TAB_SIZE 256
 
-static int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
-{
-  mp_int  M[TAB_SIZE], res, mu;
-  mp_digit buf;
-  int     err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
-  int (*redux)(mp_int*,mp_int*,mp_int*);
-
-  /* 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;
-  }
-
-  /* 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 LBL_M;
-  }
-  
-  if (redmode == 0) {
-     if ((err = mp_reduce_setup (&mu, P)) != MP_OKAY) {
-        goto LBL_MU;
-     }
-     redux = mp_reduce;
-  } else {
-     if ((err = mp_reduce_2k_setup_l (P, &mu)) != MP_OKAY) {
-        goto LBL_MU;
-     }
-     redux = mp_reduce_2k_l;
-  }    
-
-  /* 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 LBL_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 LBL_MU;
-  }
-
-  for (x = 0; x < (winsize - 1); x++) {
-    /* square it */
-    if ((err = mp_sqr (&M[1 << (winsize - 1)], 
-                       &M[1 << (winsize - 1)])) != MP_OKAY) {
-      goto LBL_MU;
-    }
-
-    /* reduce modulo P */
-    if ((err = redux (&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
-      goto LBL_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 LBL_MU;
-    }
-    if ((err = redux (&M[x], P, &mu)) != MP_OKAY) {
-      goto LBL_MU;
-    }
-  }
-
-  /* setup result */
-  if ((err = mp_init (&res)) != MP_OKAY) {
-    goto LBL_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     = (unsigned)(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 LBL_RES;
-      }
-      if ((err = redux (&res, P, &mu)) != MP_OKAY) {
-        goto LBL_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 LBL_RES;
-        }
-        if ((err = redux (&res, P, &mu)) != MP_OKAY) {
-          goto LBL_RES;
-        }
-      }
-
-      /* then multiply */
-      if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
-        goto LBL_RES;
-      }
-      if ((err = redux (&res, P, &mu)) != MP_OKAY) {
-        goto LBL_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 LBL_RES;
-      }
-      if ((err = redux (&res, P, &mu)) != MP_OKAY) {
-        goto LBL_RES;
-      }
-
-      bitbuf <<= 1;
-      if ((bitbuf & (1 << winsize)) != 0) {
-        /* then multiply */
-        if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
-          goto LBL_RES;
-        }
-        if ((err = redux (&res, P, &mu)) != MP_OKAY) {
-          goto LBL_RES;
-        }
-      }
-    }
-  }
-
-  mp_exch (&res, Y);
-  err = MP_OKAY;
-LBL_RES:mp_clear (&res);
-LBL_MU:mp_clear (&mu);
+static int
+basic_exponent_mod(mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
+{
+	mp_digit buf;
+	mp_int  M[TAB_SIZE], res, mu;
+	int     err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
+	int	(*redux)(mp_int*,mp_int*,mp_int*);
+
+	winsize = find_window_size(X);
+
+	/* 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 LBL_M;
+	}
+
+	if (redmode == 0) {
+		if ((err = mp_reduce_setup(&mu, P)) != MP_OKAY) {
+			goto LBL_MU;
+		}
+		redux = mp_reduce;
+	} else {
+		if ((err = mp_reduce_2k_setup_l(P, &mu)) != MP_OKAY) {
+			goto LBL_MU;
+		}
+		redux = mp_reduce_2k_l;
+	}    
+
+	/* 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 = modulo(G, P, &M[1])) != MP_OKAY) {
+		goto LBL_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 LBL_MU;
+	}
+
+	for (x = 0; x < (winsize - 1); x++) {
+		/* square it */
+		if ((err = square(&M[1 << (winsize - 1)], 
+		       &M[1 << (winsize - 1)])) != MP_OKAY) {
+			goto LBL_MU;
+		}
+
+		/* reduce modulo P */
+		if ((err = redux(&M[1 << (winsize - 1)], P, &mu)) != MP_OKAY) {
+			goto LBL_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 = signed_multiply(&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
+			goto LBL_MU;
+		}
+		if ((err = redux(&M[x], P, &mu)) != MP_OKAY) {
+			goto LBL_MU;
+		}
+	}
+
+	/* setup result */
+	if ((err = mp_init(&res)) != MP_OKAY) {
+		goto LBL_MU;
+	}
+	set_word(&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 = (unsigned)(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 = square(&res, &res)) != MP_OKAY) {
+				goto LBL_RES;
+			}
+			if ((err = redux(&res, P, &mu)) != MP_OKAY) {
+				goto LBL_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 = square(&res, &res)) != MP_OKAY) {
+					goto LBL_RES;
+				}
+				if ((err = redux(&res, P, &mu)) != MP_OKAY) {
+					goto LBL_RES;
+				}
+			}
+
+			/* then multiply */
+			if ((err = signed_multiply(&res, &M[bitbuf], &res)) != MP_OKAY) {
+				goto LBL_RES;
+			}
+			if ((err = redux(&res, P, &mu)) != MP_OKAY) {
+				goto LBL_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 = square(&res, &res)) != MP_OKAY) {
+				goto LBL_RES;
+			}
+			if ((err = redux(&res, P, &mu)) != MP_OKAY) {
+				goto LBL_RES;
+			}
+
+			bitbuf <<= 1;
+			if ((bitbuf & (1 << winsize)) != 0) {
+				/* then multiply */
+				if ((err = signed_multiply(&res, &M[1], &res)) != MP_OKAY) {
+					goto LBL_RES;
+				}
+				if ((err = redux(&res, P, &mu)) != MP_OKAY) {
+					goto LBL_RES;
+				}
+			}
+		}
+	}
+
+	mp_exch(&res, Y);
+	err = MP_OKAY;
+LBL_RES:
+	mp_clear(&res);
+LBL_MU:
+	mp_clear(&mu);
 LBL_M:
-  mp_clear(&M[1]);
-  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
-    mp_clear (&M[x]);
-  }
-  return err;
+	mp_clear(&M[1]);
+	for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
+		mp_clear(&M[x]);
+	}
+	return err;
 }
 
 /* determines if a number is a valid DR modulus */
 static int
-mp_dr_is_modulus(mp_int *a)
+is_diminished_radix_modulus(mp_int *a)
 {
-   int ix;
+	int ix;
 
-   /* must be at least two digits */
-   if (a->used < 2) {
-      return 0;
-   }
+	/* 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;
+	/* 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;
 }
 
 /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_dr_is_modulus.c,v $ */
@@ -3520,33 +3477,36 @@ mp_dr_is_modulus(mp_int *a)
 /* Date: 2011/03/12 22:58:18 $ */
 
 /* determines if mp_reduce_2k can be used */
-static int mp_reduce_is_2k(mp_int *a)
-{
-   int ix, iy, iw;
-   mp_digit iz;
-   
-   if (a->used == 0) {
-      return MP_NO;
-   } else if (a->used == 1) {
-      return MP_YES;
-   } 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 MP_NO;
-          }
-          iz <<= 1;
-          if (iz > (mp_digit)MP_MASK) {
-             ++iw;
-             iz = 1;
-          }
-      }
-   }
-   return MP_YES;
+static int
+mp_reduce_is_2k(mp_int *a)
+{
+	int ix, iy, iw;
+	mp_digit iz;
+
+	if (a->used == 0) {
+		return MP_NO;
+	}
+	if (a->used == 1) {
+		return MP_YES;
+	}
+	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 MP_NO;
+			}
+			iz <<= 1;
+			if (iz > (mp_digit)MP_MASK) {
+				++iw;
+				iz = 1;
+			}
+		}
+	}
+	return MP_YES;
 }
 
 /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_reduce_is_2k.c,v $ */
@@ -3556,22 +3516,22 @@ static int mp_reduce_is_2k(mp_int *a)
 
 /* d = a * b (mod c) */
 static int
-mp_mulmod (mp_int *d, mp_int * a, mp_int * b, mp_int * c)
+multiply_modulo(mp_int *d, mp_int * a, mp_int * b, mp_int * c)
 {
-  int     res;
-  mp_int  t;
+	mp_int  t;
+	int     res;
 
-  if ((res = mp_init (&t)) != MP_OKAY) {
-    return res;
-  }
+	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;
+	if ((res = signed_multiply(a, b, &t)) != MP_OKAY) {
+		mp_clear(&t);
+		return res;
+	}
+	res = modulo(&t, c, d);
+	mp_clear(&t);
+	return res;
 }
 
 /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_mulmod.c,v $ */
@@ -3580,36 +3540,36 @@ mp_mulmod (mp_int *d, mp_int * a, mp_int * b, mp_int * c)
 
 /* setups the montgomery reduction stuff */
 static int
-mp_montgomery_setup (mp_int * n, mp_digit * rho)
+mp_montgomery_setup(mp_int * n, mp_digit * rho)
 {
-  mp_digit x, b;
+	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];
+	/* 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;
-  }
+	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 */
-  x *= 2 - b * x;               /* here x*a==1 mod 2**16 */
-  x *= 2 - b * x;               /* here x*a==1 mod 2**32 */
-  if (/*CONSTCOND*/sizeof(mp_digit) == 8) {
-	  x *= 2 - b * x;	/* here x*a==1 mod 2**64 */
-  }
+	x = (((b + 2) & 4) << 1) + b; /* here x*a==1 mod 2**4 */
+	x *= 2 - b * x;               /* here x*a==1 mod 2**8 */
+	x *= 2 - b * x;               /* here x*a==1 mod 2**16 */
+	x *= 2 - b * x;               /* here x*a==1 mod 2**32 */
+	if (/*CONSTCOND*/sizeof(mp_digit) == 8) {
+		x *= 2 - b * x;	/* here x*a==1 mod 2**64 */
+	}
 
-  /* rho = -1/m mod b */
-  *rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
+	/* rho = -1/m mod b */
+	*rho = (unsigned long)(((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK;
 
-  return MP_OKAY;
+	return MP_OKAY;
 }
 
 /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_montgomery_setup.c,v $ */
@@ -3625,148 +3585,148 @@ mp_montgomery_setup (mp_int * n, mp_digit * rho)
  * Based on Algorithm 14.32 on pp.601 of HAC.
 */
 static int
-fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
-{
-  int     ix, res, olduse;
-  /*LINTED*/
-  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[...]
-   */
-  {
-    mp_word *_W;
-    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)
-     */
-    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
-     */
-    {
-      int iy;
-      mp_digit *tmpn;
-      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].
-   */
-  {
-    mp_digit *tmpx;
-    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;
+fast_mp_montgomery_reduce(mp_int * x, mp_int * n, mp_digit rho)
+{
+	int     ix, res, olduse;
+	/*LINTED*/
+	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[...]
+	*/
+	{
+		mp_word *_W;
+		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)
+		*/
+		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
+		*/
+		{
+			int iy;
+			mp_digit *tmpn;
+			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].
+	*/
+	{
+		mp_digit *tmpx;
+		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 rshift_digits
+		* 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;
+	trim_unused_digits(x);
+
+	/* if A >= m then A = A - m */
+	if (compare_magnitude(x, n) != MP_LT) {
+		return basic_subtract(x, n, x);
+	}
+	return MP_OKAY;
 }
 
 /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_fast_mp_montgomery_reduce.c,v $ */
@@ -3775,99 +3735,97 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
 
 /* computes xR**-1 == x (mod N) via Montgomery Reduction */
 static 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 (((unsigned)digs < MP_WARRAY) &&
-      n->used <
-      (1 << (unsigned)((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 */
-    {
-      int iy;
-      mp_digit *tmpn, *tmpx, u;
-      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;
+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 (can_use_fast_column_array(digs, n->used)) {
+		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 */
+		{
+			int iy;
+			mp_digit *tmpn, *tmpx, carry;
+			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 */
+			carry = 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) carry) + ((mp_word) * tmpx);
+
+				/* get carry */
+				carry = (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 (carry) {
+				*tmpx += carry;
+				carry = *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 */
+	trim_unused_digits(x);
+	rshift_digits(x, n->used);
+
+	/* if x >= n then x = x - n */
+	if (compare_magnitude(x, n) != MP_LT) {
+		return basic_subtract(x, n, x);
+	}
+
+	return MP_OKAY;
 }
 
 /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_montgomery_reduce.c,v $ */
@@ -3876,13 +3834,13 @@ mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
 
 /* determines the setup value */
 static void
-mp_dr_setup(mp_int *a, mp_digit *d)
+diminished_radix_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]));
+	/* 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]));
 }
 
 /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_dr_setup.c,v $ */
@@ -3904,62 +3862,62 @@ mp_dr_setup(mp_int *a, mp_digit *d)
  * Input x must be in the range 0 <= x <= (n-1)**2
  */
 static int
-mp_dr_reduce (mp_int * x, mp_int * n, mp_digit k)
+diminished_radix_reduce(mp_int * x, mp_int * n, mp_digit k)
 {
-  int      err, i, m;
-  mp_word  r;
-  mp_digit mu, *tmpx1, *tmpx2;
+	int      err, i, m;
+	mp_word  r;
+	mp_digit mu, *tmpx1, *tmpx2;
 
-  /* m = digits in modulus */
-  m = n->used;
+	/* 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;
-    }
-  }
+	/* 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 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;
+	/* 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;
+	/* alias for upper half of x, or x/B**m */
+	tmpx2 = x->dp + m;
 
-  /* set carry to zero */
-  mu = 0;
+	/* 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));
-  }
+	/* 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;
+	/* set final carry */
+	*tmpx1++ = mu;
 
-  /* zero words above m */
-  for (i = m + 1; i < x->used; i++) {
-      *tmpx1++ = 0;
-  }
+	/* zero words above m */
+	for (i = m + 1; i < x->used; i++) {
+		*tmpx1++ = 0;
+	}
 
-  /* clamp, sub and return */
-  mp_clamp (x);
+	/* clamp, sub and return */
+	trim_unused_digits(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;
+	/* if x >= n then subtract and reduce again
+	* Each successive "recursion" makes the input smaller and smaller.
+	*/
+	if (compare_magnitude(x, n) != MP_LT) {
+		basic_subtract(x, n, x);
+		goto top;
+	}
+	return MP_OKAY;
 }
 
 /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_dr_reduce.c,v $ */
@@ -3970,27 +3928,27 @@ top:
 static 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;
+	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 = basic_subtract(&tmp, a, &tmp)) != MP_OKAY) {
+		mp_clear(&tmp);
+		return res;
+	}
+
+	*d = tmp.dp[0];
+	mp_clear(&tmp);
+	return MP_OKAY;
 }
 
 /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_reduce_2k_setup.c,v $ */
@@ -4001,40 +3959,40 @@ mp_reduce_2k_setup(mp_int *a, mp_digit *d)
 static 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);    
+	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;
-   }
-   
+	/* q = a/2**p, a = a mod 2**p */
+	if ((res = rshift_bits(a, p, &q, a)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	if (d != 1) {
+		/* q = q * d */
+		if ((res = multiply_digit(&q, d, &q)) != MP_OKAY) { 
+			 goto ERR;
+		}
+	}
+
+	/* a = a + q */
+	if ((res = basic_add(a, &q, a)) != MP_OKAY) {
+		goto ERR;
+	}
+
+	if (compare_magnitude(a, n) != MP_LT) {
+		basic_subtract(a, n, a);
+		goto top;
+	}
+
 ERR:
-   mp_clear(&q);
-   return res;
+	mp_clear(&q);
+	return res;
 }
 
 /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_reduce_2k.c,v $ */
@@ -4048,36 +4006,36 @@ ERR:
  * the leading bit of b.  This saves alot of multiple precision shifting.
  */
 static int
-mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
+mp_montgomery_calc_normalization(mp_int * a, mp_int * b)
 {
-  int     x, bits, res;
+	int     x, bits, res;
 
-  /* how many bits of last digit does b use */
-  bits = mp_count_bits (b) % DIGIT_BIT;
+	/* 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;
-  }
+	if (b->used > 1) {
+		if ((res = mp_2expt(a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) {
+			return res;
+		}
+	} else {
+		set_word(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;
-      }
-    }
-  }
+	/* now compute C = A * B mod b */
+	for (x = bits - 1; x < (int)DIGIT_BIT; x++) {
+		if ((res = doubled(a, a)) != MP_OKAY) {
+			return res;
+		}
+		if (compare_magnitude(a, b) != MP_LT) {
+			if ((res = basic_subtract(a, b, a)) != MP_OKAY) {
+				return res;
+			}
+		}
+	}
 
-  return MP_OKAY;
+	return MP_OKAY;
 }
 
 /* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_montgomery_calc_normalization.c,v $ */
@@ -4095,259 +4053,242 @@ mp_montgomery_calc_normalization (mp_int * a, mp_int * b)
 #define TAB_SIZE 256
 
 static 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;
-  }
-
-  /* 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) {
-     /* now setup montgomery  */
-     if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
-        goto LBL_M;
-     }
-
-     /* automatically pick the comba one if available (saves quite a few calls/ifs) */
-     if (((unsigned)(P->used * 2 + 1) < MP_WARRAY) &&
-          P->used < (1 << (unsigned)((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
-        redux = fast_mp_montgomery_reduce;
-     } else 
-     {
-        /* use slower baseline Montgomery method */
-        redux = mp_montgomery_reduce;
-     }
-  } else if (redmode == 1) {
-     /* setup DR reduction for moduli of the form B**k - b */
-     mp_dr_setup(P, &mp);
-     redux = mp_dr_reduce;
-  } else {
-     /* setup DR reduction for moduli of the form 2**k - b */
-     if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
-        goto LBL_M;
-     }
-     redux = mp_reduce_2k;
-  }
-
-  /* setup result */
-  if ((err = mp_init (&res)) != MP_OKAY) {
-    goto LBL_M;
-  }
-
-  /* create M table
-   *
-
-   *
-   * The first half of the table is not computed though accept for M[0] and M[1]
-   */
-
-  if (redmode == 0) {
-     /* now we need R mod m */
-     if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
-       goto LBL_RES;
-     }
-
-     /* now set M[1] to G * R mod m */
-     if ((err = mp_mulmod (&M[1], G, &res, P)) != MP_OKAY) {
-       goto LBL_RES;
-     }
-  } else {
-     mp_set(&res, 1);
-     if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
-        goto LBL_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 LBL_RES;
-  }
-
-  for (x = 0; x < (winsize - 1); x++) {
-    if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
-      goto LBL_RES;
-    }
-    if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
-      goto LBL_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 LBL_RES;
-    }
-    if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
-      goto LBL_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     = (int)(mp_digit)((mp_digit)buf >> (unsigned)(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 LBL_RES;
-      }
-      if ((err = redux (&res, P, mp)) != MP_OKAY) {
-        goto LBL_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 LBL_RES;
-        }
-        if ((err = redux (&res, P, mp)) != MP_OKAY) {
-          goto LBL_RES;
-        }
-      }
-
-      /* then multiply */
-      if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
-        goto LBL_RES;
-      }
-      if ((err = redux (&res, P, mp)) != MP_OKAY) {
-        goto LBL_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 LBL_RES;
-      }
-      if ((err = redux (&res, P, mp)) != MP_OKAY) {
-        goto LBL_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 LBL_RES;
-        }
-        if ((err = redux (&res, P, mp)) != MP_OKAY) {
-          goto LBL_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 LBL_RES;
-     }
-  }
-
-  /* swap res with Y */
-  mp_exch (&res, Y);
-  err = MP_OKAY;
-LBL_RES:mp_clear (&res);
+fast_exponent_modulo(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);
+
+	winsize = find_window_size(X);
+
+	/* 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) {
+		/* now setup montgomery  */
+		if ((err = mp_montgomery_setup(P, &mp)) != MP_OKAY) {
+			goto LBL_M;
+		}
+
+		/* automatically pick the comba one if available (saves quite a few calls/ifs) */
+		if (can_use_fast_column_array(P->used + P->used + 1, P->used)) {
+			redux = fast_mp_montgomery_reduce;
+		} else {
+			/* use slower baseline Montgomery method */
+			redux = mp_montgomery_reduce;
+		}
+	} else if (redmode == 1) {
+		/* setup DR reduction for moduli of the form B**k - b */
+		diminished_radix_setup(P, &mp);
+		redux = diminished_radix_reduce;
+	} else {
+		/* setup DR reduction for moduli of the form 2**k - b */
+		if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
+			goto LBL_M;
+		}
+		redux = mp_reduce_2k;
+	}
+
+	/* setup result */
+	if ((err = mp_init(&res)) != MP_OKAY) {
+		goto LBL_M;
+	}
+
+	/* create M table
+	*
+
+	*
+	* The first half of the table is not computed though accept for M[0] and M[1]
+	*/
+
+	if (redmode == 0) {
+		/* now we need R mod m */
+		if ((err = mp_montgomery_calc_normalization(&res, P)) != MP_OKAY) {
+			goto LBL_RES;
+		}
+
+		/* now set M[1] to G * R mod m */
+		if ((err = multiply_modulo(&M[1], G, &res, P)) != MP_OKAY) {
+			goto LBL_RES;
+		}
+	} else {
+		set_word(&res, 1);
+		if ((err = modulo(G, P, &M[1])) != MP_OKAY) {
+			goto LBL_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 LBL_RES;
+	}
+
+	for (x = 0; x < (winsize - 1); x++) {
+		if ((err = square(&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
+			goto LBL_RES;
+		}
+		if ((err = (*redux)(&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
+			goto LBL_RES;
+		}
+	}
+
+	/* create upper table */
+	for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
+		if ((err = signed_multiply(&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
+			goto LBL_RES;
+		}
+		if ((err = (*redux)(&M[x], P, mp)) != MP_OKAY) {
+			goto LBL_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 = (int)(mp_digit)((mp_digit)buf >> (unsigned)(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 = square(&res, &res)) != MP_OKAY) {
+				goto LBL_RES;
+			}
+			if ((err = (*redux)(&res, P, mp)) != MP_OKAY) {
+				goto LBL_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 = square(&res, &res)) != MP_OKAY) {
+					goto LBL_RES;
+				}
+				if ((err = (*redux)(&res, P, mp)) != MP_OKAY) {
+					goto LBL_RES;
+				}
+			}
+
+			/* then multiply */
+			if ((err = signed_multiply(&res, &M[bitbuf], &res)) != MP_OKAY) {
+				goto LBL_RES;
+			}
+			if ((err = (*redux)(&res, P, mp)) != MP_OKAY) {
+				goto LBL_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 = square(&res, &res)) != MP_OKAY) {
+				goto LBL_RES;
+			}
+			if ((err = (*redux)(&res, P, mp)) != MP_OKAY) {
+				goto LBL_RES;
+			}
+
+			/* get next bit of the window */
+			bitbuf <<= 1;
+			if ((bitbuf & (1 << winsize)) != 0) {
+				/* then multiply */
+				if ((err = signed_multiply(&res, &M[1], &res)) != MP_OKAY) {
+					goto LBL_RES;
+				}
+				if ((err = (*redux)(&res, P, mp)) != MP_OKAY) {
+					goto LBL_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 LBL_RES;
+		}
+	}
+
+	/* swap res with Y */
+	mp_exch(&res, Y);
+	err = MP_OKAY;
+LBL_RES:
+	mp_clear(&res);
 LBL_M:
-  mp_clear(&M[1]);
-  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
-    mp_clear (&M[x]);
-  }
-  return err;
+	mp_clear(&M[1]);
+	for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
+		mp_clear(&M[x]);
+	}
+	return err;
 }
 
-/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_mp_exptmod_fast.c,v $ */
+/* Source: /usr/cvsroot/libtommath/dist/libtommath/bn_fast_exponent_modulo.c,v $ */
 /* Revision: 1.4 $ */
 /* Date: 2011/03/18 16:43:04 $ */
 
@@ -4357,541 +4298,533 @@ LBL_M:
  * for nothing (since 99% of the time the Montgomery code would be called)
  */
 static 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) {
-     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(&tmpG, G, P)) != 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;
-  }
-
-/* modified diminished radix reduction */
-  if (mp_reduce_is_2k_l(P) == MP_YES) {
-     return s_mp_exptmod(G, X, P, Y, 1);
-  }
-
-  /* is it a DR modulus? */
-  dr = mp_dr_is_modulus(P);
-
-  /* if not, is it a unrestricted DR modulus? */
-  if (dr == 0) {
-     dr = mp_reduce_is_2k(P) << 1;
-  }
-    
-  /* if the modulus is odd or dr != 0 use the montgomery method */
-  if (BN_is_odd (P) == 1 || dr !=  0) {
-    return mp_exptmod_fast (G, X, P, Y, dr);
-  } else {
-    /* otherwise use the generic Barrett reduction technique */
-    return s_mp_exptmod (G, X, P, Y, 0);
-  }
+exponent_modulo(mp_int * G, mp_int * X, mp_int * P, mp_int *Y)
+{
+	int diminished_radix;
+
+	/* 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) {
+		mp_int tmpG, tmpX;
+		int err;
+
+		/* first compute 1/G mod P */
+		if ((err = mp_init(&tmpG)) != MP_OKAY) {
+			return err;
+		}
+		if ((err = modular_inverse(&tmpG, G, P)) != MP_OKAY) {
+			mp_clear(&tmpG);
+			return err;
+		}
+
+		/* now get |X| */
+		if ((err = mp_init(&tmpX)) != MP_OKAY) {
+			mp_clear(&tmpG);
+			return err;
+		}
+		if ((err = absolute(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 = exponent_modulo(&tmpG, &tmpX, P, Y);
+		mp_clear_multi(&tmpG, &tmpX, NULL);
+		return err;
+	}
+
+	/* modified diminished radix reduction */
+	if (mp_reduce_is_2k_l(P) == MP_YES) {
+		return basic_exponent_mod(G, X, P, Y, 1);
+	}
+
+	/* is it a DR modulus? */
+	diminished_radix = is_diminished_radix_modulus(P);
+
+	/* if not, is it a unrestricted DR modulus? */
+	if (!diminished_radix) {
+		diminished_radix = mp_reduce_is_2k(P) << 1;
+	}
+
+	/* if the modulus is odd or diminished_radix, use the montgomery method */
+	if (BN_is_odd(P) == 1 || diminished_radix) {
+		return fast_exponent_modulo(G, X, P, Y, diminished_radix);
+	}
+	/* otherwise use the generic Barrett reduction technique */
+	return basic_exponent_mod(G, X, P, Y, 0);
 }
 
 /* reverse an array, used for radix code */
 static void
 bn_reverse(unsigned char *s, int len)
 {
-  int     ix, iy;
-  unsigned char t;
+	int     ix, iy;
+	uint8_t t;
 
-  ix = 0;
-  iy = len - 1;
-  while (ix < iy) {
-    t     = s[ix];
-    s[ix] = s[iy];
-    s[iy] = t;
-    ++ix;
-    --iy;
-  }
+	for (ix = 0, iy = len - 1; ix < iy ; ix++, --iy) {
+		t = s[ix];
+		s[ix] = s[iy];
+		s[iy] = t;
+	}
 }
 
-static int
-s_is_power_of_two(mp_digit b, int *p)
+static inline int
+is_power_of_two(mp_digit b, int *p)
 {
-   int x;
+	int x;
 
-   /* fast return if no power of two */
-   if ((b==0) || (b & (b-1))) {
-      return 0;
-   }
+	/* fast return if no power of two */
+	if ((b==0) || (b & (b-1))) {
+		return 0;
+	}
 
-   for (x = 0; x < DIGIT_BIT; x++) {
-      if (b == (((mp_digit)1)<<x)) {
-         *p = x;
-         return 1;
-      }
-   }
-   return 0;
+	for (x = 0; x < DIGIT_BIT; x++) {
+		if (b == (((mp_digit)1)<<x)) {
+			*p = x;
+			return 1;
+		}
+	}
+	return 0;
 }
 
 /* single digit division (based on routine from MPI) */
 static 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
+signed_divide_word(mp_int *a, mp_digit b, mp_int *c, mp_digit *d)
+{
+	mp_int  q;
+	mp_word w;
+	mp_digit t;
+	int     res, ix;
 
-  /* 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;
-}
+	/* cannot divide by zero */
+	if (b == 0) {
+		return MP_VAL;
+	}
 
-static int
-mp_mod_d(mp_int *a, mp_digit b, mp_digit *c)
-{
-  return mp_div_d(a, b, NULL, c);
+	/* 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 (is_power_of_two(b, &ix) == 1) {
+		if (d != NULL) {
+			*d = a->dp[0] & ((((mp_digit)1)<<ix) - 1);
+		}
+		if (c != NULL) {
+			return rshift_bits(a, ix, c, NULL);
+		}
+		return MP_OKAY;
+	}
+
+	/* three? */
+	if (b == 3) {
+		return third(a, c, d);
+	}
+
+	/* 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) {
+		trim_unused_digits(&q);
+		mp_exch(&q, c);
+	}
+	mp_clear(&q);
+
+	return res;
 }
 
 static const mp_digit ltm_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,
+	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
+	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
 };
 
 #define PRIME_SIZE	__arraycount(ltm_prime_tab)
 
-static int
+static inline int
 mp_prime_is_divisible(mp_int *a, int *result)
 {
-  int     err, ix;
-  mp_digit res;
+	int     err, ix;
+	mp_digit res;
 
-  /* default to not */
-  *result = MP_NO;
+	/* default to not */
+	*result = MP_NO;
 
-  for (ix = 0; ix < (int)PRIME_SIZE; ix++) {
-    /* what is a mod LBL_prime_tab[ix] */
-    if ((err = mp_mod_d (a, ltm_prime_tab[ix], &res)) != MP_OKAY) {
-      return err;
-    }
+	for (ix = 0; ix < (int)PRIME_SIZE; ix++) {
+		/* what is a mod LBL_prime_tab[ix] */
+		if ((err = signed_divide_word(a, ltm_prime_tab[ix], NULL, &res)) != MP_OKAY) {
+			return err;
+		}
 
-    /* is the residue zero? */
-    if (res == 0) {
-      *result = MP_YES;
-      return MP_OKAY;
-    }
-  }
+		/* is the residue zero? */
+		if (res == 0) {
+			*result = MP_YES;
+			return MP_OKAY;
+		}
+	}
 
-  return MP_OKAY;
+	return MP_OKAY;
 }
 
 /* single digit addition */
 static 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;
-
-     /* clamp */
-     mp_clamp(c);
-
-     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;
+add_single_digit(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 = signed_subtract_word(a, b, c);
+
+		/* fix sign  */
+		a->sign = c->sign = MP_NEG;
+
+		/* clamp */
+		trim_unused_digits(c);
+
+		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;
+	}
+	trim_unused_digits(c);
+
+	return MP_OKAY;
 }
 
 /* single digit subtraction */
 static 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;
-
-     /* clamp */
-     mp_clamp(c);
-
-     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;
+signed_subtract_word(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 = add_single_digit(a, b, c);
+		a->sign = c->sign = MP_NEG;
+
+		/* clamp */
+		trim_unused_digits(c);
+
+		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;
+	}
+	trim_unused_digits(c);
+	return MP_OKAY;
 }
 
 static const int lnz[16] = { 
-   4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
+	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 */
 static int
 mp_cnt_lsb(mp_int *a)
 {
-   int x;
-   mp_digit q, qq;
+	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;
+	/* easy out */
+	if (MP_ISZERO(a) == 1) {
+		return 0;
+	}
 
-   /* now scan this digit until a 1 is found */
-   if ((q & 1) == 0) {
-      do {
-         qq  = q & 15;
-	 /* LINTED previous op ensures range of qq */
-         x  += lnz[qq];
-         q >>= 4;
-      } while (qq == 0);
-   }
-   return x;
+	/* 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;
+			 /* LINTED previous op ensures range of qq */
+			 x  += lnz[qq];
+			 q >>= 4;
+		} while (qq == 0);
+	}
+	return x;
 }
 
 /* c = a * a (mod b) */
 static int
-mp_sqrmod(mp_int *a, mp_int *b, mp_int *c)
+square_modulo(mp_int *a, mp_int *b, mp_int *c)
 {
-  int     res;
-  mp_int  t;
+	int     res;
+	mp_int  t;
 
-  if ((res = mp_init (&t)) != MP_OKAY) {
-    return res;
-  }
+	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;
+	if ((res = square(a, &t)) != MP_OKAY) {
+		mp_clear(&t);
+		return res;
+	}
+	res = modulo(&t, b, c);
+	mp_clear(&t);
+	return res;
 }
+
 static 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 LBL_N1;
-  }
-
-  /* set 2**s * r = n1 */
-  if ((err = mp_init_copy (&r, &n1)) != MP_OKAY) {
-    goto LBL_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 LBL_R;
-  }
-
-  /* compute y = b**r mod a */
-  if ((err = mp_init (&y)) != MP_OKAY) {
-    goto LBL_R;
-  }
-  if ((err = mp_exptmod (b, &r, a, &y)) != MP_OKAY) {
-    goto LBL_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 LBL_Y;
-      }
-
-      /* if y == 1 then composite */
-      if (mp_cmp_d (&y, 1) == MP_EQ) {
-         goto LBL_Y;
-      }
-
-      ++j;
-    }
-
-    /* if y != n1 then composite */
-    if (mp_cmp (&y, &n1) != MP_EQ) {
-      goto LBL_Y;
-    }
-  }
-
-  /* probably prime now */
-  *result = MP_YES;
-LBL_Y:mp_clear (&y);
-LBL_R:mp_clear (&r);
-LBL_N1:mp_clear (&n1);
-  return err;
+	mp_int  n1, y, r;
+	int     s, j, err;
+
+	/* default */
+	*result = MP_NO;
+
+	/* ensure b > 1 */
+	if (compare_digit(b, 1) != MP_GT) {
+		return MP_VAL;
+	}     
+
+	/* get n1 = a - 1 */
+	if ((err = mp_init_copy(&n1, a)) != MP_OKAY) {
+		return err;
+	}
+	if ((err = signed_subtract_word(&n1, 1, &n1)) != MP_OKAY) {
+		goto LBL_N1;
+	}
+
+	/* set 2**s * r = n1 */
+	if ((err = mp_init_copy(&r, &n1)) != MP_OKAY) {
+		goto LBL_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 = rshift_bits(&r, s, &r, NULL)) != MP_OKAY) {
+		goto LBL_R;
+	}
+
+	/* compute y = b**r mod a */
+	if ((err = mp_init(&y)) != MP_OKAY) {
+		goto LBL_R;
+	}
+	if ((err = exponent_modulo(b, &r, a, &y)) != MP_OKAY) {
+		goto LBL_Y;
+	}
+
+	/* if y != 1 and y != n1 do */
+	if (compare_digit(&y, 1) != MP_EQ && signed_compare(&y, &n1) != MP_EQ) {
+		j = 1;
+		/* while j <= s-1 and y != n1 */
+		while ((j <= (s - 1)) && signed_compare(&y, &n1) != MP_EQ) {
+			if ((err = square_modulo(&y, a, &y)) != MP_OKAY) {
+				goto LBL_Y;
+			}
+
+			/* if y == 1 then composite */
+			if (compare_digit(&y, 1) == MP_EQ) {
+				goto LBL_Y;
+			}
+
+			++j;
+		}
+
+		/* if y != n1 then composite */
+		if (signed_compare(&y, &n1) != MP_EQ) {
+			goto LBL_Y;
+		}
+	}
+
+	/* probably prime now */
+	*result = MP_YES;
+LBL_Y:
+	mp_clear(&y);
+LBL_R:
+	mp_clear(&r);
+LBL_N1:
+	mp_clear(&n1);
+	return err;
 }
 
 /* performs a variable number of rounds of Miller-Rabin
@@ -4904,114 +4837,115 @@ LBL_N1:mp_clear (&n1);
 static int
 mp_prime_is_prime(mp_int *a, int t, int *result)
 {
-  mp_int  b;
-  int     ix, err, res;
+	mp_int  b;
+	int     ix, err, res;
 
-  /* default to no */
-  *result = MP_NO;
+	/* default to no */
+	*result = MP_NO;
 
-  /* valid value of t? */
-  if (t <= 0 || t > (int)PRIME_SIZE) {
-    return MP_VAL;
-  }
+	/* valid value of t? */
+	if (t <= 0 || t > (int)PRIME_SIZE) {
+		return MP_VAL;
+	}
 
-  /* is the input equal to one of the primes in the table? */
-  for (ix = 0; ix < (int)PRIME_SIZE; ix++) {
-      if (mp_cmp_d(a, ltm_prime_tab[ix]) == MP_EQ) {
-         *result = 1;
-         return MP_OKAY;
-      }
-  }
+	/* is the input equal to one of the primes in the table? */
+	for (ix = 0; ix < (int)PRIME_SIZE; ix++) {
+		if (compare_digit(a, ltm_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;
-  }
+	/* 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;
-  }
+	/* 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;
-  }
+	/* 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, ltm_prime_tab[ix]);
+	for (ix = 0; ix < t; ix++) {
+		/* set the prime */
+		set_word(&b, ltm_prime_tab[ix]);
 
-    if ((err = mp_prime_miller_rabin (a, &b, &res)) != MP_OKAY) {
-      goto LBL_B;
-    }
+		if ((err = mp_prime_miller_rabin(a, &b, &res)) != MP_OKAY) {
+			goto LBL_B;
+		}
 
-    if (res == MP_NO) {
-      goto LBL_B;
-    }
-  }
+		if (res == MP_NO) {
+			goto LBL_B;
+		}
+	}
 
-  /* passed the test */
-  *result = MP_YES;
-LBL_B:mp_clear (&b);
-  return err;
+	/* passed the test */
+	*result = MP_YES;
+LBL_B:
+	mp_clear(&b);
+	return err;
 }
 
 /* returns size of ASCII reprensentation */
 static int
-mp_radix_size (mp_int *a, int radix, int *size)
+mp_radix_size(mp_int *a, int radix, int *size)
 {
-  int     res, digs;
-  mp_int  t;
-  mp_digit d;
+	int     res, digs;
+	mp_int  t;
+	mp_digit d;
 
-  *size = 0;
+	*size = 0;
 
-  /* special case for binary */
-  if (radix == 2) {
-    *size = mp_count_bits (a) + (a->sign == MP_NEG ? 1 : 0) + 1;
-    return MP_OKAY;
-  }
+	/* 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;
-  }
+	/* make sure the radix is in range */
+	if (radix < 2 || radix > 64) {
+		return MP_VAL;
+	}
 
-  if (mp_iszero(a) == MP_YES) {
-    *size = 2;
-    return MP_OKAY;
-  }
+	if (MP_ISZERO(a) == MP_YES) {
+		*size = 2;
+		return MP_OKAY;
+	}
 
-  /* digs is the digit count */
-  digs = 0;
+	/* digs is the digit count */
+	digs = 0;
 
-  /* if it's negative add one for the sign */
-  if (a->sign == MP_NEG) {
-    ++digs;
-  }
+	/* if it's negative add one for the sign */
+	if (a->sign == MP_NEG) {
+		++digs;
+	}
 
-  /* init a copy of the input */
-  if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
-    return res;
-  }
+	/* init a copy of the input */
+	if ((res = mp_init_copy(&t, a)) != MP_OKAY) {
+		return res;
+	}
 
-  /* force temp to positive */
-  t.sign = MP_ZPOS; 
+	/* force temp to positive */
+	t.sign = MP_ZPOS; 
 
-  /* fetch out all of the digits */
-  while (mp_iszero (&t) == MP_NO) {
-    if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
-      mp_clear (&t);
-      return res;
-    }
-    ++digs;
-  }
-  mp_clear (&t);
+	/* fetch out all of the digits */
+	while (MP_ISZERO(&t) == MP_NO) {
+		if ((res = signed_divide_word(&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;
+	/* return digs + 1, the 1 is for the NULL byte that would be required. */
+	*size = digs + 1;
+	return MP_OKAY;
 }
 
 static const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/";
@@ -5023,65 +4957,65 @@ static const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijkl
 static 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 < 2 || radix < 2 || radix > 64) {
-    return MP_VAL;
-  }
-
-  /* quick out if its zero */
-  if (mp_iszero(a) == MP_YES) {
-     *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 (--maxlen < 1) {
-       /* no more room */
-       break;
-    }
-    if ((res = mp_div_d (&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
-      mp_clear (&t);
-      return res;
-    }
-    /* LINTED -- radix' range is checked above, limits d's range */
-    *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;
+	int     res, digs;
+	mp_int  t;
+	mp_digit d;
+	char   *_s = str;
+
+	/* check range of the maxlen, radix */
+	if (maxlen < 2 || radix < 2 || radix > 64) {
+		return MP_VAL;
+	}
+
+	/* quick out if its zero */
+	if (MP_ISZERO(a) == MP_YES) {
+		*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 (--maxlen < 1) {
+			/* no more room */
+			break;
+		}
+		if ((res = signed_divide_word(&t, (mp_digit) radix, &t, &d)) != MP_OKAY) {
+			mp_clear(&t);
+			return res;
+		}
+		/* LINTED -- radix' range is checked above, limits d's range */
+		*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;
 }
 
 static char *
@@ -5093,9 +5027,9 @@ formatbn(const BIGNUM *a, const int radix)
 	if (mp_radix_size(__UNCONST(a), radix, &len) != MP_OKAY) {
 		return NULL;
 	}
-	if ((s = netpgp_allocate(1, (size_t)len)) != NULL) {
+	if ((s = allocate(1, (size_t)len)) != NULL) {
 		if (mp_toradix_n(__UNCONST(a), s, radix, len) != MP_OKAY) {
-			netpgp_deallocate(s, (size_t)len);
+			deallocate(s, (size_t)len);
 			return NULL;
 		}
 	}
@@ -5105,45 +5039,45 @@ formatbn(const BIGNUM *a, const int radix)
 static int
 mp_getradix_num(mp_int *a, int radix, char *s)
 {
-   int err, ch, neg, y;
-   
-   /* clear a */
-   mp_zero(a);
-   
-   /* if first digit is - then set negative */
-   if ((ch = *s++) == '-') {
-      neg = MP_NEG;
-      ch = *s++;
-   } 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 = *s++;
-   }
-   if (mp_cmp_d(a, 0) != MP_EQ) {
-      a->sign = neg;
-   }
-   
-   return MP_OKAY;
+	int err, ch, neg, y;
+
+	/* clear a */
+	mp_zero(a);
+
+	/* if first digit is - then set negative */
+	if ((ch = *s++) == '-') {
+		neg = MP_NEG;
+		ch = *s++;
+	} 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 = multiply_digit(a, radix, a)) != MP_OKAY) {
+			return err;
+		}
+		if ((err = add_single_digit(a, y, a)) != MP_OKAY) {
+			return err;
+		}
+
+		ch = *s++;
+	}
+	if (compare_digit(a, 0) != MP_EQ) {
+		a->sign = neg;
+	}
+
+	return MP_OKAY;
 }
 
 static int
@@ -5157,29 +5091,29 @@ getbn(BIGNUM **a, const char *str, int radix)
 	if (mp_getradix_num(*a, radix, __UNCONST(str)) != MP_OKAY) {
 		return 0;
 	}
-	mp_radix_size(__UNCONST(a), radix, &len);
+	mp_radix_size(__UNCONST(*a), radix, &len);
 	return len - 1;
 }
 
 /* d = a - b (mod c) */
 static int
-mp_submod(mp_int *a, mp_int *b, mp_int *c, mp_int *d)
+subtract_modulo(mp_int *a, mp_int *b, mp_int *c, mp_int *d)
 {
-  int     res;
-  mp_int  t;
+	int     res;
+	mp_int  t;
 
 
-  if ((res = mp_init (&t)) != MP_OKAY) {
-    return res;
-  }
+	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;
+	if ((res = signed_subtract(a, b, &t)) != MP_OKAY) {
+		mp_clear(&t);
+		return res;
+	}
+	res = modulo(&t, c, d);
+	mp_clear(&t);
+	return res;
 }
 
 /**************************************************************************/
@@ -5218,7 +5152,7 @@ BN_bn2bin(const BIGNUM *a, unsigned char *b)
 	}
 	for (x = 0; !BN_is_zero(&t) ; ) {
 		b[x++] = (unsigned char) (t.dp[0] & 0xff);
-		if (mp_div_2d (&t, 8, &t, NULL) != MP_OKAY) {
+		if (rshift_bits(&t, 8, &t, NULL) != MP_OKAY) {
 			mp_clear(&t);
 			return -1;
 		}
@@ -5241,7 +5175,7 @@ BN_new(void)
 {
 	BIGNUM	*a;
 
-	if ((a = netpgp_allocate(1, sizeof(*a))) != NULL) {
+	if ((a = allocate(1, sizeof(*a))) != NULL) {
 		mp_init(a);
 	}
 	return a;
@@ -5286,7 +5220,7 @@ BN_lshift(BIGNUM *r, const BIGNUM *a, int n)
 		return 0;
 	}
 	BN_copy(r, a);
-	return mp_lshd(r, n) == MP_OKAY;
+	return lshift_digits(r, n) == MP_OKAY;
 }
 
 int
@@ -5296,7 +5230,7 @@ BN_lshift1(BIGNUM *r, BIGNUM *a)
 		return 0;
 	}
 	BN_copy(r, a);
-	return mp_lshd(r, 1) == MP_OKAY;
+	return lshift_digits(r, 1) == MP_OKAY;
 }
 
 int
@@ -5306,7 +5240,7 @@ BN_rshift(BIGNUM *r, const BIGNUM *a, int n)
 		return MP_VAL;
 	}
 	BN_copy(r, a);
-	return mp_rshd(r, n) == MP_OKAY;
+	return rshift_digits(r, n) == MP_OKAY;
 }
 
 int
@@ -5316,7 +5250,7 @@ BN_rshift1(BIGNUM *r, BIGNUM *a)
 		return 0;
 	}
 	BN_copy(r, a);
-	return mp_rshd(r, 1) == MP_OKAY;
+	return rshift_digits(r, 1) == MP_OKAY;
 }
 
 int
@@ -5325,7 +5259,7 @@ BN_set_word(BIGNUM *a, BN_ULONG w)
 	if (a == NULL) {
 		return 0;
 	}
-	mp_set(a, w);
+	set_word(a, w);
 	return 1;
 }
 
@@ -5335,7 +5269,7 @@ BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b)
 	if (a == NULL || b == NULL || r == NULL) {
 		return 0;
 	}
-	return mp_add(__UNCONST(a), __UNCONST(b), r) == MP_OKAY;
+	return signed_add(__UNCONST(a), __UNCONST(b), r) == MP_OKAY;
 }
 
 int
@@ -5344,7 +5278,7 @@ BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b)
 	if (a == NULL || b == NULL || r == NULL) {
 		return 0;
 	}
-	return mp_sub(__UNCONST(a), __UNCONST(b), r) == MP_OKAY;
+	return signed_subtract(__UNCONST(a), __UNCONST(b), r) == MP_OKAY;
 }
 
 int
@@ -5354,7 +5288,7 @@ BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
 		return 0;
 	}
 	USE_ARG(ctx);
-	return mp_mul(__UNCONST(a), __UNCONST(b), r) == MP_OKAY;
+	return signed_multiply(__UNCONST(a), __UNCONST(b), r) == MP_OKAY;
 }
 
 int
@@ -5364,7 +5298,46 @@ BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d, BN_CTX *ctx)
 		return 0;
 	}
 	USE_ARG(ctx);
-	return mp_div(dv, rem, __UNCONST(a), __UNCONST(d)) == MP_OKAY;
+	return signed_divide(dv, rem, __UNCONST(a), __UNCONST(d)) == MP_OKAY;
+}
+
+/* perform a bit operation on the 2 bignums */
+int
+BN_bitop(BIGNUM *r, const BIGNUM *a, char op, const BIGNUM *b)
+{
+	unsigned	ndigits;
+	mp_digit	ad;
+	mp_digit	bd;
+	int		i;
+
+	if (a == NULL || b == NULL || r == NULL) {
+		return 0;
+	}
+	if (BN_cmp(__UNCONST(a), __UNCONST(b)) >= 0) {
+		BN_copy(r, a);
+		ndigits = a->used;
+	} else {
+		BN_copy(r, b);
+		ndigits = b->used;
+	}
+	for (i = 0 ; i < (int)ndigits ; i++) {
+		ad = (i > a->used) ? 0 : a->dp[i];
+		bd = (i > b->used) ? 0 : b->dp[i];
+		switch(op) {
+		case '&':
+			r->dp[i] = (ad & bd);
+			break;
+		case '|':
+			r->dp[i] = (ad | bd);
+			break;
+		case '^':
+			r->dp[i] = (ad ^ bd);
+			break;
+		default:
+			break;
+		}
+	}
+	return 1;
 }
 
 void
@@ -5423,7 +5396,7 @@ BN_cmp(BIGNUM *a, BIGNUM *b)
 	if (a == NULL || b == NULL) {
 		return MP_VAL;
 	}
-	switch(mp_cmp(a, b)) {
+	switch(signed_compare(a, b)) {
 	case MP_LT:
 		return -1;
 	case MP_GT:
@@ -5441,7 +5414,7 @@ BN_mod_exp(BIGNUM *Y, BIGNUM *G, BIGNUM *X, BIGNUM *P, BN_CTX *ctx)
 		return MP_VAL;
 	}
 	USE_ARG(ctx);
-	return mp_exptmod(G, X, P, Y) == MP_OKAY;
+	return exponent_modulo(G, X, P, Y) == MP_OKAY;
 }
 
 BIGNUM *
@@ -5451,7 +5424,7 @@ BN_mod_inverse(BIGNUM *r, BIGNUM *a, const BIGNUM *n, BN_CTX *ctx)
 	if (r == NULL || a == NULL || n == NULL) {
 		return NULL;
 	}
-	return (mp_invmod(r, a, __UNCONST(n)) == MP_OKAY) ? r : NULL;
+	return (modular_inverse(r, a, __UNCONST(n)) == MP_OKAY) ? r : NULL;
 }
 
 int
@@ -5461,13 +5434,13 @@ BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx)
 	if (ret == NULL || a == NULL || b == NULL || m == NULL) {
 		return 0;
 	}
-	return mp_mulmod(ret, a, b, __UNCONST(m)) == MP_OKAY;
+	return multiply_modulo(ret, a, b, __UNCONST(m)) == MP_OKAY;
 }
 
 BN_CTX *
 BN_CTX_new(void)
 {
-	return netpgp_allocate(1, sizeof(BN_CTX));
+	return allocate(1, sizeof(BN_CTX));
 }
 
 void
@@ -5475,7 +5448,7 @@ BN_CTX_init(BN_CTX *c)
 {
 	if (c != NULL) {
 		c->arraysize = 15;
-		if ((c->v = netpgp_allocate(sizeof(*c->v), c->arraysize)) == NULL) {
+		if ((c->v = allocate(sizeof(*c->v), c->arraysize)) == NULL) {
 			c->arraysize = 0;
 		}
 	}
@@ -5505,7 +5478,7 @@ BN_CTX_free(BN_CTX *c)
 		for (i = 0 ; i < c->count ; i++) {
 			BN_clear_free(c->v[i]);
 		}
-		netpgp_deallocate(c->v, sizeof(*c->v) * c->arraysize);
+		deallocate(c->v, sizeof(*c->v) * c->arraysize);
 	}
 }
 
@@ -5527,6 +5500,12 @@ BN_bn2dec(const BIGNUM *a)
 	return (a == NULL) ? NULL : formatbn(a, 10);
 }
 
+char *
+BN_bn2radix(const BIGNUM *a, unsigned radix)
+{
+	return (a == NULL) ? NULL : formatbn(a, (int)radix);
+}
+
 #ifndef _KERNEL
 int
 BN_print_fp(FILE *fp, const BIGNUM *a)
@@ -5539,7 +5518,7 @@ BN_print_fp(FILE *fp, const BIGNUM *a)
 	}
 	s = BN_bn2hex(a);
 	ret = fprintf(fp, "%s", s);
-	netpgp_deallocate(s, strlen(s) + 1);
+	deallocate(s, strlen(s) + 1);
 	return ret;
 }
 #endif
@@ -5582,7 +5561,7 @@ BN_rand_range(BIGNUM *rnd, BIGNUM *range)
 		return 0;
 	}
 	BN_rand(rnd, BN_num_bits(range), 1, 0);
-	return mp_mod(rnd, range, rnd) == MP_OKAY;
+	return modulo(rnd, range, rnd) == MP_OKAY;
 }
 #endif
 
@@ -5622,13 +5601,19 @@ BN_dec2bn(BIGNUM **a, const char *str)
 }
 
 int
+BN_radix2bn(BIGNUM **a, const char *str, unsigned radix)
+{
+	return getbn(a, str, (int)radix);
+}
+
+int
 BN_mod_sub(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx)
 {
 	USE_ARG(ctx);
 	if (r == NULL || a == NULL || b == NULL || m == NULL) {
 		return 0;
 	}
-	return mp_submod(a, b, __UNCONST(m), r) == MP_OKAY;
+	return subtract_modulo(a, b, __UNCONST(m), r) == MP_OKAY;
 }
 
 int
@@ -5639,3 +5624,55 @@ BN_is_bit_set(const BIGNUM *a, int n)
 	}
 	return (a->dp[n / DIGIT_BIT] & (1 << (n % DIGIT_BIT))) ? 1 : 0;
 }
+
+/* raise 'a' to power of 'b' */
+int
+BN_raise(BIGNUM *res, BIGNUM *a, BIGNUM *b)
+{
+	uint64_t	 exponent;
+	BIGNUM		*power;
+	BIGNUM		*temp;
+	char		*t;
+
+	t = BN_bn2dec(b);
+	exponent = (uint64_t)strtoull(t, NULL, 10);
+	free(t);
+	if (exponent == 0) {
+		BN_copy(res, BN_value_one());
+	} else {
+		power = BN_dup(a);
+		for ( ; (exponent & 1) == 0 ; exponent >>= 1) {
+			BN_mul(power, power, power, NULL);
+		}
+		temp = BN_dup(power);
+		for (exponent >>= 1 ; exponent > 0 ; exponent >>= 1) {
+			BN_mul(power, power, power, NULL);
+			if (exponent & 1) {
+				BN_mul(temp, power, temp, NULL);
+			}
+		}
+		BN_copy(res, temp);
+		BN_free(power);
+		BN_free(temp);
+	}
+	return 1;
+}
+
+/* compute the factorial */
+int
+BN_factorial(BIGNUM *res, BIGNUM *f)
+{
+	BIGNUM	*one;
+	BIGNUM	*i;
+
+	i = BN_dup(f);
+	one = __UNCONST(BN_value_one());
+	BN_sub(i, i, one);
+	BN_copy(res, f);
+	while (BN_cmp(i, one) > 0) {
+		BN_mul(res, res, i, NULL);
+		BN_sub(i, i, one);
+	}
+	BN_free(i);
+	return 1;
+}
diff --git a/security/netpgpverify/files/bn.h b/security/netpgpverify/files/bn.h
index fdc49d8760a..c4e772f583c 100644
--- a/security/netpgpverify/files/bn.h
+++ b/security/netpgpverify/files/bn.h
@@ -100,8 +100,10 @@ BIGNUM *BN_bin2bn(const uint8_t */*buf*/, int /*size*/, BIGNUM */*bn*/);
 int BN_bn2bin(const BIGNUM */*a*/, unsigned char */*b*/);
 char *BN_bn2hex(const BIGNUM */*a*/);
 char *BN_bn2dec(const BIGNUM */*a*/);
+char *BN_bn2radix(const BIGNUM */*a*/, unsigned /*radix*/);
 int BN_hex2bn(BIGNUM **/*a*/, const char */*str*/);
 int BN_dec2bn(BIGNUM **/*a*/, const char */*str*/);
+int BN_radix2bn(BIGNUM **/*a*/, const char */*str*/, unsigned /*radix*/);
 #ifndef _KERNEL
 int BN_print_fp(FILE */*fp*/, const BIGNUM */*a*/);
 #endif
@@ -111,6 +113,7 @@ int BN_sub(BIGNUM */*r*/, const BIGNUM */*a*/, const BIGNUM */*b*/);
 int BN_mul(BIGNUM */*r*/, const BIGNUM */*a*/, const BIGNUM */*b*/, BN_CTX */*ctx*/);
 int BN_div(BIGNUM */*q*/, BIGNUM */*r*/, const BIGNUM */*a*/, const BIGNUM */*b*/, BN_CTX */*ctx*/);
 void BN_swap(BIGNUM */*a*/, BIGNUM */*b*/);
+int BN_bitop(BIGNUM */*r*/, const BIGNUM */*a*/, char /*op*/, const BIGNUM */*b*/);
 int BN_lshift(BIGNUM */*r*/, const BIGNUM */*a*/, int /*n*/);
 int BN_lshift1(BIGNUM */*r*/, BIGNUM */*a*/);
 int BN_rshift(BIGNUM */*r*/, const BIGNUM */*a*/, int /*n*/);
@@ -126,6 +129,9 @@ BIGNUM *BN_mod_inverse(BIGNUM */*ret*/, BIGNUM */*a*/, const BIGNUM */*n*/, BN_C
 int BN_mod_mul(BIGNUM */*ret*/, BIGNUM */*a*/, BIGNUM */*b*/, const BIGNUM */*m*/, BN_CTX */*ctx*/);
 int BN_mod_sub(BIGNUM */*r*/, BIGNUM */*a*/, BIGNUM */*b*/, const BIGNUM */*m*/, BN_CTX */*ctx*/);
 
+int BN_raise(BIGNUM */*res*/, BIGNUM */*a*/, BIGNUM */*b*/);
+int BN_factorial(BIGNUM */*fact*/, BIGNUM */*f*/);
+
 BN_CTX *BN_CTX_new(void);
 BIGNUM *BN_CTX_get(BN_CTX */*ctx*/);
 void BN_CTX_start(BN_CTX */*ctx*/);