r23456: Update Samba4 to current lorikeet-heimdal.

Andrew Bartlett
(This used to be commit ae0f81ab235c72cceb120bcdeb051a483cf3cc4f)

5 files changed, 3745 insertions, 0 deletions

diff --git a/source4/heimdal/lib/hcrypto/imath/LICENSE b/source4/heimdal/lib/hcrypto/imath/LICENSE
new file mode 100644
index 0000000000..cecfb11404
--- /dev/null
+++ b/source4/heimdal/lib/hcrypto/imath/LICENSE
@@ -0,0 +1,21 @@
+IMath is Copyright 2002-2006 Michael J. Fromberger
+You may use it subject to the following Licensing Terms:
+
+Permission is hereby granted, free of charge, to any person obtaining
+a copy of this software and associated documentation files (the
+"Software"), to deal in the Software without restriction, including
+without limitation the rights to use, copy, modify, merge, publish,
+distribute, sublicense, and/or sell copies of the Software, and to
+permit persons to whom the Software is furnished to do so, subject to
+the following conditions:
+
+The above copyright notice and this permission notice shall be
+included in all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
+CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
+TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
+SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
diff --git a/source4/heimdal/lib/hcrypto/imath/imath.c b/source4/heimdal/lib/hcrypto/imath/imath.c
new file mode 100755
index 0000000000..376425788b
--- /dev/null
+++ b/source4/heimdal/lib/hcrypto/imath/imath.c
@@ -0,0 +1,3267 @@
+/*
+  Name:     imath.c
+  Purpose:  Arbitrary precision integer arithmetic routines.
+  Author:   M. J. Fromberger <http://www.dartmouth.edu/~sting/>
+  Info:     $Id: imath.c 20854 2007-06-03 18:04:10Z lha $
+
+  Copyright (C) 2002-2007 Michael J. Fromberger, All Rights Reserved.
+
+  Permission is hereby granted, free of charge, to any person
+  obtaining a copy of this software and associated documentation files
+  (the "Software"), to deal in the Software without restriction,
+  including without limitation the rights to use, copy, modify, merge,
+  publish, distribute, sublicense, and/or sell copies of the Software,
+  and to permit persons to whom the Software is furnished to do so,
+  subject to the following conditions:
+
+  The above copyright notice and this permission notice shall be
+  included in all copies or substantial portions of the Software.
+
+  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+  MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+  NONINFRINGEMENT.  IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+  BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+  ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+  CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+  SOFTWARE.
+ */
+
+#include "imath.h"
+
+#if DEBUG
+#include <stdio.h>
+#endif
+
+#include <stdlib.h>
+#include <string.h>
+#include <ctype.h>
+
+#include <assert.h>
+
+#if DEBUG
+#define static
+#endif
+
+/* {{{ Constants */
+
+const mp_result MP_OK     = 0;  /* no error, all is well  */
+const mp_result MP_FALSE  = 0;  /* boolean false          */
+const mp_result MP_TRUE   = -1; /* boolean true           */
+const mp_result MP_MEMORY = -2; /* out of memory          */
+const mp_result MP_RANGE  = -3; /* argument out of range  */
+const mp_result MP_UNDEF  = -4; /* result undefined       */
+const mp_result MP_TRUNC  = -5; /* output truncated       */
+const mp_result MP_BADARG = -6; /* invalid null argument  */
+
+const mp_sign   MP_NEG  = 1;    /* value is strictly negative */
+const mp_sign   MP_ZPOS = 0;    /* value is non-negative      */
+
+static const char *s_unknown_err = "unknown result code";
+static const char *s_error_msg[] = {
+  "error code 0",
+  "boolean true",
+  "out of memory",
+  "argument out of range",
+  "result undefined",
+  "output truncated",
+  "invalid null argument",
+  NULL
+};
+
+/* }}} */
+
+/* Argument checking macros 
+   Use CHECK() where a return value is required; NRCHECK() elsewhere */
+#define CHECK(TEST)   assert(TEST)
+#define NRCHECK(TEST) assert(TEST)
+
+/* {{{ Logarithm table for computing output sizes */
+
+/* The ith entry of this table gives the value of log_i(2).
+
+   An integer value n requires ceil(log_i(n)) digits to be represented
+   in base i.  Since it is easy to compute lg(n), by counting bits, we
+   can compute log_i(n) = lg(n) * log_i(2).
+
+   The use of this table eliminates a dependency upon linkage against
+   the standard math libraries.
+ */
+static const double s_log2[] = {
+   0.000000000, 0.000000000, 1.000000000, 0.630929754, 	/*  0  1  2  3 */
+   0.500000000, 0.430676558, 0.386852807, 0.356207187, 	/*  4  5  6  7 */
+   0.333333333, 0.315464877, 0.301029996, 0.289064826, 	/*  8  9 10 11 */
+   0.278942946, 0.270238154, 0.262649535, 0.255958025, 	/* 12 13 14 15 */
+   0.250000000, 0.244650542, 0.239812467, 0.235408913, 	/* 16 17 18 19 */
+   0.231378213, 0.227670249, 0.224243824, 0.221064729, 	/* 20 21 22 23 */
+   0.218104292, 0.215338279, 0.212746054, 0.210309918, 	/* 24 25 26 27 */
+   0.208014598, 0.205846832, 0.203795047, 0.201849087, 	/* 28 29 30 31 */
+   0.200000000, 0.198239863, 0.196561632, 0.194959022, 	/* 32 33 34 35 */
+   0.193426404, 0.191958720, 0.190551412, 0.189200360, 	/* 36 37 38 39 */
+   0.187901825, 0.186652411, 0.185449023, 0.184288833, 	/* 40 41 42 43 */
+   0.183169251, 0.182087900, 0.181042597, 0.180031327, 	/* 44 45 46 47 */
+   0.179052232, 0.178103594, 0.177183820, 0.176291434, 	/* 48 49 50 51 */
+   0.175425064, 0.174583430, 0.173765343, 0.172969690, 	/* 52 53 54 55 */
+   0.172195434, 0.171441601, 0.170707280, 0.169991616, 	/* 56 57 58 59 */
+   0.169293808, 0.168613099, 0.167948779, 0.167300179, 	/* 60 61 62 63 */
+   0.166666667
+};
+
+/* }}} */
+/* {{{ Various macros */
+
+/* Return the number of digits needed to represent a static value */
+#define MP_VALUE_DIGITS(V) \
+((sizeof(V)+(sizeof(mp_digit)-1))/sizeof(mp_digit))
+
+/* Round precision P to nearest word boundary */
+#define ROUND_PREC(P) ((mp_size)(2*(((P)+1)/2)))
+
+/* Set array P of S digits to zero */
+#define ZERO(P, S) \
+do{mp_size i__=(S)*sizeof(mp_digit);mp_digit *p__=(P);memset(p__,0,i__);}while(0)
+
+/* Copy S digits from array P to array Q */
+#define COPY(P, Q, S) \
+do{mp_size i__=(S)*sizeof(mp_digit);mp_digit *p__=(P),*q__=(Q);\
+memcpy(q__,p__,i__);}while(0)
+
+/* Reverse N elements of type T in array A */
+#define REV(T, A, N) \
+do{T *u_=(A),*v_=u_+(N)-1;while(u_<v_){T xch=*u_;*u_++=*v_;*v_--=xch;}}while(0)
+
+#if TRACEABLE_CLAMP
+#define CLAMP(Z) s_clamp(Z)
+#else
+#define CLAMP(Z) \
+do{mp_int z_=(Z);mp_size uz_=MP_USED(z_);mp_digit *dz_=MP_DIGITS(z_)+uz_-1;\
+while(uz_ > 1 && (*dz_-- == 0)) --uz_;MP_USED(z_)=uz_;}while(0)
+#endif
+
+#define MIN(A, B) ((B)<(A)?(B):(A))
+#define MAX(A, B) ((B)>(A)?(B):(A))
+#define SWAP(T, A, B) do{T t_=(A);A=(B);B=t_;}while(0)
+
+#define TEMP(K) (temp + (K))
+#define SETUP(E, C) \
+do{if((res = (E)) != MP_OK) goto CLEANUP; ++(C);}while(0)
+
+#define CMPZ(Z) \
+(((Z)->used==1&&(Z)->digits[0]==0)?0:((Z)->sign==MP_NEG)?-1:1)
+
+#define UMUL(X, Y, Z) \
+do{mp_size ua_=MP_USED(X),ub_=MP_USED(Y);mp_size o_=ua_+ub_;\
+ZERO(MP_DIGITS(Z),o_);\
+(void) s_kmul(MP_DIGITS(X),MP_DIGITS(Y),MP_DIGITS(Z),ua_,ub_);\
+MP_USED(Z)=o_;CLAMP(Z);}while(0)
+
+#define USQR(X, Z) \
+do{mp_size ua_=MP_USED(X),o_=ua_+ua_;ZERO(MP_DIGITS(Z),o_);\
+(void) s_ksqr(MP_DIGITS(X),MP_DIGITS(Z),ua_);MP_USED(Z)=o_;CLAMP(Z);}while(0)
+
+#define UPPER_HALF(W)           ((mp_word)((W) >> MP_DIGIT_BIT))
+#define LOWER_HALF(W)           ((mp_digit)(W))
+#define HIGH_BIT_SET(W)         ((W) >> (MP_WORD_BIT - 1))
+#define ADD_WILL_OVERFLOW(W, V) ((MP_WORD_MAX - (V)) < (W))
+
+/* }}} */
+/* {{{ Default configuration settings */
+
+/* Default number of digits allocated to a new mp_int */
+#if IMATH_TEST
+mp_size default_precision = MP_DEFAULT_PREC;
+#else
+static const mp_size default_precision = MP_DEFAULT_PREC;
+#endif
+
+/* Minimum number of digits to invoke recursive multiply */
+#if IMATH_TEST
+mp_size multiply_threshold = MP_MULT_THRESH;
+#else
+static const mp_size multiply_threshold = MP_MULT_THRESH;
+#endif
+
+/* }}} */
+
+/* Allocate a buffer of (at least) num digits, or return
+   NULL if that couldn't be done.  */
+static mp_digit *s_alloc(mp_size num);
+
+/* Release a buffer of digits allocated by s_alloc(). */
+static void s_free(void *ptr);
+
+/* Insure that z has at least min digits allocated, resizing if
+   necessary.  Returns true if successful, false if out of memory. */
+static int  s_pad(mp_int z, mp_size min);
+
+/* Normalize by removing leading zeroes (except when z = 0) */
+#if TRACEABLE_CLAMP
+static void      s_clamp(mp_int z);
+#endif
+
+/* Fill in a "fake" mp_int on the stack with a given value */
+static void      s_fake(mp_int z, int value, mp_digit vbuf[]);
+
+/* Compare two runs of digits of given length, returns <0, 0, >0 */
+static int       s_cdig(mp_digit *da, mp_digit *db, mp_size len);
+
+/* Pack the unsigned digits of v into array t */
+static int       s_vpack(int v, mp_digit t[]);
+
+/* Compare magnitudes of a and b, returns <0, 0, >0 */
+static int       s_ucmp(mp_int a, mp_int b);
+
+/* Compare magnitudes of a and v, returns <0, 0, >0 */
+static int       s_vcmp(mp_int a, int v);
+
+/* Unsigned magnitude addition; assumes dc is big enough.
+   Carry out is returned (no memory allocated). */
+static mp_digit  s_uadd(mp_digit *da, mp_digit *db, mp_digit *dc, 
+		        mp_size size_a, mp_size size_b);
+
+/* Unsigned magnitude subtraction.  Assumes dc is big enough. */
+static void      s_usub(mp_digit *da, mp_digit *db, mp_digit *dc,
+		        mp_size size_a, mp_size size_b);
+
+/* Unsigned recursive multiplication.  Assumes dc is big enough. */
+static int       s_kmul(mp_digit *da, mp_digit *db, mp_digit *dc,
+			mp_size size_a, mp_size size_b);
+
+/* Unsigned magnitude multiplication.  Assumes dc is big enough. */
+static void      s_umul(mp_digit *da, mp_digit *db, mp_digit *dc,
+			mp_size size_a, mp_size size_b);
+
+/* Unsigned recursive squaring.  Assumes dc is big enough. */
+static int       s_ksqr(mp_digit *da, mp_digit *dc, mp_size size_a);
+
+/* Unsigned magnitude squaring.  Assumes dc is big enough. */
+static void      s_usqr(mp_digit *da, mp_digit *dc, mp_size size_a);
+
+/* Single digit addition.  Assumes a is big enough. */
+static void      s_dadd(mp_int a, mp_digit b);
+
+/* Single digit multiplication.  Assumes a is big enough. */
+static void      s_dmul(mp_int a, mp_digit b);
+
+/* Single digit multiplication on buffers; assumes dc is big enough. */
+static void      s_dbmul(mp_digit *da, mp_digit b, mp_digit *dc,
+			 mp_size size_a);
+
+/* Single digit division.  Replaces a with the quotient, 
+   returns the remainder.  */
+static mp_digit  s_ddiv(mp_int a, mp_digit b);
+
+/* Quick division by a power of 2, replaces z (no allocation) */
+static void      s_qdiv(mp_int z, mp_size p2);
+
+/* Quick remainder by a power of 2, replaces z (no allocation) */
+static void      s_qmod(mp_int z, mp_size p2);
+
+/* Quick multiplication by a power of 2, replaces z. 
+   Allocates if necessary; returns false in case this fails. */
+static int       s_qmul(mp_int z, mp_size p2);
+
+/* Quick subtraction from a power of 2, replaces z.
+   Allocates if necessary; returns false in case this fails. */
+static int       s_qsub(mp_int z, mp_size p2);
+
+/* Return maximum k such that 2^k divides z. */
+static int       s_dp2k(mp_int z);
+
+/* Return k >= 0 such that z = 2^k, or -1 if there is no such k. */
+static int       s_isp2(mp_int z);
+
+/* Set z to 2^k.  May allocate; returns false in case this fails. */
+static int       s_2expt(mp_int z, int k);
+
+/* Normalize a and b for division, returns normalization constant */
+static int       s_norm(mp_int a, mp_int b);
+
+/* Compute constant mu for Barrett reduction, given modulus m, result
+   replaces z, m is untouched. */
+static mp_result s_brmu(mp_int z, mp_int m);
+
+/* Reduce a modulo m, using Barrett's algorithm. */
+static int       s_reduce(mp_int x, mp_int m, mp_int mu, mp_int q1, mp_int q2);
+
+/* Modular exponentiation, using Barrett reduction */
+static mp_result s_embar(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c);
+
+/* Unsigned magnitude division.  Assumes |a| > |b|.  Allocates
+   temporaries; overwrites a with quotient, b with remainder. */
+static mp_result s_udiv(mp_int a, mp_int b);
+
+/* Compute the number of digits in radix r required to represent the
+   given value.  Does not account for sign flags, terminators, etc. */
+static int       s_outlen(mp_int z, mp_size r);
+
+/* Guess how many digits of precision will be needed to represent a
+   radix r value of the specified number of digits.  Returns a value
+   guaranteed to be no smaller than the actual number required. */
+static mp_size   s_inlen(int len, mp_size r);
+
+/* Convert a character to a digit value in radix r, or 
+   -1 if out of range */
+static int       s_ch2val(char c, int r);
+
+/* Convert a digit value to a character */
+static char      s_val2ch(int v, int caps);
+
+/* Take 2's complement of a buffer in place */
+static void      s_2comp(unsigned char *buf, int len);
+
+/* Convert a value to binary, ignoring sign.  On input, *limpos is the
+   bound on how many bytes should be written to buf; on output, *limpos
+   is set to the number of bytes actually written. */
+static mp_result s_tobin(mp_int z, unsigned char *buf, int *limpos, int pad);
+
+#if DEBUG
+/* Dump a representation of the mp_int to standard output */
+void      s_print(char *tag, mp_int z);
+void      s_print_buf(char *tag, mp_digit *buf, mp_size num);
+#endif
+
+/* {{{ mp_int_init(z) */
+
+mp_result mp_int_init(mp_int z)
+{
+  if(z == NULL)
+    return MP_BADARG;
+
+  z->single = 0;
+  z->digits = &(z->single);
+  z->alloc  = 1;
+  z->used   = 1;
+  z->sign   = MP_ZPOS;
+
+  return MP_OK;
+}
+
+/* }}} */
+
+/* {{{ mp_int_alloc() */
+
+mp_int    mp_int_alloc(void)
+{
+  mp_int out = malloc(sizeof(mpz_t));
+  
+  if(out != NULL) 
+    mp_int_init(out);
+
+  return out;
+}
+
+/* }}} */
+
+/* {{{ mp_int_init_size(z, prec) */
+
+mp_result mp_int_init_size(mp_int z, mp_size prec)
+{
+  CHECK(z != NULL);
+
+  if(prec == 0)
+    prec = default_precision;
+  else if(prec == 1) 
+    return mp_int_init(z);
+  else 
+    prec = (mp_size) ROUND_PREC(prec);
+  
+  if((MP_DIGITS(z) = s_alloc(prec)) == NULL)
+    return MP_MEMORY;
+
+  z->digits[0] = 0;
+  MP_USED(z) = 1;
+  MP_ALLOC(z) = prec;
+  MP_SIGN(z) = MP_ZPOS;
+  
+  return MP_OK;
+}
+
+/* }}} */
+
+/* {{{ mp_int_init_copy(z, old) */
+
+mp_result mp_int_init_copy(mp_int z, mp_int old)
+{
+  mp_result  res;
+  mp_size    uold;
+
+  CHECK(z != NULL && old != NULL);
+
+  uold = MP_USED(old);
+  if(uold == 1) {
+    mp_int_init(z);
+  }
+  else {
+    mp_size target = MAX(uold, default_precision);
+
+    if((res = mp_int_init_size(z, target)) != MP_OK)
+      return res;
+  }
+
+  MP_USED(z) = uold;
+  MP_SIGN(z) = MP_SIGN(old);
+  COPY(MP_DIGITS(old), MP_DIGITS(z), uold);
+
+  return MP_OK;
+}
+
+/* }}} */
+
+/* {{{ mp_int_init_value(z, value) */
+
+mp_result mp_int_init_value(mp_int z, int value)
+{
+  mpz_t     vtmp;
+  mp_digit  vbuf[MP_VALUE_DIGITS(value)];
+
+  s_fake(&vtmp, value, vbuf);
+  return mp_int_init_copy(z, &vtmp);
+}
+
+/* }}} */
+
+/* {{{ mp_int_set_value(z, value) */
+
+mp_result  mp_int_set_value(mp_int z, int value)
+{
+  mpz_t    vtmp;
+  mp_digit vbuf[MP_VALUE_DIGITS(value)];
+
+  s_fake(&vtmp, value, vbuf);
+  return mp_int_copy(&vtmp, z);
+}
+
+/* }}} */
+
+/* {{{ mp_int_clear(z) */
+
+void      mp_int_clear(mp_int z)
+{
+  if(z == NULL)
+    return;
+
+  if(MP_DIGITS(z) != NULL) {
+    if((void *) MP_DIGITS(z) != (void *) z)
+      s_free(MP_DIGITS(z));
+
+    MP_DIGITS(z) = NULL;
+  }
+}
+
+/* }}} */
+
+/* {{{ mp_int_free(z) */
+
+void      mp_int_free(mp_int z)
+{
+  NRCHECK(z != NULL);
+
+  mp_int_clear(z);
+  free(z); /* note: NOT s_free() */
+}
+
+/* }}} */
+
+/* {{{ mp_int_copy(a, c) */
+
+mp_result mp_int_copy(mp_int a, mp_int c)
+{
+  CHECK(a != NULL && c != NULL);
+
+  if(a != c) {
+    mp_size   ua = MP_USED(a);
+    mp_digit *da, *dc;
+
+    if(!s_pad(c, ua))
+      return MP_MEMORY;
+
+    da = MP_DIGITS(a); dc = MP_DIGITS(c);
+    COPY(da, dc, ua);
+
+    MP_USED(c) = ua;
+    MP_SIGN(c) = MP_SIGN(a);
+  }
+
+  return MP_OK;
+}
+
+/* }}} */
+
+/* {{{ mp_int_swap(a, c) */
+
+void      mp_int_swap(mp_int a, mp_int c)
+{
+  if(a != c) {
+    mpz_t tmp = *a;
+
+    *a = *c;
+    *c = tmp;
+  }
+}
+
+/* }}} */
+
+/* {{{ mp_int_zero(z) */
+
+void      mp_int_zero(mp_int z)
+{
+  NRCHECK(z != NULL);
+
+  z->digits[0] = 0;
+  MP_USED(z) = 1;
+  MP_SIGN(z) = MP_ZPOS;
+}
+
+/* }}} */
+
+/* {{{ mp_int_abs(a, c) */
+
+mp_result mp_int_abs(mp_int a, mp_int c)
+{
+  mp_result res;
+
+  CHECK(a != NULL && c != NULL);
+
+  if((res = mp_int_copy(a, c)) != MP_OK)
+    return res;
+
+  MP_SIGN(c) = MP_ZPOS;
+  return MP_OK;
+}
+
+/* }}} */
+
+/* {{{ mp_int_neg(a, c) */
+
+mp_result mp_int_neg(mp_int a, mp_int c)
+{
+  mp_result res;
+
+  CHECK(a != NULL && c != NULL);
+
+  if((res = mp_int_copy(a, c)) != MP_OK)
+    return res;
+
+  if(CMPZ(c) != 0)
+    MP_SIGN(c) = 1 - MP_SIGN(a);
+
+  return MP_OK;
+}
+
+/* }}} */
+
+/* {{{ mp_int_add(a, b, c) */
+
+mp_result mp_int_add(mp_int a, mp_int b, mp_int c)
+{ 
+  mp_size  ua, ub, uc, max;
+
+  CHECK(a != NULL && b != NULL && c != NULL);
+
+  ua = MP_USED(a); ub = MP_USED(b); uc = MP_USED(c);
+  max = MAX(ua, ub);
+
+  if(MP_SIGN(a) == MP_SIGN(b)) {
+    /* Same sign -- add magnitudes, preserve sign of addends */
+    mp_digit carry;
+
+    if(!s_pad(c, max))
+      return MP_MEMORY;
+
+    carry = s_uadd(MP_DIGITS(a), MP_DIGITS(b), MP_DIGITS(c), ua, ub);
+    uc = max;
+
+    if(carry) {
+      if(!s_pad(c, max + 1))
+	return MP_MEMORY;
+
+      c->digits[max] = carry;
+      ++uc;
+    }
+
+    MP_USED(c) = uc;
+    MP_SIGN(c) = MP_SIGN(a);
+
+  } 
+  else {
+    /* Different signs -- subtract magnitudes, preserve sign of greater */
+    mp_int  x, y;
+    int     cmp = s_ucmp(a, b); /* magnitude comparision, sign ignored */
+
+    /* Set x to max(a, b), y to min(a, b) to simplify later code */
+    if(cmp >= 0) {
+      x = a; y = b;
+    } 
+    else {
+      x = b; y = a; 
+    }
+
+    if(!s_pad(c, MP_USED(x)))
+      return MP_MEMORY;
+
+    /* Subtract smaller from larger */
+    s_usub(MP_DIGITS(x), MP_DIGITS(y), MP_DIGITS(c), MP_USED(x), MP_USED(y));
+    MP_USED(c) = MP_USED(x);
+    CLAMP(c);
+    
+    /* Give result the sign of the larger */
+    MP_SIGN(c) = MP_SIGN(x);
+  }
+
+  return MP_OK;
+}
+
+/* }}} */
+
+/* {{{ mp_int_add_value(a, value, c) */
+
+mp_result mp_int_add_value(mp_int a, int value, mp_int c)
+{
+  mpz_t     vtmp;
+  mp_digit  vbuf[MP_VALUE_DIGITS(value)];
+
+  s_fake(&vtmp, value, vbuf);
+
+  return mp_int_add(a, &vtmp, c);
+}
+
+/* }}} */
+
+/* {{{ mp_int_sub(a, b, c) */
+
+mp_result mp_int_sub(mp_int a, mp_int b, mp_int c)
+{
+  mp_size  ua, ub, uc, max;
+
+  CHECK(a != NULL && b != NULL && c != NULL);
+
+  ua = MP_USED(a); ub = MP_USED(b); uc = MP_USED(c);
+  max = MAX(ua, ub);
+
+  if(MP_SIGN(a) != MP_SIGN(b)) {
+    /* Different signs -- add magnitudes and keep sign of a */
+    mp_digit carry;
+
+    if(!s_pad(c, max))
+      return MP_MEMORY;
+
+    carry = s_uadd(MP_DIGITS(a), MP_DIGITS(b), MP_DIGITS(c), ua, ub);
+    uc = max;
+
+    if(carry) {
+      if(!s_pad(c, max + 1))
+	return MP_MEMORY;
+
+      c->digits[max] = carry;
+      ++uc;
+    }
+
+    MP_USED(c) = uc;
+    MP_SIGN(c) = MP_SIGN(a);
+
+  } 
+  else {
+    /* Same signs -- subtract magnitudes */
+    mp_int  x, y;
+    mp_sign osign;
+    int     cmp = s_ucmp(a, b);
+
+    if(!s_pad(c, max))
+      return MP_MEMORY;
+
+    if(cmp >= 0) {
+      x = a; y = b; osign = MP_ZPOS;
+    } 
+    else {
+      x = b; y = a; osign = MP_NEG;
+    }
+
+    if(MP_SIGN(a) == MP_NEG && cmp != 0)
+      osign = 1 - osign;
+
+    s_usub(MP_DIGITS(x), MP_DIGITS(y), MP_DIGITS(c), MP_USED(x), MP_USED(y));
+    MP_USED(c) = MP_USED(x);
+    CLAMP(c);
+
+    MP_SIGN(c) = osign;
+  }
+
+  return MP_OK;
+}
+
+/* }}} */
+
+/* {{{ mp_int_sub_value(a, value, c) */
+
+mp_result mp_int_sub_value(mp_int a, int value, mp_int c)
+{
+  mpz_t     vtmp;
+  mp_digit  vbuf[MP_VALUE_DIGITS(value)];
+
+  s_fake(&vtmp, value, vbuf);
+
+  return mp_int_sub(a, &vtmp, c);
+}
+
+/* }}} */
+
+/* {{{ mp_int_mul(a, b, c) */
+
+mp_result mp_int_mul(mp_int a, mp_int b, mp_int c)
+{ 
+  mp_digit *out;
+  mp_size   osize, ua, ub, p = 0;
+  mp_sign   osign;
+
+  CHECK(a != NULL && b != NULL && c != NULL);
+
+  /* If either input is zero, we can shortcut multiplication */
+  if(mp_int_compare_zero(a) == 0 || mp_int_compare_zero(b) == 0) {
+    mp_int_zero(c);
+    return MP_OK;
+  }
+  
+  /* Output is positive if inputs have same sign, otherwise negative */
+  osign = (MP_SIGN(a) == MP_SIGN(b)) ? MP_ZPOS : MP_NEG;
+
+  /* If the output is not identical to any of the inputs, we'll write
+     the results directly; otherwise, allocate a temporary space. */
+  ua = MP_USED(a); ub = MP_USED(b);
+  osize = MAX(ua, ub);
+  osize = 4 * ((osize + 1) / 2);
+
+  if(c == a || c == b) {
+    p = ROUND_PREC(osize);
+    p = MAX(p, default_precision);
+
+    if((out = s_alloc(p)) == NULL)
+      return MP_MEMORY;
+  } 
+  else {
+    if(!s_pad(c, osize))
+      return MP_MEMORY;
+    
+    out = MP_DIGITS(c);
+  }
+  ZERO(out, osize);
+
+  if(!s_kmul(MP_DIGITS(a), MP_DIGITS(b), out, ua, ub))
+    return MP_MEMORY;
+
+  /* If we allocated a new buffer, get rid of whatever memory c was
+     already using, and fix up its fields to reflect that.
+   */
+  if(out != MP_DIGITS(c)) {
+    if((void *) MP_DIGITS(c) != (void *) c)
+      s_free(MP_DIGITS(c));
+    MP_DIGITS(c) = out;
+    MP_ALLOC(c) = p;
+  }
+
+  MP_USED(c) = osize; /* might not be true, but we'll fix it ... */
+  CLAMP(c);           /* ... right here */
+  MP_SIGN(c) = osign;
+  
+  return MP_OK;
+}
+
+/* }}} */
+
+/* {{{ mp_int_mul_value(a, value, c) */
+
+mp_result mp_int_mul_value(mp_int a, int value, mp_int c)
+{
+  mpz_t     vtmp;
+  mp_digit  vbuf[MP_VALUE_DIGITS(value)];
+
+  s_fake(&vtmp, value, vbuf);
+
+  return mp_int_mul(a, &vtmp, c);
+}
+
+/* }}} */
+
+/* {{{ mp_int_mul_pow2(a, p2, c) */
+
+mp_result mp_int_mul_pow2(mp_int a, int p2, mp_int c)
+{
+  mp_result res;
+  CHECK(a != NULL && c != NULL && p2 >= 0);
+
+  if((res = mp_int_copy(a, c)) != MP_OK)
+    return res;
+
+  if(s_qmul(c, (mp_size) p2))
+    return MP_OK;
+  else
+    return MP_MEMORY;
+}
+
+/* }}} */
+
+/* {{{ mp_int_sqr(a, c) */
+
+mp_result mp_int_sqr(mp_int a, mp_int c)
+{ 
+  mp_digit *out;
+  mp_size   osize, p = 0;
+
+  CHECK(a != NULL && c != NULL);
+
+  /* Get a temporary buffer big enough to hold the result */
+  osize = (mp_size) 4 * ((MP_USED(a) + 1) / 2);
+  if(a == c) {
+    p = ROUND_PREC(osize);
+    p = MAX(p, default_precision);
+
+    if((out = s_alloc(p)) == NULL)
+      return MP_MEMORY;
+  } 
+  else {
+    if(!s_pad(c, osize)) 
+      return MP_MEMORY;
+
+    out = MP_DIGITS(c);
+  }
+  ZERO(out, osize);
+
+  s_ksqr(MP_DIGITS(a), out, MP_USED(a));
+
+  /* Get rid of whatever memory c was already using, and fix up its
+     fields to reflect the new digit array it's using
+   */
+  if(out != MP_DIGITS(c)) {
+    if((void *) MP_DIGITS(c) != (void *) c)
+      s_free(MP_DIGITS(c));
+    MP_DIGITS(c) = out;
+    MP_ALLOC(c) = p;
+  }
+
+  MP_USED(c) = osize; /* might not be true, but we'll fix it ... */
+  CLAMP(c);           /* ... right here */
+  MP_SIGN(c) = MP_ZPOS;
+  
+  return MP_OK;
+}
+
+/* }}} */
+
+/* {{{ mp_int_div(a, b, q, r) */
+
+mp_result mp_int_div(mp_int a, mp_int b, mp_int q, mp_int r)
+{
+  int       cmp, last = 0, lg;
+  mp_result res = MP_OK;
+  mpz_t     temp[2];
+  mp_int    qout, rout;
+  mp_sign   sa = MP_SIGN(a), sb = MP_SIGN(b);
+
+  CHECK(a != NULL && b != NULL && q != r);
+  
+  if(CMPZ(b) == 0)
+    return MP_UNDEF;
+  else if((cmp = s_ucmp(a, b)) < 0) {
+    /* If |a| < |b|, no division is required:
+       q = 0, r = a
+     */
+    if(r && (res = mp_int_copy(a, r)) != MP_OK)
+      return res;
+
+    if(q)
+      mp_int_zero(q);
+
+    return MP_OK;
+  } 
+  else if(cmp == 0) {
+    /* If |a| = |b|, no division is required:
+       q = 1 or -1, r = 0
+     */
+    if(r)
+      mp_int_zero(r);
+
+    if(q) {
+      mp_int_zero(q);
+      q->digits[0] = 1;
+
+      if(sa != sb)
+	MP_SIGN(q) = MP_NEG;
+    }
+
+    return MP_OK;
+  } 
+
+  /* When |a| > |b|, real division is required.  We need someplace to
+     store quotient and remainder, but q and r are allowed to be NULL
+     or to overlap with the inputs.
+   */
+  if((lg = s_isp2(b)) < 0) {
+    if(q && b != q && (res = mp_int_copy(a, q)) == MP_OK) {
+      qout = q;
+    } 
+    else {
+      qout = TEMP(last);
+      SETUP(mp_int_init_copy(TEMP(last), a), last);
+    }
+
+    if(r && a != r && (res = mp_int_copy(b, r)) == MP_OK) {
+      rout = r;
+    } 
+    else {
+      rout = TEMP(last);
+      SETUP(mp_int_init_copy(TEMP(last), b), last);
+    }
+
+    if((res = s_udiv(qout, rout)) != MP_OK) goto CLEANUP;
+  } 
+  else {
+    if(q && (res = mp_int_copy(a, q)) != MP_OK) goto CLEANUP;
+    if(r && (res = mp_int_copy(a, r)) != MP_OK) goto CLEANUP;
+
+    if(q) s_qdiv(q, (mp_size) lg); qout = q;
+    if(r) s_qmod(r, (mp_size) lg); rout = r;
+  }
+
+  /* Recompute signs for output */
+  if(rout) { 
+    MP_SIGN(rout) = sa;
+    if(CMPZ(rout) == 0)
+      MP_SIGN(rout) = MP_ZPOS;
+  }
+  if(qout) {
+    MP_SIGN(qout) = (sa == sb) ? MP_ZPOS : MP_NEG;
+    if(CMPZ(qout) == 0)
+      MP_SIGN(qout) = MP_ZPOS;
+  }
+
+  if(q && (res = mp_int_copy(qout, q)) != MP_OK) goto CLEANUP;
+  if(r && (res = mp_int_copy(rout, r)) != MP_OK) goto CLEANUP;
+
+ CLEANUP:
+  while(--last >= 0)
+    mp_int_clear(TEMP(last));
+
+  return res;
+}
+
+/* }}} */
+
+/* {{{ mp_int_mod(a, m, c) */
+
+mp_result mp_int_mod(mp_int a, mp_int m, mp_int c)
+{
+  mp_result res;
+  mpz_t     tmp;
+  mp_int    out;
+
+  if(m == c) {
+    mp_int_init(&tmp);
+    out = &tmp;
+  } 
+  else {
+    out = c;
+  }
+
+  if((res = mp_int_div(a, m, NULL, out)) != MP_OK)
+    goto CLEANUP;
+
+  if(CMPZ(out) < 0)
+    res = mp_int_add(out, m, c);
+  else
+    res = mp_int_copy(out, c);
+
+ CLEANUP:
+  if(out != c)
+    mp_int_clear(&tmp);
+
+  return res;
+}
+
+/* }}} */
+
+/* {{{ mp_int_div_value(a, value, q, r) */
+
+mp_result mp_int_div_value(mp_int a, int value, mp_int q, int *r)
+{
+  mpz_t     vtmp, rtmp;
+  mp_digit  vbuf[MP_VALUE_DIGITS(value)];
+  mp_result res;
+
+  mp_int_init(&rtmp);
+  s_fake(&vtmp, value, vbuf);
+
+  if((res = mp_int_div(a, &vtmp, q, &rtmp)) != MP_OK)
+    goto CLEANUP;
+
+  if(r)
+    (void) mp_int_to_int(&rtmp, r); /* can't fail */
+
+ CLEANUP:
+  mp_int_clear(&rtmp);
+  return res;
+}
+
+/* }}} */
+
+/* {{{ mp_int_div_pow2(a, p2, q, r) */
+
+mp_result mp_int_div_pow2(mp_int a, int p2, mp_int q, mp_int r)
+{
+  mp_result res = MP_OK;
+
+  CHECK(a != NULL && p2 >= 0 && q != r);
+
+  if(q != NULL && (res = mp_int_copy(a, q)) == MP_OK)
+    s_qdiv(q, (mp_size) p2);
+  
+  if(res == MP_OK && r != NULL && (res = mp_int_copy(a, r)) == MP_OK)
+    s_qmod(r, (mp_size) p2);
+
+  return res;
+}
+
+/* }}} */
+
+/* {{{ mp_int_expt(a, b, c) */
+
+mp_result mp_int_expt(mp_int a, int b, mp_int c)
+{
+  mpz_t     t;
+  mp_result res;
+  unsigned int v = abs(b);
+  
+  CHECK(b >= 0 && c != NULL);
+
+  if((res = mp_int_init_copy(&t, a)) != MP_OK)
+    return res;
+
+  (void) mp_int_set_value(c, 1);
+  while(v != 0) {
+    if(v & 1) {
+      if((res = mp_int_mul(c, &t, c)) != MP_OK)
+	goto CLEANUP;
+    }
+
+    v >>= 1;
+    if(v == 0) break;
+
+    if((res = mp_int_sqr(&t, &t)) != MP_OK)
+      goto CLEANUP;
+  }
+  
+ CLEANUP:
+  mp_int_clear(&t);
+  return res;
+}
+
+/* }}} */
+
+/* {{{ mp_int_expt_value(a, b, c) */
+
+mp_result mp_int_expt_value(int a, int b, mp_int c)
+{
+  mpz_t     t;
+  mp_result res;
+  unsigned int v = abs(b);
+  
+  CHECK(b >= 0 && c != NULL);
+
+  if((res = mp_int_init_value(&t, a)) != MP_OK)
+    return res;
+
+  (void) mp_int_set_value(c, 1);
+  while(v != 0) {
+    if(v & 1) {
+      if((res = mp_int_mul(c, &t, c)) != MP_OK)
+	goto CLEANUP;
+    }
+
+    v >>= 1;
+    if(v == 0) break;
+
+    if((res = mp_int_sqr(&t, &t)) != MP_OK)
+      goto CLEANUP;
+  }
+  
+ CLEANUP:
+  mp_int_clear(&t);
+  return res;
+}
+
+/* }}} */
+
+/* {{{ mp_int_compare(a, b) */
+
+int       mp_int_compare(mp_int a, mp_int b)
+{ 
+  mp_sign sa;
+
+  CHECK(a != NULL && b != NULL);
+
+  sa = MP_SIGN(a);
+  if(sa == MP_SIGN(b)) {
+    int cmp = s_ucmp(a, b);
+
+    /* If they're both zero or positive, the normal comparison
+       applies; if both negative, the sense is reversed. */
+    if(sa == MP_ZPOS) 
+      return cmp;
+    else
+      return -cmp;
+
+  } 
+  else {
+    if(sa == MP_ZPOS)
+      return 1;
+    else
+      return -1;
+  }
+}
+
+/* }}} */
+
+/* {{{ mp_int_compare_unsigned(a, b) */
+
+int       mp_int_compare_unsigned(mp_int a, mp_int b)
+{ 
+  NRCHECK(a != NULL && b != NULL);
+
+  return s_ucmp(a, b);
+}
+
+/* }}} */
+
+/* {{{ mp_int_compare_zero(z) */
+
+int       mp_int_compare_zero(mp_int z)
+{ 
+  NRCHECK(z != NULL);
+
+  if(MP_USED(z) == 1 && z->digits[0] == 0)
+    return 0;
+  else if(MP_SIGN(z) == MP_ZPOS)
+    return 1;
+  else 
+    return -1;
+}
+
+/* }}} */
+
+/* {{{ mp_int_compare_value(z, value) */
+
+int       mp_int_compare_value(mp_int z, int value)
+{
+  mp_sign vsign = (value < 0) ? MP_NEG : MP_ZPOS;
+  int     cmp;
+
+  CHECK(z != NULL);
+
+  if(vsign == MP_SIGN(z)) {
+    cmp = s_vcmp(z, value);
+
+    if(vsign == MP_ZPOS)
+      return cmp;
+    else
+      return -cmp;
+  } 
+  else {
+    if(value < 0)
+      return 1;
+    else
+      return -1;
+  }
+}
+
+/* }}} */
+
+/* {{{ mp_int_exptmod(a, b, m, c) */
+
+mp_result mp_int_exptmod(mp_int a, mp_int b, mp_int m, mp_int c)
+{ 
+  mp_result res;
+  mp_size   um;
+  mpz_t     temp[3];
+  mp_int    s;
+  int       last = 0;
+
+  CHECK(a != NULL && b != NULL && c != NULL && m != NULL);
+
+  /* Zero moduli and negative exponents are not considered. */
+  if(CMPZ(m) == 0)
+    return MP_UNDEF;
+  if(CMPZ(b) < 0)
+    return MP_RANGE;
+
+  um = MP_USED(m);
+  SETUP(mp_int_init_size(TEMP(0), 2 * um), last);
+  SETUP(mp_int_init_size(TEMP(1), 2 * um), last);
+
+  if(c == b || c == m) {
+    SETUP(mp_int_init_size(TEMP(2), 2 * um), last);
+    s = TEMP(2);
+  } 
+  else {
+    s = c;
+  }
+  
+  if((res = mp_int_mod(a, m, TEMP(0))) != MP_OK) goto CLEANUP;
+
+  if((res = s_brmu(TEMP(1), m)) != MP_OK) goto CLEANUP;
+
+  if((res = s_embar(TEMP(0), b, m, TEMP(1), s)) != MP_OK)
+    goto CLEANUP;
+
+  res = mp_int_copy(s, c);
+
+ CLEANUP:
+  while(--last >= 0)
+    mp_int_clear(TEMP(last));
+
+  return res;
+}
+
+/* }}} */
+
+/* {{{ mp_int_exptmod_evalue(a, value, m, c) */
+
+mp_result mp_int_exptmod_evalue(mp_int a, int value, mp_int m, mp_int c)
+{
+  mpz_t    vtmp;
+  mp_digit vbuf[MP_VALUE_DIGITS(value)];
+
+  s_fake(&vtmp, value, vbuf);
+
+  return mp_int_exptmod(a, &vtmp, m, c);
+}
+
+/* }}} */
+
+/* {{{ mp_int_exptmod_bvalue(v, b, m, c) */
+
+mp_result mp_int_exptmod_bvalue(int value, mp_int b,
+				mp_int m, mp_int c)
+{
+  mpz_t    vtmp;
+  mp_digit vbuf[MP_VALUE_DIGITS(value)];
+
+  s_fake(&vtmp, value, vbuf);
+
+  return mp_int_exptmod(&vtmp, b, m, c);
+}
+
+/* }}} */
+
+/* {{{ mp_int_exptmod_known(a, b, m, mu, c) */
+
+mp_result mp_int_exptmod_known(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c)
+{
+  mp_result res;
+  mp_size   um;
+  mpz_t     temp[2];
+  mp_int    s;
+  int       last = 0;
+
+  CHECK(a && b && m && c);
+
+  /* Zero moduli and negative exponents are not considered. */
+  if(CMPZ(m) == 0)
+    return MP_UNDEF;
+  if(CMPZ(b) < 0)
+    return MP_RANGE;
+
+  um = MP_USED(m);
+  SETUP(mp_int_init_size(TEMP(0), 2 * um), last);
+
+  if(c == b || c == m) {
+    SETUP(mp_int_init_size(TEMP(1), 2 * um), last);
+    s = TEMP(1);
+  } 
+  else {
+    s = c;
+  }
+  
+  if((res = mp_int_mod(a, m, TEMP(0))) != MP_OK) goto CLEANUP;
+
+  if((res = s_embar(TEMP(0), b, m, mu, s)) != MP_OK)
+    goto CLEANUP;
+
+  res = mp_int_copy(s, c);
+
+ CLEANUP:
+  while(--last >= 0)
+    mp_int_clear(TEMP(last));
+
+  return res;
+}
+
+/* }}} */
+
+/* {{{ mp_int_redux_const(m, c) */
+
+mp_result mp_int_redux_const(mp_int m, mp_int c)
+{
+  CHECK(m != NULL && c != NULL && m != c);
+
+  return s_brmu(c, m);
+}
+
+/* }}} */
+
+/* {{{ mp_int_invmod(a, m, c) */
+
+mp_result mp_int_invmod(mp_int a, mp_int m, mp_int c)
+{
+  mp_result res;
+  mp_sign   sa;
+  int       last = 0;
+  mpz_t     temp[2];
+
+  CHECK(a != NULL && m != NULL && c != NULL);
+
+  if(CMPZ(a) == 0 || CMPZ(m) <= 0)
+    return MP_RANGE;
+
+  sa = MP_SIGN(a); /* need this for the result later */
+
+  for(last = 0; last < 2; ++last)
+    mp_int_init(TEMP(last));
+
+  if((res = mp_int_egcd(a, m, TEMP(0), TEMP(1), NULL)) != MP_OK) 
+    goto CLEANUP;
+
+  if(mp_int_compare_value(TEMP(0), 1) != 0) {
+    res = MP_UNDEF;
+    goto CLEANUP;
+  }
+
+  /* It is first necessary to constrain the value to the proper range */
+  if((res = mp_int_mod(TEMP(1), m, TEMP(1))) != MP_OK)
+    goto CLEANUP;
+
+  /* Now, if 'a' was originally negative, the value we have is
+     actually the magnitude of the negative representative; to get the
+     positive value we have to subtract from the modulus.  Otherwise,
+     the value is okay as it stands.
+   */
+  if(sa == MP_NEG)
+    res = mp_int_sub(m, TEMP(1), c);
+  else
+    res = mp_int_copy(TEMP(1), c);
+
+ CLEANUP:
+  while(--last >= 0)
+    mp_int_clear(TEMP(last));
+
+  return res;
+}
+
+/* }}} */
+
+/* {{{ mp_int_gcd(a, b, c) */
+
+/* Binary GCD algorithm due to Josef Stein, 1961 */
+mp_result mp_int_gcd(mp_int a, mp_int b, mp_int c)
+{ 
+  int       ca, cb, k = 0;
+  mpz_t     u, v, t;
+  mp_result res;
+
+  CHECK(a != NULL && b != NULL && c != NULL);
+
+  ca = CMPZ(a);
+  cb = CMPZ(b);
+  if(ca == 0 && cb == 0)
+    return MP_UNDEF;
+  else if(ca == 0) 
+    return mp_int_abs(b, c);
+  else if(cb == 0) 
+    return mp_int_abs(a, c);
+
+  mp_int_init(&t);
+  if((res = mp_int_init_copy(&u, a)) != MP_OK)
+    goto U;
+  if((res = mp_int_init_copy(&v, b)) != MP_OK)
+    goto V;
+
+  MP_SIGN(&u) = MP_ZPOS; MP_SIGN(&v) = MP_ZPOS;
+
+  { /* Divide out common factors of 2 from u and v */
+    int div2_u = s_dp2k(&u), div2_v = s_dp2k(&v);
+   
+    k = MIN(div2_u, div2_v);
+    s_qdiv(&u, (mp_size) k);
+    s_qdiv(&v, (mp_size) k);
+  }
+  
+  if(mp_int_is_odd(&u)) {
+    if((res = mp_int_neg(&v, &t)) != MP_OK)
+      goto CLEANUP;
+  } 
+  else {
+    if((res = mp_int_copy(&u, &t)) != MP_OK)
+      goto CLEANUP;
+  }
+
+  for(;;) {
+    s_qdiv(&t, s_dp2k(&t));
+
+    if(CMPZ(&t) > 0) {
+      if((res = mp_int_copy(&t, &u)) != MP_OK)
+	goto CLEANUP;
+    } 
+    else {
+      if((res = mp_int_neg(&t, &v)) != MP_OK)
+	goto CLEANUP;
+    }
+
+    if((res = mp_int_sub(&u, &v, &t)) != MP_OK)
+      goto CLEANUP;
+
+    if(CMPZ(&t) == 0)
+      break;
+  } 
+
+  if((res = mp_int_abs(&u, c)) != MP_OK)
+    goto CLEANUP;
+  if(!s_qmul(c, (mp_size) k))
+    res = MP_MEMORY;
+  
+ CLEANUP:
+  mp_int_clear(&v);
+ V: mp_int_clear(&u);
+ U: mp_int_clear(&t);
+
+  return res;
+}
+
+/* }}} */
+
+/* {{{ mp_int_egcd(a, b, c, x, y) */
+
+/* This is the binary GCD algorithm again, but this time we keep track
+   of the elementary matrix operations as we go, so we can get values
+   x and y satisfying c = ax + by.
+ */
+mp_result mp_int_egcd(mp_int a, mp_int b, mp_int c, 
+		      mp_int x, mp_int y)
+{ 
+  int       k, last = 0, ca, cb;
+  mpz_t     temp[8];
+  mp_result res;
+  
+  CHECK(a != NULL && b != NULL && c != NULL && 
+	(x != NULL || y != NULL));
+
+  ca = CMPZ(a);
+  cb = CMPZ(b);
+  if(ca == 0 && cb == 0)
+    return MP_UNDEF;
+  else if(ca == 0) {
+    if((res = mp_int_abs(b, c)) != MP_OK) return res;
+    mp_int_zero(x); (void) mp_int_set_value(y, 1); return MP_OK;
+  } 
+  else if(cb == 0) {
+    if((res = mp_int_abs(a, c)) != MP_OK) return res;
+    (void) mp_int_set_value(x, 1); mp_int_zero(y); return MP_OK;
+  }
+
+  /* Initialize temporaries:
+     A:0, B:1, C:2, D:3, u:4, v:5, ou:6, ov:7 */
+  for(last = 0; last < 4; ++last) 
+    mp_int_init(TEMP(last));
+  TEMP(0)->digits[0] = 1;
+  TEMP(3)->digits[0] = 1;
+
+  SETUP(mp_int_init_copy(TEMP(4), a), last);
+  SETUP(mp_int_init_copy(TEMP(5), b), last);
+
+  /* We will work with absolute values here */
+  MP_SIGN(TEMP(4)) = MP_ZPOS;
+  MP_SIGN(TEMP(5)) = MP_ZPOS;
+
+  { /* Divide out common factors of 2 from u and v */
+    int  div2_u = s_dp2k(TEMP(4)), div2_v = s_dp2k(TEMP(5));
+    
+    k = MIN(div2_u, div2_v);
+    s_qdiv(TEMP(4), k);
+    s_qdiv(TEMP(5), k);
+  }
+
+  SETUP(mp_int_init_copy(TEMP(6), TEMP(4)), last);
+  SETUP(mp_int_init_copy(TEMP(7), TEMP(5)), last);
+
+  for(;;) {
+    while(mp_int_is_even(TEMP(4))) {
+      s_qdiv(TEMP(4), 1);
+      
+      if(mp_int_is_odd(TEMP(0)) || mp_int_is_odd(TEMP(1))) {
+	if((res = mp_int_add(TEMP(0), TEMP(7), TEMP(0))) != MP_OK) 
+	  goto CLEANUP;
+	if((res = mp_int_sub(TEMP(1), TEMP(6), TEMP(1))) != MP_OK) 
+	  goto CLEANUP;
+      }
+
+      s_qdiv(TEMP(0), 1);
+      s_qdiv(TEMP(1), 1);
+    }
+    
+    while(mp_int_is_even(TEMP(5))) {
+      s_qdiv(TEMP(5), 1);
+
+      if(mp_int_is_odd(TEMP(2)) || mp_int_is_odd(TEMP(3))) {
+	if((res = mp_int_add(TEMP(2), TEMP(7), TEMP(2))) != MP_OK) 
+	  goto CLEANUP;
+	if((res = mp_int_sub(TEMP(3), TEMP(6), TEMP(3))) != MP_OK) 
+	  goto CLEANUP;
+      }
+
+      s_qdiv(TEMP(2), 1);
+      s_qdiv(TEMP(3), 1);
+    }
+
+    if(mp_int_compare(TEMP(4), TEMP(5)) >= 0) {
+      if((res = mp_int_sub(TEMP(4), TEMP(5), TEMP(4))) != MP_OK) goto CLEANUP;
+      if((res = mp_int_sub(TEMP(0), TEMP(2), TEMP(0))) != MP_OK) goto CLEANUP;
+      if((res = mp_int_sub(TEMP(1), TEMP(3), TEMP(1))) != MP_OK) goto CLEANUP;
+    } 
+    else {
+      if((res = mp_int_sub(TEMP(5), TEMP(4), TEMP(5))) != MP_OK) goto CLEANUP;
+      if((res = mp_int_sub(TEMP(2), TEMP(0), TEMP(2))) != MP_OK) goto CLEANUP;
+      if((res = mp_int_sub(TEMP(3), TEMP(1), TEMP(3))) != MP_OK) goto CLEANUP;
+    }
+
+    if(CMPZ(TEMP(4)) == 0) {
+      if(x && (res = mp_int_copy(TEMP(2), x)) != MP_OK) goto CLEANUP;
+      if(y && (res = mp_int_copy(TEMP(3), y)) != MP_OK) goto CLEANUP;
+      if(c) {
+	if(!s_qmul(TEMP(5), k)) {
+	  res = MP_MEMORY;
+	  goto CLEANUP;
+	}
+	 
+	res = mp_int_copy(TEMP(5), c);
+      }
+
+      break;
+    }
+  }
+
+ CLEANUP:
+  while(--last >= 0)
+    mp_int_clear(TEMP(last));
+
+  return res;
+}
+
+/* }}} */
+
+/* {{{ mp_int_divisible_value(a, v) */
+
+int       mp_int_divisible_value(mp_int a, int v)
+{
+  int       rem = 0;
+
+  if(mp_int_div_value(a, v, NULL, &rem) != MP_OK)
+    return 0;
+
+  return rem == 0;
+}
+
+/* }}} */
+
+/* {{{ mp_int_is_pow2(z) */
+
+int       mp_int_is_pow2(mp_int z)
+{
+  CHECK(z != NULL);
+
+  return s_isp2(z);
+}
+
+/* }}} */
+
+/* {{{ mp_int_sqrt(a, c) */
+
+mp_result mp_int_sqrt(mp_int a, mp_int c)
+{
+  mp_result  res = MP_OK;
+  mpz_t      temp[2];
+  int        last = 0;
+
+  CHECK(a != NULL && c != NULL);
+
+  /* The square root of a negative value does not exist in the integers. */
+  if(MP_SIGN(a) == MP_NEG)
+    return MP_UNDEF;
+
+  SETUP(mp_int_init_copy(TEMP(last), a), last);
+  SETUP(mp_int_init(TEMP(last)), last);
+
+  for(;;) {
+    if((res = mp_int_sqr(TEMP(0), TEMP(1))) != MP_OK)
+      goto CLEANUP;
+
+    if(mp_int_compare_unsigned(a, TEMP(1)) == 0) break;
+
+    if((res = mp_int_copy(a, TEMP(1))) != MP_OK) 
+      goto CLEANUP;
+    if((res = mp_int_div(TEMP(1), TEMP(0), TEMP(1), NULL)) != MP_OK) 
+      goto CLEANUP;
+    if((res = mp_int_add(TEMP(0), TEMP(1), TEMP(1))) != MP_OK) 
+      goto CLEANUP;
+    if((res = mp_int_div_pow2(TEMP(1), 1, TEMP(1), NULL)) != MP_OK)
+      goto CLEANUP;
+
+    if(mp_int_compare_unsigned(TEMP(0), TEMP(1)) == 0) break;
+    if((res = mp_int_sub_value(TEMP(0), 1, TEMP(0))) != MP_OK) goto CLEANUP;
+    if(mp_int_compare_unsigned(TEMP(0), TEMP(1)) == 0) break;
+
+    if((res = mp_int_copy(TEMP(1), TEMP(0))) != MP_OK) goto CLEANUP;
+  }
+  
+  res = mp_int_copy(TEMP(0), c);
+
+ CLEANUP:
+  while(--last >= 0)
+    mp_int_clear(TEMP(last));
+  
+  return res;
+}
+
+/* }}} */
+
+/* {{{ mp_int_to_int(z, out) */
+
+mp_result mp_int_to_int(mp_int z, int *out)
+{
+  unsigned int uv = 0;
+  mp_size   uz;
+  mp_digit *dz;
+  mp_sign   sz;
+
+  CHECK(z != NULL);
+
+  /* Make sure the value is representable as an int */
+  sz = MP_SIGN(z);
+  if((sz == MP_ZPOS && mp_int_compare_value(z, INT_MAX) > 0) ||
+     mp_int_compare_value(z, INT_MIN) < 0)
+    return MP_RANGE;
+     
+  uz = MP_USED(z);
+  dz = MP_DIGITS(z) + uz - 1;
+  
+  while(uz > 0) {
+    uv <<= MP_DIGIT_BIT/2;
+    uv = (uv << (MP_DIGIT_BIT/2)) | *dz--;
+    --uz;
+  }
+
+  if(out)
+    *out = (sz == MP_NEG) ? -(int)uv : (int)uv;
+
+  return MP_OK;
+}
+
+/* }}} */
+
+/* {{{ mp_int_to_string(z, radix, str, limit) */
+
+mp_result mp_int_to_string(mp_int z, mp_size radix, 
+			   char *str, int limit)
+{
+  mp_result res;
+  int       cmp = 0;
+
+  CHECK(z != NULL && str != NULL && limit >= 2);
+
+  if(radix < MP_MIN_RADIX || radix > MP_MAX_RADIX)
+    return MP_RANGE;
+
+  if(CMPZ(z) == 0) {
+    *str++ = s_val2ch(0, 1);
+  } 
+  else {
+    mpz_t tmp;
+    char  *h, *t;
+
+    if((res = mp_int_init_copy(&tmp, z)) != MP_OK)
+      return res;
+
+    if(MP_SIGN(z) == MP_NEG) {
+      *str++ = '-';
+      --limit;
+    }
+    h = str;
+
+    /* Generate digits in reverse order until finished or limit reached */
+    for(/* */; limit > 0; --limit) {
+      mp_digit d;
+
+      if((cmp = CMPZ(&tmp)) == 0)
+	break;
+
+      d = s_ddiv(&tmp, (mp_digit)radix);
+      *str++ = s_val2ch(d, 1);
+    }
+    t = str - 1;
+
+    /* Put digits back in correct output order */
+    while(h < t) {
+      char tc = *h;
+      *h++ = *t;
+      *t-- = tc;
+    }
+
+    mp_int_clear(&tmp);
+  }
+
+  *str = '\0';
+  if(cmp == 0)
+    return MP_OK;
+  else
+    return MP_TRUNC;
+}
+
+/* }}} */
+
+/* {{{ mp_int_string_len(z, radix) */
+
+mp_result mp_int_string_len(mp_int z, mp_size radix)
+{ 
+  int  len;
+
+  CHECK(z != NULL);
+
+  if(radix < MP_MIN_RADIX || radix > MP_MAX_RADIX)
+    return MP_RANGE;
+
+  len = s_outlen(z, radix) + 1; /* for terminator */
+
+  /* Allow for sign marker on negatives */
+  if(MP_SIGN(z) == MP_NEG)
+    len += 1;
+
+  return len;
+}
+
+/* }}} */
+
+/* {{{ mp_int_read_string(z, radix, *str) */
+
+/* Read zero-terminated string into z */
+mp_result mp_int_read_string(mp_int z, mp_size radix, const char *str)
+{
+  return mp_int_read_cstring(z, radix, str, NULL);
+
+}
+
+/* }}} */
+
+/* {{{ mp_int_read_cstring(z, radix, *str, **end) */
+
+mp_result mp_int_read_cstring(mp_int z, mp_size radix, const char *str, char **end)
+{ 
+  int       ch;
+
+  CHECK(z != NULL && str != NULL);
+
+  if(radix < MP_MIN_RADIX || radix > MP_MAX_RADIX)
+    return MP_RANGE;
+
+  /* Skip leading whitespace */
+  while(isspace((int)*str))
+    ++str;
+
+  /* Handle leading sign tag (+/-, positive default) */
+  switch(*str) {
+  case '-':
+    MP_SIGN(z) = MP_NEG;
+    ++str;
+    break;
+  case '+':
+    ++str; /* fallthrough */
+  default:
+    MP_SIGN(z) = MP_ZPOS;
+    break;
+  }
+
+  /* Skip leading zeroes */
+  while((ch = s_ch2val(*str, radix)) == 0) 
+    ++str;
+
+  /* Make sure there is enough space for the value */
+  if(!s_pad(z, s_inlen(strlen(str), radix)))
+    return MP_MEMORY;
+
+  MP_USED(z) = 1; z->digits[0] = 0;
+
+  while(*str != '\0' && ((ch = s_ch2val(*str, radix)) >= 0)) {
+    s_dmul(z, (mp_digit)radix);
+    s_dadd(z, (mp_digit)ch);
+    ++str;
+  }
+  
+  CLAMP(z);
+
+  /* Override sign for zero, even if negative specified. */
+  if(CMPZ(z) == 0)
+    MP_SIGN(z) = MP_ZPOS;
+  
+  if(end != NULL)
+    *end = (char *)str;
+
+  /* Return a truncation error if the string has unprocessed
+     characters remaining, so the caller can tell if the whole string
+     was done */
+  if(*str != '\0') 
+    return MP_TRUNC;
+  else
+    return MP_OK;
+}
+
+/* }}} */
+
+/* {{{ mp_int_count_bits(z) */
+
+mp_result mp_int_count_bits(mp_int z)
+{
+  mp_size  nbits = 0, uz;
+  mp_digit d;
+
+  CHECK(z != NULL);
+
+  uz = MP_USED(z);
+  if(uz == 1 && z->digits[0] == 0)
+    return 1;
+
+  --uz;
+  nbits = uz * MP_DIGIT_BIT;
+  d = z->digits[uz];
+
+  while(d != 0) {
+    d >>= 1;
+    ++nbits;
+  }
+
+  return nbits;
+}
+
+/* }}} */
+
+/* {{{ mp_int_to_binary(z, buf, limit) */
+
+mp_result mp_int_to_binary(mp_int z, unsigned char *buf, int limit)
+{
+  static const int PAD_FOR_2C = 1;
+
+  mp_result res;
+  int       limpos = limit;
+
+  CHECK(z != NULL && buf != NULL);
+  
+  res = s_tobin(z, buf, &limpos, PAD_FOR_2C);
+
+  if(MP_SIGN(z) == MP_NEG)
+    s_2comp(buf, limpos);
+
+  return res;
+}
+
+/* }}} */
+
+/* {{{ mp_int_read_binary(z, buf, len) */
+
+mp_result mp_int_read_binary(mp_int z, unsigned char *buf, int len)
+{
+  mp_size need, i;
+  unsigned char *tmp;
+  mp_digit *dz;
+
+  CHECK(z != NULL && buf != NULL && len > 0);
+
+  /* Figure out how many digits are needed to represent this value */
+  need = ((len * CHAR_BIT) + (MP_DIGIT_BIT - 1)) / MP_DIGIT_BIT;
+  if(!s_pad(z, need))
+    return MP_MEMORY;
+
+  mp_int_zero(z);
+
+  /* If the high-order bit is set, take the 2's complement before
+     reading the value (it will be restored afterward) */
+  if(buf[0] >> (CHAR_BIT - 1)) {
+    MP_SIGN(z) = MP_NEG;
+    s_2comp(buf, len);
+  }
+  
+  dz = MP_DIGITS(z);
+  for(tmp = buf, i = len; i > 0; --i, ++tmp) {
+    s_qmul(z, (mp_size) CHAR_BIT);
+    *dz |= *tmp;
+  }
+
+  /* Restore 2's complement if we took it before */
+  if(MP_SIGN(z) == MP_NEG)
+    s_2comp(buf, len);
+
+  return MP_OK;
+}
+
+/* }}} */
+
+/* {{{ mp_int_binary_len(z) */
+
+mp_result mp_int_binary_len(mp_int z)
+{
+  mp_result  res = mp_int_count_bits(z);
+  int        bytes = mp_int_unsigned_len(z);
+
+  if(res <= 0)
+    return res;
+
+  bytes = (res + (CHAR_BIT - 1)) / CHAR_BIT;
+
+  /* If the highest-order bit falls exactly on a byte boundary, we
+     need to pad with an extra byte so that the sign will be read
+     correctly when reading it back in. */
+  if(bytes * CHAR_BIT == res)
+    ++bytes;
+
+  return bytes;
+}
+
+/* }}} */
+
+/* {{{ mp_int_to_unsigned(z, buf, limit) */
+
+mp_result mp_int_to_unsigned(mp_int z, unsigned char *buf, int limit)
+{
+  static const int NO_PADDING = 0;
+
+  CHECK(z != NULL && buf != NULL);
+
+  return s_tobin(z, buf, &limit, NO_PADDING);
+}
+
+/* }}} */
+
+/* {{{ mp_int_read_unsigned(z, buf, len) */
+
+mp_result mp_int_read_unsigned(mp_int z, unsigned char *buf, int len)
+{
+  mp_size need, i;
+  unsigned char *tmp;
+  mp_digit *dz;
+
+  CHECK(z != NULL && buf != NULL && len > 0);
+
+  /* Figure out how many digits are needed to represent this value */
+  need = ((len * CHAR_BIT) + (MP_DIGIT_BIT - 1)) / MP_DIGIT_BIT;
+  if(!s_pad(z, need))
+    return MP_MEMORY;
+
+  mp_int_zero(z);
+
+  dz = MP_DIGITS(z);
+  for(tmp = buf, i = len; i > 0; --i, ++tmp) {
+    (void) s_qmul(z, CHAR_BIT);
+    *dz |= *tmp;
+  }
+
+  return MP_OK;
+}
+
+/* }}} */
+
+/* {{{ mp_int_unsigned_len(z) */
+
+mp_result mp_int_unsigned_len(mp_int z)
+{
+  mp_result  res = mp_int_count_bits(z);
+  int        bytes;
+
+  if(res <= 0)
+    return res;
+
+  bytes = (res + (CHAR_BIT - 1)) / CHAR_BIT;
+
+  return bytes;
+}
+
+/* }}} */
+
+/* {{{ mp_error_string(res) */
+
+const char *mp_error_string(mp_result res)
+{
+  int ix;
+  if(res > 0)
+    return s_unknown_err;
+
+  res = -res;
+  for(ix = 0; ix < res && s_error_msg[ix] != NULL; ++ix)
+    ;
+
+  if(s_error_msg[ix] != NULL)
+    return s_error_msg[ix];
+  else
+    return s_unknown_err;
+}
+
+/* }}} */
+
+/*------------------------------------------------------------------------*/
+/* Private functions for internal use.  These make assumptions.           */
+
+/* {{{ s_alloc(num) */
+
+static mp_digit *s_alloc(mp_size num)
+{
+  mp_digit *out = malloc(num * sizeof(mp_digit));
+
+  assert(out != NULL); /* for debugging */
+#if DEBUG > 1
+  {
+    mp_digit v = (mp_digit) 0xdeadbeef;
+    int      ix;
+
+    for(ix = 0; ix < num; ++ix)
+      out[ix] = v;
+  }
+#endif
+
+  return out;
+}
+
+/* }}} */
+
+/* {{{ s_realloc(old, osize, nsize) */
+
+static mp_digit *s_realloc(mp_digit *old, mp_size osize, mp_size nsize)
+{
+#if DEBUG > 1
+  mp_digit *new = s_alloc(nsize);
+  int       ix;
+
+  for(ix = 0; ix < nsize; ++ix)
+    new[ix] = (mp_digit) 0xdeadbeef;
+
+  memcpy(new, old, osize * sizeof(mp_digit));
+#else
+  mp_digit *new = realloc(old, nsize * sizeof(mp_digit));
+
+  assert(new != NULL); /* for debugging */
+#endif
+  return new;
+}
+
+/* }}} */
+
+/* {{{ s_free(ptr) */
+
+static void s_free(void *ptr)
+{
+  free(ptr);
+}
+
+/* }}} */
+
+/* {{{ s_pad(z, min) */
+
+static int      s_pad(mp_int z, mp_size min)
+{
+  if(MP_ALLOC(z) < min) {
+    mp_size nsize = ROUND_PREC(min);
+    mp_digit *tmp;
+
+    if((void *)z->digits == (void *)z) {
+      if((tmp = s_alloc(nsize)) == NULL)
+        return 0;
+
+      COPY(MP_DIGITS(z), tmp, MP_USED(z));
+    }
+    else if((tmp = s_realloc(MP_DIGITS(z), MP_ALLOC(z), nsize)) == NULL)
+      return 0;
+    
+    MP_DIGITS(z) = tmp;
+    MP_ALLOC(z) = nsize;
+  }
+
+  return 1;
+}
+
+/* }}} */
+
+/* {{{ s_clamp(z) */
+
+#if TRACEABLE_CLAMP
+static void     s_clamp(mp_int z)
+{
+  mp_size   uz = MP_USED(z);
+  mp_digit *zd = MP_DIGITS(z) + uz - 1;
+
+  while(uz > 1 && (*zd-- == 0))
+    --uz;
+
+  MP_USED(z) = uz;
+}
+#endif
+
+/* }}} */
+
+/* {{{ s_fake(z, value, vbuf) */
+
+static void      s_fake(mp_int z, int value, mp_digit vbuf[])
+{
+  mp_size uv = (mp_size) s_vpack(value, vbuf);
+
+  z->used = uv;
+  z->alloc = MP_VALUE_DIGITS(value);
+  z->sign = (value < 0) ? MP_NEG : MP_ZPOS;
+  z->digits = vbuf;
+}
+
+/* }}} */
+
+/* {{{ s_cdig(da, db, len) */
+
+static int      s_cdig(mp_digit *da, mp_digit *db, mp_size len)
+{
+  mp_digit *dat = da + len - 1, *dbt = db + len - 1;
+
+  for(/* */; len != 0; --len, --dat, --dbt) {
+    if(*dat > *dbt)
+      return 1;
+    else if(*dat < *dbt)
+      return -1;
+  }
+
+  return 0;
+}
+
+/* }}} */
+
+/* {{{ s_vpack(v, t[]) */
+
+static int       s_vpack(int v, mp_digit t[])
+{
+  unsigned int uv = (unsigned int)((v < 0) ? -v : v);
+  int          ndig = 0;
+  
+  if(uv == 0)
+    t[ndig++] = 0;
+  else {
+    while(uv != 0) {
+      t[ndig++] = (mp_digit) uv;
+      uv >>= MP_DIGIT_BIT/2;
+      uv >>= MP_DIGIT_BIT/2;
+    }
+  }
+
+  return ndig;
+}
+
+/* }}} */
+
+/* {{{ s_ucmp(a, b) */
+
+static int      s_ucmp(mp_int a, mp_int b)
+{
+  mp_size  ua = MP_USED(a), ub = MP_USED(b);
+  
+  if(ua > ub)
+    return 1;
+  else if(ub > ua) 
+    return -1;
+  else 
+    return s_cdig(MP_DIGITS(a), MP_DIGITS(b), ua);
+}
+
+/* }}} */
+
+/* {{{ s_vcmp(a, v) */
+
+static int      s_vcmp(mp_int a, int v)
+{
+  mp_digit     vdig[MP_VALUE_DIGITS(v)];
+  int          ndig = 0;
+  mp_size      ua = MP_USED(a);
+
+  ndig = s_vpack(v, vdig);
+
+  if(ua > ndig)
+    return 1;
+  else if(ua < ndig)
+    return -1;
+  else
+    return s_cdig(MP_DIGITS(a), vdig, ndig);
+}
+
+/* }}} */
+
+/* {{{ s_uadd(da, db, dc, size_a, size_b) */
+
+static mp_digit s_uadd(mp_digit *da, mp_digit *db, mp_digit *dc, 
+		       mp_size size_a, mp_size size_b)
+{
+  mp_size pos;
+  mp_word w = 0;
+
+  /* Insure that da is the longer of the two to simplify later code */
+  if(size_b > size_a) {
+    SWAP(mp_digit *, da, db);
+    SWAP(mp_size, size_a, size_b);
+  }
+
+  /* Add corresponding digits until the shorter number runs out */
+  for(pos = 0; pos < size_b; ++pos, ++da, ++db, ++dc) {
+    w = w + (mp_word) *da + (mp_word) *db;
+    *dc = LOWER_HALF(w);
+    w = UPPER_HALF(w);
+  }
+
+  /* Propagate carries as far as necessary */
+  for(/* */; pos < size_a; ++pos, ++da, ++dc) {
+    w = w + *da;
+
+    *dc = LOWER_HALF(w);
+    w = UPPER_HALF(w);
+  }
+
+  /* Return carry out */
+  return (mp_digit)w;
+}
+
+/* }}} */
+
+/* {{{ s_usub(da, db, dc, size_a, size_b) */
+
+static void     s_usub(mp_digit *da, mp_digit *db, mp_digit *dc,
+		       mp_size size_a, mp_size size_b)
+{
+  mp_size pos;
+  mp_word w = 0;
+
+  /* We assume that |a| >= |b| so this should definitely hold */
+  assert(size_a >= size_b);
+
+  /* Subtract corresponding digits and propagate borrow */
+  for(pos = 0; pos < size_b; ++pos, ++da, ++db, ++dc) {
+    w = ((mp_word)MP_DIGIT_MAX + 1 +  /* MP_RADIX */
+	 (mp_word)*da) - w - (mp_word)*db;
+
+    *dc = LOWER_HALF(w);
+    w = (UPPER_HALF(w) == 0);
+  }
+
+  /* Finish the subtraction for remaining upper digits of da */
+  for(/* */; pos < size_a; ++pos, ++da, ++dc) {
+    w = ((mp_word)MP_DIGIT_MAX + 1 +  /* MP_RADIX */
+	 (mp_word)*da) - w; 
+
+    *dc = LOWER_HALF(w);
+    w = (UPPER_HALF(w) == 0);
+  }
+
+  /* If there is a borrow out at the end, it violates the precondition */
+  assert(w == 0);
+}
+
+/* }}} */
+
+/* {{{ s_kmul(da, db, dc, size_a, size_b) */
+
+static int       s_kmul(mp_digit *da, mp_digit *db, mp_digit *dc,
+			mp_size size_a, mp_size size_b)
+{
+  mp_size  bot_size;
+
+  /* Make sure b is the smaller of the two input values */
+  if(size_b > size_a) {
+    SWAP(mp_digit *, da, db);
+    SWAP(mp_size, size_a, size_b);
+  }
+
+  /* Insure that the bottom is the larger half in an odd-length split;
+     the code below relies on this being true.
+   */
+  bot_size = (size_a + 1) / 2;
+
+  /* If the values are big enough to bother with recursion, use the
+     Karatsuba algorithm to compute the product; otherwise use the
+     normal multiplication algorithm
+   */
+  if(multiply_threshold && 
+     size_a >= multiply_threshold && 
+     size_b > bot_size) {
+
+    mp_digit *t1, *t2, *t3, carry;
+
+    mp_digit *a_top = da + bot_size; 
+    mp_digit *b_top = db + bot_size;
+
+    mp_size  at_size = size_a - bot_size;
+    mp_size  bt_size = size_b - bot_size;
+    mp_size  buf_size = 2 * bot_size;
+
+    /* Do a single allocation for all three temporary buffers needed;
+       each buffer must be big enough to hold the product of two
+       bottom halves, and one buffer needs space for the completed 
+       product; twice the space is plenty.
+     */
+    if((t1 = s_alloc(4 * buf_size)) == NULL) return 0;
+    t2 = t1 + buf_size;
+    t3 = t2 + buf_size;
+    ZERO(t1, 4 * buf_size);
+
+    /* t1 and t2 are initially used as temporaries to compute the inner product
+       (a1 + a0)(b1 + b0) = a1b1 + a1b0 + a0b1 + a0b0
+     */
+    carry = s_uadd(da, a_top, t1, bot_size, at_size);      /* t1 = a1 + a0 */
+    t1[bot_size] = carry;
+
+    carry = s_uadd(db, b_top, t2, bot_size, bt_size);      /* t2 = b1 + b0 */
+    t2[bot_size] = carry;
+
+    (void) s_kmul(t1, t2, t3, bot_size + 1, bot_size + 1); /* t3 = t1 * t2 */
+
+    /* Now we'll get t1 = a0b0 and t2 = a1b1, and subtract them out so that
+       we're left with only the pieces we want:  t3 = a1b0 + a0b1
+     */
+    ZERO(t1, buf_size);
+    ZERO(t2, buf_size);
+    (void) s_kmul(da, db, t1, bot_size, bot_size);     /* t1 = a0 * b0 */
+    (void) s_kmul(a_top, b_top, t2, at_size, bt_size); /* t2 = a1 * b1 */
+
+    /* Subtract out t1 and t2 to get the inner product */
+    s_usub(t3, t1, t3, buf_size + 2, buf_size);
+    s_usub(t3, t2, t3, buf_size + 2, buf_size);
+
+    /* Assemble the output value */
+    COPY(t1, dc, buf_size);
+    carry = s_uadd(t3, dc + bot_size, dc + bot_size,
+		   buf_size + 1, buf_size); 
+    assert(carry == 0);
+    
+    carry = s_uadd(t2, dc + 2*bot_size, dc + 2*bot_size,
+		   buf_size, buf_size); 
+    assert(carry == 0);
+    
+    s_free(t1); /* note t2 and t3 are just internal pointers to t1 */
+  } 
+  else {
+    s_umul(da, db, dc, size_a, size_b);
+  }
+
+  return 1;
+}
+
+/* }}} */
+
+/* {{{ s_umul(da, db, dc, size_a, size_b) */
+
+static void     s_umul(mp_digit *da, mp_digit *db, mp_digit *dc,
+		       mp_size size_a, mp_size size_b)
+{
+  mp_size   a, b;
+  mp_word   w;
+
+  for(a = 0; a < size_a; ++a, ++dc, ++da) {
+    mp_digit *dct = dc;
+    mp_digit *dbt = db;
+
+    if(*da == 0)
+      continue;
+
+    w = 0;
+    for(b = 0; b < size_b; ++b, ++dbt, ++dct) {
+      w = (mp_word)*da * (mp_word)*dbt + w + (mp_word)*dct;
+
+      *dct = LOWER_HALF(w);
+      w = UPPER_HALF(w);
+    }
+
+    *dct = (mp_digit)w;
+  }
+}
+
+/* }}} */
+
+/* {{{ s_ksqr(da, dc, size_a) */
+
+static int       s_ksqr(mp_digit *da, mp_digit *dc, mp_size size_a)
+{
+  if(multiply_threshold && size_a > multiply_threshold) {
+    mp_size    bot_size = (size_a + 1) / 2;
+    mp_digit  *a_top = da + bot_size;
+    mp_digit  *t1, *t2, *t3, carry;
+    mp_size    at_size = size_a - bot_size;
+    mp_size    buf_size = 2 * bot_size;
+
+    if((t1 = s_alloc(4 * buf_size)) == NULL) return 0;
+    t2 = t1 + buf_size;
+    t3 = t2 + buf_size;
+    ZERO(t1, 4 * buf_size);
+
+    (void) s_ksqr(da, t1, bot_size);    /* t1 = a0 ^ 2 */
+    (void) s_ksqr(a_top, t2, at_size);  /* t2 = a1 ^ 2 */
+
+    (void) s_kmul(da, a_top, t3, bot_size, at_size);  /* t3 = a0 * a1 */
+
+    /* Quick multiply t3 by 2, shifting left (can't overflow) */
+    {
+      int     i, top = bot_size + at_size;
+      mp_word w, save = 0;
+
+      for(i = 0; i < top; ++i) {
+	w = t3[i];
+	w = (w << 1) | save;
+	t3[i] = LOWER_HALF(w);
+	save = UPPER_HALF(w);
+      }
+      t3[i] = LOWER_HALF(save);
+    }
+
+    /* Assemble the output value */
+    COPY(t1, dc, 2 * bot_size);
+    carry = s_uadd(t3, dc + bot_size, dc + bot_size,
+		   buf_size + 1, buf_size);
+    assert(carry == 0);
+
+    carry = s_uadd(t2, dc + 2*bot_size, dc + 2*bot_size,
+		   buf_size, buf_size);
+    assert(carry == 0);
+
+    s_free(t1); /* note that t2 and t2 are internal pointers only */
+
+  } 
+  else {
+    s_usqr(da, dc, size_a);
+  }
+
+  return 1;
+}
+
+/* }}} */
+
+/* {{{ s_usqr(da, dc, size_a) */
+
+static void      s_usqr(mp_digit *da, mp_digit *dc, mp_size size_a)
+{
+  mp_size  i, j;
+  mp_word  w;
+
+  for(i = 0; i < size_a; ++i, dc += 2, ++da) {
+    mp_digit  *dct = dc, *dat = da;
+
+    if(*da == 0)
+      continue;
+
+    /* Take care of the first digit, no rollover */
+    w = (mp_word)*dat * (mp_word)*dat + (mp_word)*dct;
+    *dct = LOWER_HALF(w);
+    w = UPPER_HALF(w);
+    ++dat; ++dct;
+
+    for(j = i + 1; j < size_a; ++j, ++dat, ++dct) {
+      mp_word  t = (mp_word)*da * (mp_word)*dat;
+      mp_word  u = w + (mp_word)*dct, ov = 0;
+
+      /* Check if doubling t will overflow a word */
+      if(HIGH_BIT_SET(t))
+	ov = 1;
+
+      w = t + t;
+
+      /* Check if adding u to w will overflow a word */
+      if(ADD_WILL_OVERFLOW(w, u))
+	ov = 1;
+
+      w += u;
+
+      *dct = LOWER_HALF(w);
+      w = UPPER_HALF(w);
+      if(ov) {
+	w += MP_DIGIT_MAX; /* MP_RADIX */
+	++w;
+      }
+    }
+
+    w = w + *dct;
+    *dct = (mp_digit)w; 
+    while((w = UPPER_HALF(w)) != 0) {
+      ++dct; w = w + *dct;
+      *dct = LOWER_HALF(w);
+    }
+
+    assert(w == 0);
+  }
+}
+
+/* }}} */
+
+/* {{{ s_dadd(a, b) */
+
+static void      s_dadd(mp_int a, mp_digit b)
+{
+  mp_word   w = 0;
+  mp_digit *da = MP_DIGITS(a);
+  mp_size   ua = MP_USED(a);
+
+  w = (mp_word)*da + b;
+  *da++ = LOWER_HALF(w);
+  w = UPPER_HALF(w);
+
+  for(ua -= 1; ua > 0; --ua, ++da) {
+    w = (mp_word)*da + w;
+
+    *da = LOWER_HALF(w);
+    w = UPPER_HALF(w);
+  }
+
+  if(w) {
+    *da = (mp_digit)w;
+    MP_USED(a) += 1;
+  }
+}
+
+/* }}} */
+
+/* {{{ s_dmul(a, b) */
+
+static void      s_dmul(mp_int a, mp_digit b)
+{
+  mp_word   w = 0;
+  mp_digit *da = MP_DIGITS(a);
+  mp_size   ua = MP_USED(a);
+
+  while(ua > 0) {
+    w = (mp_word)*da * b + w;
+    *da++ = LOWER_HALF(w);
+    w = UPPER_HALF(w);
+    --ua;
+  }
+
+  if(w) {
+    *da = (mp_digit)w;
+    MP_USED(a) += 1;
+  }
+}
+
+/* }}} */
+
+/* {{{ s_dbmul(da, b, dc, size_a) */
+
+static void      s_dbmul(mp_digit *da, mp_digit b, mp_digit *dc, mp_size size_a)
+{
+  mp_word  w = 0;
+
+  while(size_a > 0) {
+    w = (mp_word)*da++ * (mp_word)b + w;
+
+    *dc++ = LOWER_HALF(w);
+    w = UPPER_HALF(w);
+    --size_a;
+  }
+
+  if(w)
+    *dc = LOWER_HALF(w);
+}
+
+/* }}} */
+
+/* {{{ s_ddiv(da, d, dc, size_a) */
+
+static mp_digit  s_ddiv(mp_int a, mp_digit b)
+{
+  mp_word   w = 0, qdigit;
+  mp_size   ua = MP_USED(a);
+  mp_digit *da = MP_DIGITS(a) + ua - 1;
+  
+  for(/* */; ua > 0; --ua, --da) {
+    w = (w << MP_DIGIT_BIT) | *da;
+
+    if(w >= b) {
+      qdigit = w / b;
+      w = w % b;
+    } 
+    else {
+      qdigit = 0;
+    }
+      
+    *da = (mp_digit)qdigit;
+  }
+
+  CLAMP(a);
+  return (mp_digit)w;
+}
+
+/* }}} */
+
+/* {{{ s_qdiv(z, p2) */
+
+static void     s_qdiv(mp_int z, mp_size p2)
+{
+  mp_size ndig = p2 / MP_DIGIT_BIT, nbits = p2 % MP_DIGIT_BIT;
+  mp_size uz = MP_USED(z);
+
+  if(ndig) {
+    mp_size  mark;
+    mp_digit *to, *from;
+
+    if(ndig >= uz) {
+      mp_int_zero(z);
+      return;
+    }
+
+    to = MP_DIGITS(z); from = to + ndig;
+
+    for(mark = ndig; mark < uz; ++mark) 
+      *to++ = *from++;
+
+    MP_USED(z) = uz - ndig;
+  }
+
+  if(nbits) {
+    mp_digit d = 0, *dz, save;
+    mp_size  up = MP_DIGIT_BIT - nbits;
+
+    uz = MP_USED(z);
+    dz = MP_DIGITS(z) + uz - 1;
+
+    for(/* */; uz > 0; --uz, --dz) {
+      save = *dz;
+
+      *dz = (*dz >> nbits) | (d << up);
+      d = save;
+    }
+
+    CLAMP(z);
+  }
+
+  if(MP_USED(z) == 1 && z->digits[0] == 0)
+    MP_SIGN(z) = MP_ZPOS;
+}
+
+/* }}} */
+
+/* {{{ s_qmod(z, p2) */
+
+static void     s_qmod(mp_int z, mp_size p2)
+{
+  mp_size   start = p2 / MP_DIGIT_BIT + 1, rest = p2 % MP_DIGIT_BIT;
+  mp_size   uz = MP_USED(z);
+  mp_digit  mask = (1 << rest) - 1;
+
+  if(start <= uz) {
+    MP_USED(z) = start;
+    z->digits[start - 1] &= mask;
+    CLAMP(z);
+  }
+}
+
+/* }}} */
+
+/* {{{ s_qmul(z, p2) */
+
+static int      s_qmul(mp_int z, mp_size p2)
+{
+  mp_size   uz, need, rest, extra, i;
+  mp_digit *from, *to, d;
+
+  if(p2 == 0)
+    return 1;
+
+  uz = MP_USED(z); 
+  need = p2 / MP_DIGIT_BIT; rest = p2 % MP_DIGIT_BIT;
+
+  /* Figure out if we need an extra digit at the top end; this occurs
+     if the topmost `rest' bits of the high-order digit of z are not
+     zero, meaning they will be shifted off the end if not preserved */
+  extra = 0;
+  if(rest != 0) {
+    mp_digit *dz = MP_DIGITS(z) + uz - 1;
+
+    if((*dz >> (MP_DIGIT_BIT - rest)) != 0)
+      extra = 1;
+  }
+
+  if(!s_pad(z, uz + need + extra))
+    return 0;
+
+  /* If we need to shift by whole digits, do that in one pass, then
+     to back and shift by partial digits.
+   */
+  if(need > 0) {
+    from = MP_DIGITS(z) + uz - 1;
+    to = from + need;
+
+    for(i = 0; i < uz; ++i)
+      *to-- = *from--;
+
+    ZERO(MP_DIGITS(z), need);
+    uz += need;
+  }
+
+  if(rest) {
+    d = 0;
+    for(i = need, from = MP_DIGITS(z) + need; i < uz; ++i, ++from) {
+      mp_digit save = *from;
+      
+      *from = (*from << rest) | (d >> (MP_DIGIT_BIT - rest));
+      d = save;
+    }
+
+    d >>= (MP_DIGIT_BIT - rest);
+    if(d != 0) {
+      *from = d;
+      uz += extra;
+    }
+  }
+
+  MP_USED(z) = uz;
+  CLAMP(z);
+
+  return 1;
+}
+
+/* }}} */
+
+/* {{{ s_qsub(z, p2) */
+
+/* Compute z = 2^p2 - |z|; requires that 2^p2 >= |z|
+   The sign of the result is always zero/positive.
+ */
+static int       s_qsub(mp_int z, mp_size p2)
+{
+  mp_digit hi = (1 << (p2 % MP_DIGIT_BIT)), *zp;
+  mp_size  tdig = (p2 / MP_DIGIT_BIT), pos;
+  mp_word  w = 0;
+
+  if(!s_pad(z, tdig + 1))
+    return 0;
+
+  for(pos = 0, zp = MP_DIGITS(z); pos < tdig; ++pos, ++zp) {
+    w = ((mp_word) MP_DIGIT_MAX + 1) - w - (mp_word)*zp;
+
+    *zp = LOWER_HALF(w);
+    w = UPPER_HALF(w) ? 0 : 1;
+  }
+
+  w = ((mp_word) MP_DIGIT_MAX + 1 + hi) - w - (mp_word)*zp;
+  *zp = LOWER_HALF(w);
+
+  assert(UPPER_HALF(w) != 0); /* no borrow out should be possible */
+  
+  MP_SIGN(z) = MP_ZPOS;
+  CLAMP(z);
+
+  return 1;
+}
+
+/* }}} */
+
+/* {{{ s_dp2k(z) */
+
+static int      s_dp2k(mp_int z)
+{
+  int       k = 0;
+  mp_digit *dp = MP_DIGITS(z), d;
+
+  if(MP_USED(z) == 1 && *dp == 0)
+    return 1;
+
+  while(*dp == 0) {
+    k += MP_DIGIT_BIT;
+    ++dp;
+  }
+  
+  d = *dp;
+  while((d & 1) == 0) {
+    d >>= 1;
+    ++k;
+  }
+
+  return k;
+}
+
+/* }}} */
+
+/* {{{ s_isp2(z) */
+
+static int       s_isp2(mp_int z)
+{
+  mp_size uz = MP_USED(z), k = 0;
+  mp_digit *dz = MP_DIGITS(z), d;
+
+  while(uz > 1) {
+    if(*dz++ != 0)
+      return -1;
+    k += MP_DIGIT_BIT;
+    --uz;
+  }
+
+  d = *dz;
+  while(d > 1) {
+    if(d & 1)
+      return -1;
+    ++k; d >>= 1;
+  }
+
+  return (int) k;
+}
+
+/* }}} */
+
+/* {{{ s_2expt(z, k) */
+
+static int       s_2expt(mp_int z, int k)
+{
+  mp_size  ndig, rest;
+  mp_digit *dz;
+
+  ndig = (k + MP_DIGIT_BIT) / MP_DIGIT_BIT;
+  rest = k % MP_DIGIT_BIT;
+
+  if(!s_pad(z, ndig))
+    return 0;
+
+  dz = MP_DIGITS(z);
+  ZERO(dz, ndig);
+  *(dz + ndig - 1) = (1 << rest);
+  MP_USED(z) = ndig;
+
+  return 1;
+}
+
+/* }}} */
+
+/* {{{ s_norm(a, b) */
+
+static int      s_norm(mp_int a, mp_int b)
+{
+  mp_digit d = b->digits[MP_USED(b) - 1];
+  int      k = 0;
+
+  while(d < (mp_digit) (1 << (MP_DIGIT_BIT - 1))) { /* d < (MP_RADIX / 2) */
+    d <<= 1;
+    ++k;
+  }
+
+  /* These multiplications can't fail */
+  if(k != 0) {
+    (void) s_qmul(a, (mp_size) k);
+    (void) s_qmul(b, (mp_size) k);
+  }
+
+  return k;
+}
+
+/* }}} */
+
+/* {{{ s_brmu(z, m) */
+
+static mp_result s_brmu(mp_int z, mp_int m)
+{
+  mp_size um = MP_USED(m) * 2;
+
+  if(!s_pad(z, um))
+    return MP_MEMORY;
+
+  s_2expt(z, MP_DIGIT_BIT * um);
+  return mp_int_div(z, m, z, NULL);
+}
+
+/* }}} */
+
+/* {{{ s_reduce(x, m, mu, q1, q2) */
+
+static int       s_reduce(mp_int x, mp_int m, mp_int mu, mp_int q1, mp_int q2)
+{
+  mp_size   um = MP_USED(m), umb_p1, umb_m1;
+
+  umb_p1 = (um + 1) * MP_DIGIT_BIT;
+  umb_m1 = (um - 1) * MP_DIGIT_BIT;
+
+  if(mp_int_copy(x, q1) != MP_OK)
+    return 0;
+
+  /* Compute q2 = floor((floor(x / b^(k-1)) * mu) / b^(k+1)) */
+  s_qdiv(q1, umb_m1);
+  UMUL(q1, mu, q2);
+  s_qdiv(q2, umb_p1);
+
+  /* Set x = x mod b^(k+1) */
+  s_qmod(x, umb_p1);
+
+  /* Now, q is a guess for the quotient a / m.
+     Compute x - q * m mod b^(k+1), replacing x.  This may be off
+     by a factor of 2m, but no more than that.
+   */
+  UMUL(q2, m, q1);
+  s_qmod(q1, umb_p1);
+  (void) mp_int_sub(x, q1, x); /* can't fail */
+
+  /* The result may be < 0; if it is, add b^(k+1) to pin it in the
+     proper range. */
+  if((CMPZ(x) < 0) && !s_qsub(x, umb_p1))
+    return 0;
+
+  /* If x > m, we need to back it off until it is in range.
+     This will be required at most twice.  */
+  if(mp_int_compare(x, m) >= 0) {
+    (void) mp_int_sub(x, m, x);
+    if(mp_int_compare(x, m) >= 0)
+      (void) mp_int_sub(x, m, x);
+  }
+
+  /* At this point, x has been properly reduced. */
+  return 1;
+}
+
+/* }}} */
+
+/* {{{ s_embar(a, b, m, mu, c) */
+
+/* Perform modular exponentiation using Barrett's method, where mu is
+   the reduction constant for m.  Assumes a < m, b > 0. */
+static mp_result s_embar(mp_int a, mp_int b, mp_int m, mp_int mu, mp_int c)
+{
+  mp_digit  *db, *dbt, umu, d;
+  mpz_t     temp[3]; 
+  mp_result res;
+  int       last = 0;
+
+  umu = MP_USED(mu); db = MP_DIGITS(b); dbt = db + MP_USED(b) - 1;
+
+  while(last < 3) {
+    SETUP(mp_int_init_size(TEMP(last), 4 * umu), last);
+    ZERO(MP_DIGITS(TEMP(last - 1)), MP_ALLOC(TEMP(last - 1)));
+  }
+
+  (void) mp_int_set_value(c, 1);
+
+  /* Take care of low-order digits */
+  while(db < dbt) {
+    int      i;
+
+    for(d = *db, i = MP_DIGIT_BIT; i > 0; --i, d >>= 1) {
+      if(d & 1) {
+	/* The use of a second temporary avoids allocation */
+	UMUL(c, a, TEMP(0));
+	if(!s_reduce(TEMP(0), m, mu, TEMP(1), TEMP(2))) {
+	  res = MP_MEMORY; goto CLEANUP;
+	}
+	mp_int_copy(TEMP(0), c);
+      }
+
+
+      USQR(a, TEMP(0));
+      assert(MP_SIGN(TEMP(0)) == MP_ZPOS);
+      if(!s_reduce(TEMP(0), m, mu, TEMP(1), TEMP(2))) {
+	res = MP_MEMORY; goto CLEANUP;
+      }
+      assert(MP_SIGN(TEMP(0)) == MP_ZPOS);
+      mp_int_copy(TEMP(0), a);
+
+
+    }
+
+    ++db;
+  }
+
+  /* Take care of highest-order digit */
+  d = *dbt;
+  for(;;) {
+    if(d & 1) {
+      UMUL(c, a, TEMP(0));
+      if(!s_reduce(TEMP(0), m, mu, TEMP(1), TEMP(2))) {
+	res = MP_MEMORY; goto CLEANUP;
+      }
+      mp_int_copy(TEMP(0), c);
+    }
+    
+    d >>= 1;
+    if(!d) break;
+
+    USQR(a, TEMP(0));
+    if(!s_reduce(TEMP(0), m, mu, TEMP(1), TEMP(2))) {
+      res = MP_MEMORY; goto CLEANUP;
+    }
+    (void) mp_int_copy(TEMP(0), a);
+  }
+
+ CLEANUP:
+  while(--last >= 0)
+    mp_int_clear(TEMP(last));
+  
+  return res;
+}
+
+/* }}} */
+
+/* {{{ s_udiv(a, b) */
+
+/* Precondition:  a >= b and b > 0
+   Postcondition: a' = a / b, b' = a % b
+ */
+static mp_result s_udiv(mp_int a, mp_int b)
+{
+  mpz_t     q, r, t;
+  mp_size   ua, ub, qpos = 0;
+  mp_digit *da, btop;
+  mp_result res = MP_OK;
+  int       k, skip = 0;
+
+  /* Force signs to positive */
+  MP_SIGN(a) = MP_ZPOS;
+  MP_SIGN(b) = MP_ZPOS;
+
+  /* Normalize, per Knuth */
+  k = s_norm(a, b);
+
+  ua = MP_USED(a); ub = MP_USED(b); btop = b->digits[ub - 1];
+  if((res = mp_int_init_size(&q, ua)) != MP_OK) return res;
+  if((res = mp_int_init_size(&t, ua + 1)) != MP_OK) goto CLEANUP;
+
+  da = MP_DIGITS(a);
+  r.digits = da + ua - 1;  /* The contents of r are shared with a */
+  r.used   = 1;
+  r.sign   = MP_ZPOS;
+  r.alloc  = MP_ALLOC(a);
+  ZERO(t.digits, t.alloc);
+
+  /* Solve for quotient digits, store in q.digits in reverse order */
+  while(r.digits >= da) {
+    assert(qpos <= q.alloc);
+
+    if(s_ucmp(b, &r) > 0) {
+      r.digits -= 1;
+      r.used += 1;
+      
+      if(++skip > 1 && qpos > 0) 
+	q.digits[qpos++] = 0;
+      
+      CLAMP(&r);
+    }
+    else {
+      mp_word  pfx = r.digits[r.used - 1];
+      mp_word  qdigit;
+      
+      if(r.used > 1 && pfx <= btop) {
+	pfx <<= MP_DIGIT_BIT / 2;
+	pfx <<= MP_DIGIT_BIT / 2;
+	pfx |= r.digits[r.used - 2];
+      }
+
+      qdigit = pfx / btop;
+      if(qdigit > MP_DIGIT_MAX) {
+	if(qdigit & MP_DIGIT_MAX)
+	  qdigit = MP_DIGIT_MAX;
+	else
+	  qdigit = 1;
+      }
+      
+      s_dbmul(MP_DIGITS(b), (mp_digit) qdigit, t.digits, ub);
+      t.used = ub + 1; CLAMP(&t);
+      while(s_ucmp(&t, &r) > 0) {
+	--qdigit;
+	(void) mp_int_sub(&t, b, &t); /* cannot fail */
+      }
+      
+      s_usub(r.digits, t.digits, r.digits, r.used, t.used);
+      CLAMP(&r);
+      
+      q.digits[qpos++] = (mp_digit) qdigit;
+      ZERO(t.digits, t.used);
+      skip = 0;
+    }
+  }
+
+  /* Put quotient digits in the correct order, and discard extra zeroes */
+  q.used = qpos;
+  REV(mp_digit, q.digits, qpos);
+  CLAMP(&q);
+
+  /* Denormalize the remainder */
+  CLAMP(a);
+  if(k != 0)
+    s_qdiv(a, k);
+  
+  mp_int_copy(a, b);  /* ok:  0 <= r < b */
+  mp_int_copy(&q, a); /* ok:  q <= a     */
+  
+  mp_int_clear(&t);
+ CLEANUP:
+  mp_int_clear(&q);
+  return res;
+}
+
+/* }}} */
+
+/* {{{ s_outlen(z, r) */
+
+/* Precondition:  2 <= r < 64 */
+static int       s_outlen(mp_int z, mp_size r)
+{
+  mp_result  bits;
+  double     raw;
+
+  bits = mp_int_count_bits(z);
+  raw = (double)bits * s_log2[r];
+
+  return (int)(raw + 0.999999);
+}
+
+/* }}} */
+
+/* {{{ s_inlen(len, r) */
+
+static mp_size   s_inlen(int len, mp_size r)
+{
+  double  raw = (double)len / s_log2[r];
+  mp_size bits = (mp_size)(raw + 0.5);
+
+  return (mp_size)((bits + (MP_DIGIT_BIT - 1)) / MP_DIGIT_BIT);
+}
+
+/* }}} */
+
+/* {{{ s_ch2val(c, r) */
+
+static int       s_ch2val(char c, int r)
+{
+  int out;
+
+  if(isdigit((unsigned char) c))
+    out = c - '0';
+  else if(r > 10 && isalpha((unsigned char) c))
+    out = toupper(c) - 'A' + 10;
+  else
+    return -1;
+
+  return (out >= r) ? -1 : out;
+}
+
+/* }}} */
+
+/* {{{ s_val2ch(v, caps) */
+
+static char      s_val2ch(int v, int caps)
+{
+  assert(v >= 0);
+
+  if(v < 10)
+    return v + '0';
+  else {
+    char out = (v - 10) + 'a';
+
+    if(caps)
+      return toupper(out);
+    else
+      return out;
+  }
+}
+
+/* }}} */
+
+/* {{{ s_2comp(buf, len) */
+
+static void      s_2comp(unsigned char *buf, int len)
+{
+  int i;
+  unsigned short s = 1;
+
+  for(i = len - 1; i >= 0; --i) {
+    unsigned char c = ~buf[i];
+
+    s = c + s;
+    c = s & UCHAR_MAX;
+    s >>= CHAR_BIT;
+
+    buf[i] = c;
+  }
+
+  /* last carry out is ignored */
+}
+
+/* }}} */
+
+/* {{{ s_tobin(z, buf, *limpos) */
+
+static mp_result s_tobin(mp_int z, unsigned char *buf, int *limpos, int pad)
+{
+  mp_size uz;
+  mp_digit *dz;
+  int pos = 0, limit = *limpos;
+
+  uz = MP_USED(z); dz = MP_DIGITS(z);
+  while(uz > 0 && pos < limit) {
+    mp_digit d = *dz++;
+    int i;
+
+    for(i = sizeof(mp_digit); i > 0 && pos < limit; --i) {
+      buf[pos++] = (unsigned char)d;
+      d >>= CHAR_BIT;
+
+      /* Don't write leading zeroes */
+      if(d == 0 && uz == 1)
+	i = 0; /* exit loop without signaling truncation */
+    }
+
+    /* Detect truncation (loop exited with pos >= limit) */
+    if(i > 0) break;
+
+    --uz;
+  }
+
+  if(pad != 0 && (buf[pos - 1] >> (CHAR_BIT - 1))) {
+    if(pos < limit)
+      buf[pos++] = 0;
+    else
+      uz = 1;
+  }
+
+  /* Digits are in reverse order, fix that */
+  REV(unsigned char, buf, pos);
+
+  /* Return the number of bytes actually written */
+  *limpos = pos;
+
+  return (uz == 0) ? MP_OK : MP_TRUNC;
+}
+
+/* }}} */
+
+/* {{{ s_print(tag, z) */
+
+#if DEBUG
+void      s_print(char *tag, mp_int z)
+{
+  int  i;
+
+  fprintf(stderr, "%s: %c ", tag,
+	  (MP_SIGN(z) == MP_NEG) ? '-' : '+');
+
+  for(i = MP_USED(z) - 1; i >= 0; --i)
+    fprintf(stderr, "%0*X", (int)(MP_DIGIT_BIT / 4), z->digits[i]);
+
+  fputc('\n', stderr);
+
+}
+
+void      s_print_buf(char *tag, mp_digit *buf, mp_size num)
+{
+  int  i;
+
+  fprintf(stderr, "%s: ", tag);
+
+  for(i = num - 1; i >= 0; --i) 
+    fprintf(stderr, "%0*X", (int)(MP_DIGIT_BIT / 4), buf[i]);
+
+  fputc('\n', stderr);
+}
+#endif
+
+/* }}} */
+
+/* HERE THERE BE DRAGONS */
diff --git a/source4/heimdal/lib/hcrypto/imath/imath.h b/source4/heimdal/lib/hcrypto/imath/imath.h
new file mode 100755
index 0000000000..f13c09d1a2
--- /dev/null
+++ b/source4/heimdal/lib/hcrypto/imath/imath.h
@@ -0,0 +1,220 @@
+/*
+  Name:     imath.h
+  Purpose:  Arbitrary precision integer arithmetic routines.
+  Author:   M. J. Fromberger <http://www.dartmouth.edu/~sting/>
+  Info:     $Id: imath.h 20764 2007-06-01 03:55:14Z lha $
+
+  Copyright (C) 2002-2007 Michael J. Fromberger, All Rights Reserved.
+
+  Permission is hereby granted, free of charge, to any person
+  obtaining a copy of this software and associated documentation files
+  (the "Software"), to deal in the Software without restriction,
+  including without limitation the rights to use, copy, modify, merge,
+  publish, distribute, sublicense, and/or sell copies of the Software,
+  and to permit persons to whom the Software is furnished to do so,
+  subject to the following conditions:
+
+  The above copyright notice and this permission notice shall be
+  included in all copies or substantial portions of the Software.
+
+  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+  MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+  NONINFRINGEMENT.  IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+  BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+  ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+  CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+  SOFTWARE.
+ */
+
+#ifndef IMATH_H_
+#define IMATH_H_
+
+#include <limits.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+typedef unsigned char      mp_sign;
+typedef unsigned int       mp_size;
+typedef int                mp_result;
+#ifdef USE_LONG_LONG
+typedef unsigned int       mp_digit;
+typedef unsigned long long mp_word;
+#else
+typedef unsigned short     mp_digit;
+typedef unsigned int       mp_word;
+#endif
+
+typedef struct mpz {
+  mp_digit    single;
+  mp_digit   *digits;
+  mp_size     alloc;
+  mp_size     used;
+  mp_sign     sign;
+} mpz_t, *mp_int;
+
+#define MP_DIGITS(Z) ((Z)->digits)
+#define MP_ALLOC(Z)  ((Z)->alloc)
+#define MP_USED(Z)   ((Z)->used)
+#define MP_SIGN(Z)   ((Z)->sign)
+
+extern const mp_result MP_OK;
+extern const mp_result MP_FALSE;
+extern const mp_result MP_TRUE;
+extern const mp_result MP_MEMORY;
+extern const mp_result MP_RANGE;
+extern const mp_result MP_UNDEF;
+extern const mp_result MP_TRUNC;
+extern const mp_result MP_BADARG;
+
+#define MP_DIGIT_BIT    (sizeof(mp_digit) * CHAR_BIT)
+#define MP_WORD_BIT     (sizeof(mp_word) * CHAR_BIT)
+
+#ifdef USE_LONG_LONG
+#  ifndef ULONG_LONG_MAX
+#    ifdef ULLONG_MAX
+#      define ULONG_LONG_MAX   ULLONG_MAX
+#    else
+#      error "Maximum value of unsigned long long not defined!"
+#    endif
+#  endif
+#  define MP_DIGIT_MAX   (ULONG_MAX * 1ULL)
+#  define MP_WORD_MAX    ULONG_LONG_MAX
+#else
+#  define MP_DIGIT_MAX    (USHRT_MAX * 1UL)
+#  define MP_WORD_MAX     (UINT_MAX * 1UL)
+#endif
+
+#define MP_MIN_RADIX    2
+#define MP_MAX_RADIX    36
+
+/* Values with fewer than this many significant digits use the
+   standard multiplication algorithm; otherwise, a recursive algorithm
+   is used.  Choose a value to suit your platform.  
+ */
+#define MP_MULT_THRESH  22
+
+#define MP_DEFAULT_PREC 8   /* default memory allocation, in digits */
+
+extern const mp_sign   MP_NEG;
+extern const mp_sign   MP_ZPOS;
+
+#define mp_int_is_odd(Z)  ((Z)->digits[0] & 1)
+#define mp_int_is_even(Z) !((Z)->digits[0] & 1)
+
+mp_result mp_int_init(mp_int z);
+mp_int    mp_int_alloc(void);
+mp_result mp_int_init_size(mp_int z, mp_size prec);
+mp_result mp_int_init_copy(mp_int z, mp_int old);
+mp_result mp_int_init_value(mp_int z, int value);
+mp_result mp_int_set_value(mp_int z, int value);
+void      mp_int_clear(mp_int z);
+void      mp_int_free(mp_int z);
+
+mp_result mp_int_copy(mp_int a, mp_int c);           /* c = a     */
+void      mp_int_swap(mp_int a, mp_int c);           /* swap a, c */
+void      mp_int_zero(mp_int z);                     /* z = 0     */
+mp_result mp_int_abs(mp_int a, mp_int c);            /* c = |a|   */
+mp_result mp_int_neg(mp_int a, mp_int c);            /* c = -a    */
+mp_result mp_int_add(mp_int a, mp_int b, mp_int c);  /* c = a + b */
+mp_result mp_int_add_value(mp_int a, int value, mp_int c);
+mp_result mp_int_sub(mp_int a, mp_int b, mp_int c);  /* c = a - b */
+mp_result mp_int_sub_value(mp_int a, int value, mp_int c);
+mp_result mp_int_mul(mp_int a, mp_int b, mp_int c);  /* c = a * b */
+mp_result mp_int_mul_value(mp_int a, int value, mp_int c);
+mp_result mp_int_mul_pow2(mp_int a, int p2, mp_int c);
+mp_result mp_int_sqr(mp_int a, mp_int c);            /* c = a * a */
+mp_result mp_int_div(mp_int a, mp_int b,             /* q = a / b */
+		     mp_int q, mp_int r);            /* r = a % b */
+mp_result mp_int_div_value(mp_int a, int value,      /* q = a / value */
+			   mp_int q, int *r);        /* r = a % value */
+mp_result mp_int_div_pow2(mp_int a, int p2,          /* q = a / 2^p2  */
+			  mp_int q, mp_int r);       /* r = q % 2^p2  */
+mp_result mp_int_mod(mp_int a, mp_int m, mp_int c);  /* c = a % m */
+#define   mp_int_mod_value(A, V, R) mp_int_div_value((A), (V), 0, (R))
+mp_result mp_int_expt(mp_int a, int b, mp_int c);    /* c = a^b   */
+mp_result mp_int_expt_value(int a, int b, mp_int c); /* c = a^b   */
+
+int       mp_int_compare(mp_int a, mp_int b);          /* a <=> b     */
+int       mp_int_compare_unsigned(mp_int a, mp_int b); /* |a| <=> |b| */
+int       mp_int_compare_zero(mp_int z);               /* a <=> 0     */
+int       mp_int_compare_value(mp_int z, int value);   /* a <=> v     */
+
+/* Returns true if v|a, false otherwise (including errors) */
+int       mp_int_divisible_value(mp_int a, int v);
+
+/* Returns k >= 0 such that z = 2^k, if one exists; otherwise < 0 */
+int       mp_int_is_pow2(mp_int z);
+
+mp_result mp_int_exptmod(mp_int a, mp_int b, mp_int m,
+			 mp_int c);                    /* c = a^b (mod m) */
+mp_result mp_int_exptmod_evalue(mp_int a, int value, 
+				mp_int m, mp_int c);   /* c = a^v (mod m) */
+mp_result mp_int_exptmod_bvalue(int value, mp_int b,
+				mp_int m, mp_int c);   /* c = v^b (mod m) */
+mp_result mp_int_exptmod_known(mp_int a, mp_int b,
+			       mp_int m, mp_int mu,
+			       mp_int c);              /* c = a^b (mod m) */
+mp_result mp_int_redux_const(mp_int m, mp_int c); 
+
+mp_result mp_int_invmod(mp_int a, mp_int m, mp_int c); /* c = 1/a (mod m) */
+
+mp_result mp_int_gcd(mp_int a, mp_int b, mp_int c);    /* c = gcd(a, b)   */
+
+mp_result mp_int_egcd(mp_int a, mp_int b, mp_int c,    /* c = gcd(a, b)   */
+		      mp_int x, mp_int y);             /* c = ax + by     */
+
+mp_result mp_int_sqrt(mp_int a, mp_int c);          /* c = floor(sqrt(q)) */
+
+/* Convert to an int, if representable (returns MP_RANGE if not). */
+mp_result mp_int_to_int(mp_int z, int *out);
+
+/* Convert to nul-terminated string with the specified radix, writing at
+   most limit characters including the nul terminator  */
+mp_result mp_int_to_string(mp_int z, mp_size radix, 
+			   char *str, int limit);
+
+/* Return the number of characters required to represent 
+   z in the given radix.  May over-estimate. */
+mp_result mp_int_string_len(mp_int z, mp_size radix);
+
+/* Read zero-terminated string into z */
+mp_result mp_int_read_string(mp_int z, mp_size radix, const char *str);
+mp_result mp_int_read_cstring(mp_int z, mp_size radix, const char *str, 
+			      char **end);
+
+/* Return the number of significant bits in z */
+mp_result mp_int_count_bits(mp_int z);
+
+/* Convert z to two's complement binary, writing at most limit bytes */
+mp_result mp_int_to_binary(mp_int z, unsigned char *buf, int limit);
+
+/* Read a two's complement binary value into z from the given buffer */
+mp_result mp_int_read_binary(mp_int z, unsigned char *buf, int len);
+
+/* Return the number of bytes required to represent z in binary. */
+mp_result mp_int_binary_len(mp_int z);
+
+/* Convert z to unsigned binary, writing at most limit bytes */
+mp_result mp_int_to_unsigned(mp_int z, unsigned char *buf, int limit);
+
+/* Read an unsigned binary value into z from the given buffer */
+mp_result mp_int_read_unsigned(mp_int z, unsigned char *buf, int len);
+
+/* Return the number of bytes required to represent z as unsigned output */
+mp_result mp_int_unsigned_len(mp_int z);
+
+/* Return a statically allocated string describing error code res */
+const char *mp_error_string(mp_result res);
+
+#if DEBUG
+void      s_print(char *tag, mp_int z);
+void      s_print_buf(char *tag, mp_digit *buf, mp_size num);
+#endif
+
+#ifdef __cplusplus
+}
+#endif
+#endif /* end IMATH_H_ */
diff --git a/source4/heimdal/lib/hcrypto/imath/iprime.c b/source4/heimdal/lib/hcrypto/imath/iprime.c
new file mode 100755
index 0000000000..6313bab1b7
--- /dev/null
+++ b/source4/heimdal/lib/hcrypto/imath/iprime.c
@@ -0,0 +1,186 @@
+/*
+  Name:     iprime.c
+  Purpose:  Pseudoprimality testing routines
+  Author:   M. J. Fromberger <http://www.dartmouth.edu/~sting/>
+  Info:     $Id: iprime.c 19737 2007-01-05 21:01:48Z lha $
+
+  Copyright (C) 2002 Michael J. Fromberger, All Rights Reserved.
+
+  Permission is hereby granted, free of charge, to any person
+  obtaining a copy of this software and associated documentation files
+  (the "Software"), to deal in the Software without restriction,
+  including without limitation the rights to use, copy, modify, merge,
+  publish, distribute, sublicense, and/or sell copies of the Software,
+  and to permit persons to whom the Software is furnished to do so,
+  subject to the following conditions:
+
+  The above copyright notice and this permission notice shall be
+  included in all copies or substantial portions of the Software.
+
+  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+  MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+  NONINFRINGEMENT.  IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+  BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+  ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+  CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+  SOFTWARE.
+ */
+
+#include "iprime.h"
+#include <stdlib.h>
+
+static const int s_ptab[] = {
+    3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
+    47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101,
+    103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
+    157, 163, 167, 173, 179, 181, 191, 193, 197, 199,
+    211, 223, 227, 229, 233, 239, 241, 251, 257, 263,
+    269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
+    331, 337, 347, 349, 353, 359, 367, 373, 379, 383,
+    389, 397, 401, 409, 419, 421, 431, 433, 439, 443,
+    449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
+    509, 521, 523, 541, 547, 557, 563, 569, 571, 577,
+    587, 593, 599, 601, 607, 613, 617, 619, 631, 641,
+    643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
+    709, 719, 727, 733, 739, 743, 751, 757, 761, 769,
+    773, 787, 797, 809, 811, 821, 823, 827, 829, 839,
+    853, 857, 859, 863, 877, 881, 883, 887, 907, 911,
+    919, 929, 937, 941, 947, 953, 967, 971, 977, 983,
+    991, 997, 1009, 1013, 1019, 1021, 1031, 1033,
+    1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091,
+    1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151,
+    1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213,
+    1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277,
+    1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307,
+    1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399,
+    1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451,
+    1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493,
+    1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559,
+    1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609,
+    1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667,
+    1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733,
+    1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789,
+    1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871,
+    1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931,
+    1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997,
+    1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053,
+    2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111,
+    2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161,
+    2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243,
+    2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297,
+    2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357,
+    2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411,
+    2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473,
+    2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551,
+    2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633,
+    2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687,
+    2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729,
+    2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791,
+    2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851,
+    2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917,
+    2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999,
+    3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061,
+    3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137,
+    3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209,
+    3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271,
+    3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331,
+    3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391,
+    3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467,
+    3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533,
+    3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583,
+    3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643,
+    3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709,
+    3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779,
+    3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851,
+    3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917,
+    3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989,
+    4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049,
+    4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111,
+    4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177,
+    4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243,
+    4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297,
+    4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391,
+    4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457,
+    4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519,
+    4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597,
+    4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657,
+    4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729,
+    4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799,
+    4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889,
+    4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951,
+    4957, 4967, 4969, 4973, 4987, 4993, 4999
+};
+static const int s_ptab_size = sizeof(s_ptab)/sizeof(s_ptab[0]);
+
+
+/* {{{ mp_int_is_prime(z) */
+
+/* Test whether z is likely to be prime:
+   MP_TRUE  means it is probably prime
+   MP_FALSE means it is definitely composite
+ */
+mp_result mp_int_is_prime(mp_int z)
+{
+  int       i, rem;
+  mp_result res;
+
+  /* First check for divisibility by small primes; this eliminates a
+     large number of composite candidates quickly
+   */
+  for(i = 0; i < s_ptab_size; ++i) {
+    if((res = mp_int_div_value(z, s_ptab[i], NULL, &rem)) != MP_OK)
+      return res;
+
+    if(rem == 0)
+      return MP_FALSE;
+  }
+
+  /* Now try Fermat's test for several prime witnesses (since we now
+     know from the above that z is not a multiple of any of them)
+   */
+  {
+    mpz_t  tmp;
+
+    if((res = mp_int_init(&tmp)) != MP_OK) return res;
+
+    for(i = 0; i < 10 && i < s_ptab_size; ++i) {
+      if((res = mp_int_exptmod_bvalue(s_ptab[i], z, z, &tmp)) != MP_OK)
+	return res;
+
+      if(mp_int_compare_value(&tmp, s_ptab[i]) != 0) {
+	mp_int_clear(&tmp);
+	return MP_FALSE;
+      }
+    }
+
+    mp_int_clear(&tmp);
+  }
+
+  return MP_TRUE;
+}
+
+/* }}} */
+
+/* {{{ mp_int_find_prime(z) */
+
+/* Find the first apparent prime in ascending order from z */
+mp_result mp_int_find_prime(mp_int z)
+{
+  mp_result  res;
+
+  if(mp_int_is_even(z) && ((res = mp_int_add_value(z, 1, z)) != MP_OK))
+    return res;
+
+  while((res = mp_int_is_prime(z)) == MP_FALSE) {
+    if((res = mp_int_add_value(z, 2, z)) != MP_OK)
+      break;
+
+  }
+
+  return res;
+}
+
+/* }}} */
+
+/* Here there be dragons */
diff --git a/source4/heimdal/lib/hcrypto/imath/iprime.h b/source4/heimdal/lib/hcrypto/imath/iprime.h
new file mode 100755
index 0000000000..c935cdc111
--- /dev/null
+++ b/source4/heimdal/lib/hcrypto/imath/iprime.h
@@ -0,0 +1,51 @@
+/*
+  Name:     iprime.h
+  Purpose:  Pseudoprimality testing routines
+  Author:   M. J. Fromberger <http://www.dartmouth.edu/~sting/>
+  Info:     $Id: iprime.h 18759 2006-10-21 16:32:36Z lha $
+
+  Copyright (C) 2002 Michael J. Fromberger, All Rights Reserved.
+
+  Permission is hereby granted, free of charge, to any person
+  obtaining a copy of this software and associated documentation files
+  (the "Software"), to deal in the Software without restriction,
+  including without limitation the rights to use, copy, modify, merge,
+  publish, distribute, sublicense, and/or sell copies of the Software,
+  and to permit persons to whom the Software is furnished to do so,
+  subject to the following conditions:
+
+  The above copyright notice and this permission notice shall be
+  included in all copies or substantial portions of the Software.
+
+  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+  MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
+  NONINFRINGEMENT.  IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
+  BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+  ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
+  CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+  SOFTWARE.
+ */
+
+#ifndef IPRIME_H_
+#define IPRIME_H_
+
+#include "imath.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* Test whether z is likely to be prime
+   MP_YES means it is probably prime
+   MP_NO  means it is definitely composite
+ */
+mp_result mp_int_is_prime(mp_int z);
+
+/* Find the first apparent prime in ascending order from z */
+mp_result mp_int_find_prime(mp_int z);
+
+#ifdef __cplusplus
+}
+#endif
+#endif /* IPRIME_H_ */