added libtommath-0.25

LICENSE

@@ -0,0 +1,4 @@
+LibTomMath is hereby released into the Public Domain.  
+
+-- Tom St Denis
+

bn.tex

@@ -1,7 +1,7 @@
 \documentclass[]{article}
 \begin{document}
 
-\title{LibTomMath v0.24 \\ A Free Multiple Precision Integer Library \\ http://math.libtomcrypt.org }
+\title{LibTomMath v0.25 \\ A Free Multiple Precision Integer Library \\ http://math.libtomcrypt.org }
 \author{Tom St Denis \\ [email protected]}
 \maketitle
 \newpage

bn_error.c

@@ -0,0 +1,41 @@
+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, [email protected], http://math.libtomcrypt.org
+ */
+#include <tommath.h>
+
+static const struct {
+     int code;
+     char *msg;
+} msgs[] = {
+     { MP_OKAY, "Successful" },
+     { MP_MEM,  "Out of heap" },
+     { MP_VAL,  "Value out of range" }
+};
+
+/* return a char * string for a given code */
+char *mp_error_to_string(int code)
+{
+   int x;
+
+   /* scan the lookup table for the given message */
+   for (x = 0; x < (int)(sizeof(msgs) / sizeof(msgs[0])); x++) {
+       if (msgs[x].code == code) {
+          return msgs[x].msg;
+       }
+   }
+
+   /* generic reply for invalid code */
+   return "Invalid error code";
+}
+

bn_fast_mp_invmod.c

@@ -1,9 +1,9 @@
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
  * integer arithmetic as well as number theoretic functionality.
  *
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
  * Michael Fromberger but has been written from scratch with
  * additional optimizations in place.
  *
@@ -26,6 +26,14 @@ fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
   mp_int  x, y, u, v, B, D;
   int     res, neg;
 
+  /* 2. [modified] if a,b are both even then return an error!
+   *
+   * That is if gcd(a,b) = 2**k * q then obviously there is no inverse.
+   */
+  if (mp_iseven (a) == 1 && mp_iseven (b) == 1) {
+    return MP_VAL;
+  }
+
   /* init all our temps */
   if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
      return res;
@@ -41,15 +49,6 @@ fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
     goto __ERR;
   }
 
-  /* 2. [modified] if x,y are both even then return an error! 
-   * 
-   * That is if gcd(x,y) = 2 * k then obviously there is no inverse.
-   */
-  if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) {
-    res = MP_VAL;
-    goto __ERR;
-  }
-
   /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
   if ((res = mp_copy (&x, &u)) != MP_OKAY) {
     goto __ERR;

bn_fast_mp_montgomery_reduce.c

@@ -1,9 +1,9 @@
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
  * integer arithmetic as well as number theoretic functionality.
  *
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
  * Michael Fromberger but has been written from scratch with
  * additional optimizations in place.
  *
@@ -38,6 +38,9 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
     }
   }
 
+  /* first we have to get the digits of the input into
+   * an array of double precision words W[...]
+   */
   {
     register mp_word *_W;
     register mp_digit *tmpx;
@@ -56,6 +59,9 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
     }
   }
 
+  /* now we proceed to zero successive digits
+   * from the least significant upwards
+   */
   for (ix = 0; ix < n->used; ix++) {
     /* mu = ai * m' mod b
      *
@@ -101,12 +107,20 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
     W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
   }
 
+  /* now we have to propagate the carries and
+   * shift the words downward [all those least
+   * significant digits we zeroed].
+   */
   {
     register mp_digit *tmpx;
     register mp_word *_W, *_W1;
 
     /* nox fix rest of carries */
+
+    /* alias for current word */
     _W1 = W + ix;
+
+    /* alias for next word, where the carry goes */
     _W = W + ++ix;
 
     for (; ix <= n->used * 2 + 1; ix++) {
@@ -119,15 +133,20 @@ fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
      * array of mp_word to mp_digit than calling mp_rshd 
      * we just copy them in the right order
      */
+
+    /* alias for destination word */
     tmpx = x->dp;
+
+    /* alias for shifted double precision result */
     _W = W + n->used;
 
     for (ix = 0; ix < n->used + 1; ix++) {
       *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
     }
 
     /* zero oldused digits, if the input a was larger than
-     * m->used+1 we'll have to clear the digits */
+     * m->used+1 we'll have to clear the digits
+     */
     for (; ix < olduse; ix++) {
       *tmpx++ = 0;
     }

bn_fast_s_mp_mul_digs.c

@@ -1,9 +1,9 @@
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
  * integer arithmetic as well as number theoretic functionality.
  *
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
  * Michael Fromberger but has been written from scratch with
  * additional optimizations in place.
  *

bn_fast_s_mp_mul_high_digs.c

@@ -1,9 +1,9 @@
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
  * integer arithmetic as well as number theoretic functionality.
  *
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
  * Michael Fromberger but has been written from scratch with
  * additional optimizations in place.
  *
@@ -12,7 +12,7 @@
  *
  * Tom St Denis, [email protected], http://math.libtomcrypt.org
  */
-#include <tommath.h>
+ #include <tommath.h>
 
 /* this is a modified version of fast_s_mp_mul_digs that only produces
  * output digits *above* digs.  See the comments for fast_s_mp_mul_digs

bn_fast_s_mp_sqr.c

@@ -1,9 +1,9 @@
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
  * integer arithmetic as well as number theoretic functionality.
  *
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
  * Michael Fromberger but has been written from scratch with
  * additional optimizations in place.
  *
@@ -48,14 +48,14 @@ fast_s_mp_sqr (mp_int * a, mp_int * b)
 
   /* zero temp buffer (columns)
    * Note that there are two buffers.  Since squaring requires
-   * a outter and inner product and the inner product requires
+   * a outer and inner product and the inner product requires
    * computing a product and doubling it (a relatively expensive
    * op to perform n**2 times if you don't have to) the inner and
    * outer products are computed in different buffers.  This way
    * the inner product can be doubled using n doublings instead of
    * n**2
    */
-  memset (W, 0, newused * sizeof (mp_word));
+  memset (W,  0, newused * sizeof (mp_word));
   memset (W2, 0, newused * sizeof (mp_word));
 
   /* This computes the inner product.  To simplify the inner N**2 loop
@@ -67,6 +67,7 @@ fast_s_mp_sqr (mp_int * a, mp_int * b)
      * Note that every outer product is computed
      * for a particular column only once which means that
      * there is no need todo a double precision addition
+     * into the W2[] array.
      */
     W2[ix + ix] = ((mp_word)a->dp[ix]) * ((mp_word)a->dp[ix]);
 
@@ -95,7 +96,12 @@ fast_s_mp_sqr (mp_int * a, mp_int * b)
   olduse  = b->used;
   b->used = newused;
 
-  /* now compute digits */
+  /* now compute digits
+   *
+   * We have to double the inner product sums, add in the
+   * outer product sums, propagate carries and convert
+   * to single precision.
+   */
   {
     register mp_digit *tmpb;
 
@@ -109,16 +115,21 @@ fast_s_mp_sqr (mp_int * a, mp_int * b)
       /* double/add next digit */
       W[ix] += W[ix] + W2[ix];
 
+      /* propagate carry forwards [from the previous digit] */
       W[ix] = W[ix] + (W[ix - 1] >> ((mp_word) DIGIT_BIT));
+
+      /* store the current digit now that the carry isn't
+       * needed
+       */
       *tmpb++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
     }
-    /* set the last value.  Note even if the carry is zero 
-     * this is required since the next step will not zero 
+    /* set the last value.  Note even if the carry is zero
+     * this is required since the next step will not zero
      * it if b originally had a value at b->dp[2*a.used]
      */
     *tmpb++ = (mp_digit) (W[(newused) - 1] & ((mp_word) MP_MASK));
 
-    /* clear high digits */
+    /* clear high digits of b if there were any originally */
     for (; ix < olduse; ix++) {
       *tmpb++ = 0;
     }

bn_mp_2expt.c

@@ -1,9 +1,9 @@
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
  * integer arithmetic as well as number theoretic functionality.
  *
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
  * Michael Fromberger but has been written from scratch with
  * additional optimizations in place.
  *
@@ -24,11 +24,18 @@ mp_2expt (mp_int * a, int b)
 {
   int     res;
 
+  /* zero a as per default */
   mp_zero (a);
+
+  /* grow a to accomodate the single bit */
   if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) {
     return res;
   }
+
+  /* set the used count of where the bit will go */
   a->used = b / DIGIT_BIT + 1;
+
+  /* put the single bit in its place */
   a->dp[b / DIGIT_BIT] = 1 << (b % DIGIT_BIT);
 
   return MP_OKAY;

bn_mp_abs.c

@@ -1,9 +1,9 @@
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
  * integer arithmetic as well as number theoretic functionality.
  *
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
  * Michael Fromberger but has been written from scratch with
  * additional optimizations in place.
  *
@@ -22,9 +22,16 @@ int
 mp_abs (mp_int * a, mp_int * b)
 {
   int     res;
-  if ((res = mp_copy (a, b)) != MP_OKAY) {
-    return res;
+
+  /* copy a to b */
+  if (a != b) {
+     if ((res = mp_copy (a, b)) != MP_OKAY) {
+       return res;
+     }
   }
+
+  /* force the sign of b to positive */
   b->sign = MP_ZPOS;
+
   return MP_OKAY;
 }

bn_mp_add.c

@@ -1,9 +1,9 @@
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
  * integer arithmetic as well as number theoretic functionality.
  *
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
  * Michael Fromberger but has been written from scratch with
  * additional optimizations in place.
  *

bn_mp_add_d.c

@@ -1,9 +1,9 @@
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
  * integer arithmetic as well as number theoretic functionality.
  *
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
  * Michael Fromberger but has been written from scratch with
  * additional optimizations in place.
  *
@@ -82,7 +82,11 @@ mp_add_d (mp_int * a, mp_digit b, mp_int * c)
      c->used  = 1;
 
      /* the result is a single digit */
-     *tmpc++  =  b - a->dp[0];
+     if (a->used == 1) {
+        *tmpc++  =  b - a->dp[0];
+     } else {
+        *tmpc++  =  b;
+     }
 
      /* setup count so the clearing of oldused
       * can fall through correctly

bn_mp_addmod.c

@@ -1,9 +1,9 @@
 /* LibTomMath, multiple-precision integer library -- Tom St Denis
  *
- * LibTomMath is library that provides for multiple-precision
+ * LibTomMath is a library that provides multiple-precision
  * integer arithmetic as well as number theoretic functionality.
  *
- * The library is designed directly after the MPI library by
+ * The library was designed directly after the MPI library by
  * Michael Fromberger but has been written from scratch with
  * additional optimizations in place.
  *