--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/bn_mp_exptmod_fast.c	Mon May 31 18:23:46 2004 +0000
@@ -0,0 +1,287 @@
+/* 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>
+
+/* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85
+ *
+ * Uses a left-to-right k-ary sliding window to compute the modular exponentiation.
+ * The value of k changes based on the size of the exponent.
+ *
+ * Uses Montgomery or Diminished Radix reduction [whichever appropriate]
+ */
+
+#ifdef MP_LOW_MEM
+   #define TAB_SIZE 32
+#else
+   #define TAB_SIZE 256
+#endif
+
+int
+mp_exptmod_fast (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int redmode)
+{
+  mp_int  M[TAB_SIZE], res;
+  mp_digit buf, mp;
+  int     err, bitbuf, bitcpy, bitcnt, mode, digidx, x, y, winsize;
+
+  /* use a pointer to the reduction algorithm.  This allows us to use
+   * one of many reduction algorithms without modding the guts of
+   * the code with if statements everywhere.
+   */
+  int     (*redux)(mp_int*,mp_int*,mp_digit);
+
+  /* find window size */
+  x = mp_count_bits (X);
+  if (x <= 7) {
+    winsize = 2;
+  } else if (x <= 36) {
+    winsize = 3;
+  } else if (x <= 140) {
+    winsize = 4;
+  } else if (x <= 450) {
+    winsize = 5;
+  } else if (x <= 1303) {
+    winsize = 6;
+  } else if (x <= 3529) {
+    winsize = 7;
+  } else {
+    winsize = 8;
+  }
+
+#ifdef MP_LOW_MEM
+  if (winsize > 5) {
+     winsize = 5;
+  }
+#endif
+
+  /* init M array */
+  /* init first cell */
+  if ((err = mp_init(&M[1])) != MP_OKAY) {
+     return err;
+  }
+
+  /* now init the second half of the array */
+  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
+    if ((err = mp_init(&M[x])) != MP_OKAY) {
+      for (y = 1<<(winsize-1); y < x; y++) {
+        mp_clear (&M[y]);
+      }
+      mp_clear(&M[1]);
+      return err;
+    }
+  }
+
+  /* determine and setup reduction code */
+  if (redmode == 0) {
+     /* now setup montgomery  */
+     if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) {
+        goto __M;
+     }
+
+     /* automatically pick the comba one if available (saves quite a few calls/ifs) */
+     if (((P->used * 2 + 1) < MP_WARRAY) &&
+          P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) {
+        redux = fast_mp_montgomery_reduce;
+     } else {
+        /* use slower baseline Montgomery method */
+        redux = mp_montgomery_reduce;
+     }
+  } else if (redmode == 1) {
+     /* setup DR reduction for moduli of the form B**k - b */
+     mp_dr_setup(P, &mp);
+     redux = mp_dr_reduce;
+  } else {
+     /* setup DR reduction for moduli of the form 2**k - b */
+     if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) {
+        goto __M;
+     }
+     redux = mp_reduce_2k;
+  }
+
+  /* setup result */
+  if ((err = mp_init (&res)) != MP_OKAY) {
+    goto __M;
+  }
+
+  /* create M table
+   *
+   * The M table contains powers of the input base, e.g. M[x] = G^x mod P
+   *
+   * The first half of the table is not computed though accept for M[0] and M[1]
+   */
+
+  if (redmode == 0) {
+     /* now we need R mod m */
+     if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) {
+       goto __RES;
+     }
+
+     /* now set M[1] to G * R mod m */
+     if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) {
+       goto __RES;
+     }
+  } else {
+     mp_set(&res, 1);
+     if ((err = mp_mod(G, P, &M[1])) != MP_OKAY) {
+        goto __RES;
+     }
+  }
+
+  /* compute the value at M[1<<(winsize-1)] by squaring M[1] (winsize-1) times */
+  if ((err = mp_copy (&M[1], &M[1 << (winsize - 1)])) != MP_OKAY) {
+    goto __RES;
+  }
+
+  for (x = 0; x < (winsize - 1); x++) {
+    if ((err = mp_sqr (&M[1 << (winsize - 1)], &M[1 << (winsize - 1)])) != MP_OKAY) {
+      goto __RES;
+    }
+    if ((err = redux (&M[1 << (winsize - 1)], P, mp)) != MP_OKAY) {
+      goto __RES;
+    }
+  }
+
+  /* create upper table */
+  for (x = (1 << (winsize - 1)) + 1; x < (1 << winsize); x++) {
+    if ((err = mp_mul (&M[x - 1], &M[1], &M[x])) != MP_OKAY) {
+      goto __RES;
+    }
+    if ((err = redux (&M[x], P, mp)) != MP_OKAY) {
+      goto __RES;
+    }
+  }
+
+  /* set initial mode and bit cnt */
+  mode   = 0;
+  bitcnt = 1;
+  buf    = 0;
+  digidx = X->used - 1;
+  bitcpy = 0;
+  bitbuf = 0;
+
+  for (;;) {
+    /* grab next digit as required */
+    if (--bitcnt == 0) {
+      /* if digidx == -1 we are out of digits so break */
+      if (digidx == -1) {
+        break;
+      }
+      /* read next digit and reset bitcnt */
+      buf    = X->dp[digidx--];
+      bitcnt = (int)DIGIT_BIT;
+    }
+
+    /* grab the next msb from the exponent */
+    y     = (mp_digit)(buf >> (DIGIT_BIT - 1)) & 1;
+    buf <<= (mp_digit)1;
+
+    /* if the bit is zero and mode == 0 then we ignore it
+     * These represent the leading zero bits before the first 1 bit
+     * in the exponent.  Technically this opt is not required but it
+     * does lower the # of trivial squaring/reductions used
+     */
+    if (mode == 0 && y == 0) {
+      continue;
+    }
+
+    /* if the bit is zero and mode == 1 then we square */
+    if (mode == 1 && y == 0) {
+      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+        goto __RES;
+      }
+      if ((err = redux (&res, P, mp)) != MP_OKAY) {
+        goto __RES;
+      }
+      continue;
+    }
+
+    /* else we add it to the window */
+    bitbuf |= (y << (winsize - ++bitcpy));
+    mode    = 2;
+
+    if (bitcpy == winsize) {
+      /* ok window is filled so square as required and multiply  */
+      /* square first */
+      for (x = 0; x < winsize; x++) {
+        if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+          goto __RES;
+        }
+        if ((err = redux (&res, P, mp)) != MP_OKAY) {
+          goto __RES;
+        }
+      }
+
+      /* then multiply */
+      if ((err = mp_mul (&res, &M[bitbuf], &res)) != MP_OKAY) {
+        goto __RES;
+      }
+      if ((err = redux (&res, P, mp)) != MP_OKAY) {
+        goto __RES;
+      }
+
+      /* empty window and reset */
+      bitcpy = 0;
+      bitbuf = 0;
+      mode   = 1;
+    }
+  }
+
+  /* if bits remain then square/multiply */
+  if (mode == 2 && bitcpy > 0) {
+    /* square then multiply if the bit is set */
+    for (x = 0; x < bitcpy; x++) {
+      if ((err = mp_sqr (&res, &res)) != MP_OKAY) {
+        goto __RES;
+      }
+      if ((err = redux (&res, P, mp)) != MP_OKAY) {
+        goto __RES;
+      }
+
+      /* get next bit of the window */
+      bitbuf <<= 1;
+      if ((bitbuf & (1 << winsize)) != 0) {
+        /* then multiply */
+        if ((err = mp_mul (&res, &M[1], &res)) != MP_OKAY) {
+          goto __RES;
+        }
+        if ((err = redux (&res, P, mp)) != MP_OKAY) {
+          goto __RES;
+        }
+      }
+    }
+  }
+
+  if (redmode == 0) {
+     /* fixup result if Montgomery reduction is used
+      * recall that any value in a Montgomery system is
+      * actually multiplied by R mod n.  So we have
+      * to reduce one more time to cancel out the factor
+      * of R.
+      */
+     if ((err = mp_montgomery_reduce (&res, P, mp)) != MP_OKAY) {
+       goto __RES;
+     }
+  }
+
+  /* swap res with Y */
+  mp_exch (&res, Y);
+  err = MP_OKAY;
+__RES:mp_clear (&res);
+__M:
+  mp_clear(&M[1]);
+  for (x = 1<<(winsize-1); x < (1 << winsize); x++) {
+    mp_clear (&M[x]);
+  }
+  return err;
+}