ltm 0.30 orig import

--HG--
branch : libtommath-orig
extra : convert_revision : 29392f1198b77a2021e78879c1489e84c9e98ef4

LICENSE

+LibTomMath is hereby released into the Public Domain.  
+
+-- Tom St Denis
+

bn_error.c

+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+#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

+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+#include <tommath.h>
+
+/* computes the modular inverse via binary extended euclidean algorithm, 
+ * that is c = 1/a mod b 
+ *
+ * Based on mp_invmod except this is optimized for the case where b is 
+ * odd as per HAC Note 14.64 on pp. 610
+ */
+int
+fast_mp_invmod (mp_int * a, mp_int * b, mp_int * c)
+{
+  mp_int  x, y, u, v, B, D;
+  int     res, neg;
+
+  /* 2. [modified] b must be odd   */
+  if (mp_iseven (b) == 1) {
+    return MP_VAL;
+  }
+
+  /* init all our temps */
+  if ((res = mp_init_multi(&x, &y, &u, &v, &B, &D, NULL)) != MP_OKAY) {
+     return res;
+  }
+
+  /* x == modulus, y == value to invert */
+  if ((res = mp_copy (b, &x)) != MP_OKAY) {
+    goto __ERR;
+  }
+
+  /* we need y = |a| */
+  if ((res = mp_abs (a, &y)) != MP_OKAY) {
+    goto __ERR;
+  }
+
+  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
+  if ((res = mp_copy (&x, &u)) != MP_OKAY) {
+    goto __ERR;
+  }
+  if ((res = mp_copy (&y, &v)) != MP_OKAY) {
+    goto __ERR;
+  }
+  mp_set (&D, 1);
+
+top:
+  /* 4.  while u is even do */
+  while (mp_iseven (&u) == 1) {
+    /* 4.1 u = u/2 */
+    if ((res = mp_div_2 (&u, &u)) != MP_OKAY) {
+      goto __ERR;
+    }
+    /* 4.2 if B is odd then */
+    if (mp_isodd (&B) == 1) {
+      if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) {
+        goto __ERR;
+      }
+    }
+    /* B = B/2 */
+    if ((res = mp_div_2 (&B, &B)) != MP_OKAY) {
+      goto __ERR;
+    }
+  }
+
+  /* 5.  while v is even do */
+  while (mp_iseven (&v) == 1) {
+    /* 5.1 v = v/2 */
+    if ((res = mp_div_2 (&v, &v)) != MP_OKAY) {
+      goto __ERR;
+    }
+    /* 5.2 if D is odd then */
+    if (mp_isodd (&D) == 1) {
+      /* D = (D-x)/2 */
+      if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) {
+        goto __ERR;
+      }
+    }
+    /* D = D/2 */
+    if ((res = mp_div_2 (&D, &D)) != MP_OKAY) {
+      goto __ERR;
+    }
+  }
+
+  /* 6.  if u >= v then */
+  if (mp_cmp (&u, &v) != MP_LT) {
+    /* u = u - v, B = B - D */
+    if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) {
+      goto __ERR;
+    }
+
+    if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) {
+      goto __ERR;
+    }
+  } else {
+    /* v - v - u, D = D - B */
+    if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) {
+      goto __ERR;
+    }
+
+    if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) {
+      goto __ERR;
+    }
+  }
+
+  /* if not zero goto step 4 */
+  if (mp_iszero (&u) == 0) {
+    goto top;
+  }
+
+  /* now a = C, b = D, gcd == g*v */
+
+  /* if v != 1 then there is no inverse */
+  if (mp_cmp_d (&v, 1) != MP_EQ) {
+    res = MP_VAL;
+    goto __ERR;
+  }
+
+  /* b is now the inverse */
+  neg = a->sign;
+  while (D.sign == MP_NEG) {
+    if ((res = mp_add (&D, b, &D)) != MP_OKAY) {
+      goto __ERR;
+    }
+  }
+  mp_exch (&D, c);
+  c->sign = neg;
+  res = MP_OKAY;
+
+__ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL);
+  return res;
+}

bn_fast_mp_montgomery_reduce.c

+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+#include <tommath.h>
+
+/* computes xR**-1 == x (mod N) via Montgomery Reduction
+ *
+ * This is an optimized implementation of mp_montgomery_reduce
+ * which uses the comba method to quickly calculate the columns of the
+ * reduction.
+ *
+ * Based on Algorithm 14.32 on pp.601 of HAC.
+*/
+int
+fast_mp_montgomery_reduce (mp_int * x, mp_int * n, mp_digit rho)
+{
+  int     ix, res, olduse;
+  mp_word W[MP_WARRAY];
+
+  /* get old used count */
+  olduse = x->used;
+
+  /* grow a as required */
+  if (x->alloc < n->used + 1) {
+    if ((res = mp_grow (x, n->used + 1)) != MP_OKAY) {
+      return res;
+    }
+  }
+
+  /* first we have to get the digits of the input into
+   * an array of double precision words W[...]
+   */
+  {
+    register mp_word *_W;
+    register mp_digit *tmpx;
+
+    /* alias for the W[] array */
+    _W   = W;
+
+    /* alias for the digits of  x*/
+    tmpx = x->dp;
+
+    /* copy the digits of a into W[0..a->used-1] */
+    for (ix = 0; ix < x->used; ix++) {
+      *_W++ = *tmpx++;
+    }
+
+    /* zero the high words of W[a->used..m->used*2] */
+    for (; ix < n->used * 2 + 1; ix++) {
+      *_W++ = 0;
+    }
+  }
+
+  /* now we proceed to zero successive digits
+   * from the least significant upwards
+   */
+  for (ix = 0; ix < n->used; ix++) {
+    /* mu = ai * m' mod b
+     *
+     * We avoid a double precision multiplication (which isn't required)
+     * by casting the value down to a mp_digit.  Note this requires
+     * that W[ix-1] have  the carry cleared (see after the inner loop)
+     */
+    register mp_digit mu;
+    mu = (mp_digit) (((W[ix] & MP_MASK) * rho) & MP_MASK);
+
+    /* a = a + mu * m * b**i
+     *
+     * This is computed in place and on the fly.  The multiplication
+     * by b**i is handled by offseting which columns the results
+     * are added to.
+     *
+     * Note the comba method normally doesn't handle carries in the
+     * inner loop In this case we fix the carry from the previous
+     * column since the Montgomery reduction requires digits of the
+     * result (so far) [see above] to work.  This is
+     * handled by fixing up one carry after the inner loop.  The
+     * carry fixups are done in order so after these loops the
+     * first m->used words of W[] have the carries fixed
+     */
+    {
+      register int iy;
+      register mp_digit *tmpn;
+      register mp_word *_W;
+
+      /* alias for the digits of the modulus */
+      tmpn = n->dp;
+
+      /* Alias for the columns set by an offset of ix */
+      _W = W + ix;
+
+      /* inner loop */
+      for (iy = 0; iy < n->used; iy++) {
+          *_W++ += ((mp_word)mu) * ((mp_word)*tmpn++);
+      }
+    }
+
+    /* now fix carry for next digit, W[ix+1] */
+    W[ix + 1] += W[ix] >> ((mp_word) DIGIT_BIT);
+  }
+
+  /* now we have to propagate the carries and
+   * shift the words downward [all those least
+   * significant digits we zeroed].
+   */
+  {
+    register mp_digit *tmpx;
+    register mp_word *_W, *_W1;
+
+    /* nox fix rest of carries */
+
+    /* alias for current word */
+    _W1 = W + ix;
+
+    /* alias for next word, where the carry goes */
+    _W = W + ++ix;
+
+    for (; ix <= n->used * 2 + 1; ix++) {
+      *_W++ += *_W1++ >> ((mp_word) DIGIT_BIT);
+    }
+
+    /* copy out, A = A/b**n
+     *
+     * The result is A/b**n but instead of converting from an
+     * array of mp_word to mp_digit than calling mp_rshd
+     * we just copy them in the right order
+     */
+
+    /* alias for destination word */
+    tmpx = x->dp;
+
+    /* alias for shifted double precision result */
+    _W = W + n->used;
+
+    for (ix = 0; ix < n->used + 1; ix++) {
+      *tmpx++ = (mp_digit)(*_W++ & ((mp_word) MP_MASK));
+    }
+
+    /* zero oldused digits, if the input a was larger than
+     * m->used+1 we'll have to clear the digits
+     */
+    for (; ix < olduse; ix++) {
+      *tmpx++ = 0;
+    }
+  }
+
+  /* set the max used and clamp */
+  x->used = n->used + 1;
+  mp_clamp (x);
+
+  /* if A >= m then A = A - m */
+  if (mp_cmp_mag (x, n) != MP_LT) {
+    return s_mp_sub (x, n, x);
+  }
+  return MP_OKAY;
+}

bn_fast_s_mp_mul_digs.c

+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+#include <tommath.h>
+
+/* Fast (comba) multiplier
+ *
+ * This is the fast column-array [comba] multiplier.  It is 
+ * designed to compute the columns of the product first 
+ * then handle the carries afterwards.  This has the effect 
+ * of making the nested loops that compute the columns very
+ * simple and schedulable on super-scalar processors.
+ *
+ * This has been modified to produce a variable number of 
+ * digits of output so if say only a half-product is required 
+ * you don't have to compute the upper half (a feature 
+ * required for fast Barrett reduction).
+ *
+ * Based on Algorithm 14.12 on pp.595 of HAC.
+ *
+ */
+int
+fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+{
+  int     olduse, res, pa, ix;
+  mp_word W[MP_WARRAY];
+
+  /* grow the destination as required */
+  if (c->alloc < digs) {
+    if ((res = mp_grow (c, digs)) != MP_OKAY) {
+      return res;
+    }
+  }
+
+  /* clear temp buf (the columns) */
+  memset (W, 0, sizeof (mp_word) * digs);
+
+  /* calculate the columns */
+  pa = a->used;
+  for (ix = 0; ix < pa; ix++) {
+    /* this multiplier has been modified to allow you to 
+     * control how many digits of output are produced.  
+     * So at most we want to make upto "digs" digits of output.
+     *
+     * this adds products to distinct columns (at ix+iy) of W
+     * note that each step through the loop is not dependent on
+     * the previous which means the compiler can easily unroll
+     * the loop without scheduling problems
+     */
+    {
+      register mp_digit tmpx, *tmpy;
+      register mp_word *_W;
+      register int iy, pb;
+
+      /* alias for the the word on the left e.g. A[ix] * A[iy] */
+      tmpx = a->dp[ix];
+
+      /* alias for the right side */
+      tmpy = b->dp;
+
+      /* alias for the columns, each step through the loop adds a new
+         term to each column
+       */
+      _W = W + ix;
+
+      /* the number of digits is limited by their placement.  E.g.
+         we avoid multiplying digits that will end up above the # of
+         digits of precision requested
+       */
+      pb = MIN (b->used, digs - ix);
+
+      for (iy = 0; iy < pb; iy++) {
+        *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++);
+      }
+    }
+
+  }
+
+  /* setup dest */
+  olduse = c->used;
+  c->used = digs;
+
+  {
+    register mp_digit *tmpc;
+
+    /* At this point W[] contains the sums of each column.  To get the
+     * correct result we must take the extra bits from each column and
+     * carry them down
+     *
+     * Note that while this adds extra code to the multiplier it 
+     * saves time since the carry propagation is removed from the 
+     * above nested loop.This has the effect of reducing the work 
+     * from N*(N+N*c)==N**2 + c*N**2 to N**2 + N*c where c is the 
+     * cost of the shifting.  On very small numbers this is slower 
+     * but on most cryptographic size numbers it is faster.
+     *
+     * In this particular implementation we feed the carries from
+     * behind which means when the loop terminates we still have one
+     * last digit to copy
+     */
+    tmpc = c->dp;
+    for (ix = 1; ix < digs; ix++) {
+      /* forward the carry from the previous temp */
+      W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
+
+      /* now extract the previous digit [below the carry] */
+      *tmpc++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
+    }
+    /* fetch the last digit */
+    *tmpc++ = (mp_digit) (W[digs - 1] & ((mp_word) MP_MASK));
+
+    /* clear unused digits [that existed in the old copy of c] */
+    for (; ix < olduse; ix++) {
+      *tmpc++ = 0;
+    }
+  }
+  mp_clamp (c);
+  return MP_OKAY;
+}

bn_fast_s_mp_mul_high_digs.c

+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+ #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
+ * to see how it works.
+ *
+ * This is used in the Barrett reduction since for one of the multiplications
+ * only the higher digits were needed.  This essentially halves the work.
+ *
+ * Based on Algorithm 14.12 on pp.595 of HAC.
+ */
+int
+fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs)
+{
+  int     oldused, newused, res, pa, pb, ix;
+  mp_word W[MP_WARRAY];
+
+  /* calculate size of product and allocate more space if required */
+  newused = a->used + b->used + 1;
+  if (c->alloc < newused) {
+    if ((res = mp_grow (c, newused)) != MP_OKAY) {
+      return res;
+    }
+  }
+
+  /* like the other comba method we compute the columns first */
+  pa = a->used;
+  pb = b->used;
+  memset (W + digs, 0, (pa + pb + 1 - digs) * sizeof (mp_word));
+  for (ix = 0; ix < pa; ix++) {
+    {
+      register mp_digit tmpx, *tmpy;
+      register int iy;
+      register mp_word *_W;
+
+      /* work todo, that is we only calculate digits that are at "digs" or above  */
+      iy = digs - ix;
+
+      /* copy of word on the left of A[ix] * B[iy] */
+      tmpx = a->dp[ix];
+
+      /* alias for right side */
+      tmpy = b->dp + iy;
+     
+      /* alias for the columns of output.  Offset to be equal to or above the 
+       * smallest digit place requested 
+       */
+      _W = W + digs;     
+      
+      /* skip cases below zero where ix > digs */
+      if (iy < 0) {
+         iy    = abs(iy);
+         tmpy += iy;
+         _W   += iy;
+         iy    = 0;
+      }
+
+      /* compute column products for digits above the minimum */
+      for (; iy < pb; iy++) {
+         *_W++ += ((mp_word) tmpx) * ((mp_word)*tmpy++);
+      }
+    }
+  }
+
+  /* setup dest */
+  oldused = c->used;
+  c->used = newused;
+
+  /* now convert the array W downto what we need
+   *
+   * See comments in bn_fast_s_mp_mul_digs.c
+   */
+  for (ix = digs + 1; ix < newused; ix++) {
+    W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT));
+    c->dp[ix - 1] = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK));
+  }
+  c->dp[newused - 1] = (mp_digit) (W[newused - 1] & ((mp_word) MP_MASK));
+
+  for (; ix < oldused; ix++) {
+    c->dp[ix] = 0;
+  }
+  mp_clamp (c);
+  return MP_OKAY;
+}

bn_fast_s_mp_sqr.c

+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+#include <tommath.h>
+
+/* fast squaring
+ *
+ * This is the comba method where the columns of the product
+ * are computed first then the carries are computed.  This
+ * has the effect of making a very simple inner loop that
+ * is executed the most
+ *
+ * W2 represents the outer products and W the inner.
+ *
+ * A further optimizations is made because the inner
+ * products are of the form "A * B * 2".  The *2 part does
+ * not need to be computed until the end which is good
+ * because 64-bit shifts are slow!
+ *
+ * Based on Algorithm 14.16 on pp.597 of HAC.
+ *
+ */
+int fast_s_mp_sqr (mp_int * a, mp_int * b)
+{
+  int     olduse, newused, res, ix, pa;
+  mp_word W2[MP_WARRAY], W[MP_WARRAY];
+
+  /* calculate size of product and allocate as required */
+  pa = a->used;
+  newused = pa + pa + 1;
+  if (b->alloc < newused) {
+    if ((res = mp_grow (b, newused)) != MP_OKAY) {
+      return res;
+    }
+  }
+
+  /* zero temp buffer (columns)
+   * Note that there are two buffers.  Since squaring 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 (W2, 0, newused * sizeof (mp_word));
+
+  /* This computes the inner product.  To simplify the inner N**2 loop
+   * the multiplication by two is done afterwards in the N loop.
+   */
+  for (ix = 0; ix < pa; ix++) {
+    /* compute the outer product
+     *
+     * 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]);
+
+    {
+      register mp_digit tmpx, *tmpy;
+      register mp_word *_W;
+      register int iy;
+
+      /* copy of left side */
+      tmpx = a->dp[ix];
+
+      /* alias for right side */
+      tmpy = a->dp + (ix + 1);
+
+      /* the column to store the result in */
+      _W = W + (ix + ix + 1);
+
+      /* inner products */
+      for (iy = ix + 1; iy < pa; iy++) {
+          *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++);
+      }
+    }
+  }
+
+  /* setup dest */
+  olduse  = b->used;
+  b->used = newused;
+
+  /* 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;
+
+    /* double first value, since the inner products are
+     * half of what they should be
+     */
+    W[0] += W[0] + W2[0];
+
+    tmpb = b->dp;
+    for (ix = 1; ix < newused; ix++) {
+      /* 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
+     * 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 of b if there were any originally */
+    for (; ix < olduse; ix++) {
+      *tmpb++ = 0;
+    }
+  }
+
+  mp_clamp (b);
+  return MP_OKAY;
+}

bn_mp_2expt.c

+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+#include <tommath.h>
+
+/* computes a = 2**b 
+ *
+ * Simple algorithm which zeroes the int, grows it then just sets one bit
+ * as required.
+ */
+int
+mp_2expt (mp_int * a, int b)
+{
+  int     res;
+
+  /* zero a as per default */
+  mp_zero (a);
+
+  /* grow a to accomodate the single bit */
+  if ((res = mp_grow (a, b / DIGIT_BIT + 1)) != MP_OKAY) {
+    return res;
+  }
+
+  /* set the used count of where the bit will go */
+  a->used = b / DIGIT_BIT + 1;
+
+  /* put the single bit in its place */
+  a->dp[b / DIGIT_BIT] = 1 << (b % DIGIT_BIT);
+
+  return MP_OKAY;
+}

bn_mp_abs.c

+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+#include <tommath.h>
+
+/* b = |a| 
+ *
+ * Simple function copies the input and fixes the sign to positive
+ */
+int
+mp_abs (mp_int * a, mp_int * b)
+{
+  int     res;
+
+  /* copy a to b */
+  if (a != b) {
+     if ((res = mp_copy (a, b)) != MP_OKAY) {
+       return res;
+     }
+  }
+
+  /* force the sign of b to positive */
+  b->sign = MP_ZPOS;
+
+  return MP_OKAY;
+}

bn_mp_add.c

+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+#include <tommath.h>
+
+/* high level addition (handles signs) */
+int mp_add (mp_int * a, mp_int * b, mp_int * c)
+{
+  int     sa, sb, res;
+
+  /* get sign of both inputs */
+  sa = a->sign;
+  sb = b->sign;
+
+  /* handle two cases, not four */
+  if (sa == sb) {
+    /* both positive or both negative */
+    /* add their magnitudes, copy the sign */
+    c->sign = sa;
+    res = s_mp_add (a, b, c);
+  } else {
+    /* one positive, the other negative */
+    /* subtract the one with the greater magnitude from */
+    /* the one of the lesser magnitude.  The result gets */
+    /* the sign of the one with the greater magnitude. */
+    if (mp_cmp_mag (a, b) == MP_LT) {
+      c->sign = sb;
+      res = s_mp_sub (b, a, c);
+    } else {
+      c->sign = sa;
+      res = s_mp_sub (a, b, c);
+    }
+  }
+  return res;
+}
+

bn_mp_add_d.c

+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+#include <tommath.h>
+
+/* single digit addition */
+int
+mp_add_d (mp_int * a, mp_digit b, mp_int * c)
+{
+  int     res, ix, oldused;
+  mp_digit *tmpa, *tmpc, mu;
+
+  /* grow c as required */
+  if (c->alloc < a->used + 1) {
+     if ((res = mp_grow(c, a->used + 1)) != MP_OKAY) {
+        return res;
+     }
+  }
+
+  /* if a is negative and |a| >= b, call c = |a| - b */
+  if (a->sign == MP_NEG && (a->used > 1 || a->dp[0] >= b)) {
+     /* temporarily fix sign of a */
+     a->sign = MP_ZPOS;
+
+     /* c = |a| - b */
+     res = mp_sub_d(a, b, c);
+
+     /* fix sign  */
+     a->sign = c->sign = MP_NEG;
+
+     return res;
+  }
+
+  /* old number of used digits in c */
+  oldused = c->used;
+
+  /* sign always positive */
+  c->sign = MP_ZPOS;
+
+  /* source alias */
+  tmpa    = a->dp;
+
+  /* destination alias */
+  tmpc    = c->dp;
+
+  /* if a is positive */
+  if (a->sign == MP_ZPOS) {
+     /* add digit, after this we're propagating
+      * the carry.
+      */
+     *tmpc   = *tmpa++ + b;
+     mu      = *tmpc >> DIGIT_BIT;
+     *tmpc++ &= MP_MASK;
+
+     /* now handle rest of the digits */
+     for (ix = 1; ix < a->used; ix++) {
+        *tmpc   = *tmpa++ + mu;
+        mu      = *tmpc >> DIGIT_BIT;
+        *tmpc++ &= MP_MASK;
+     }
+     /* set final carry */
+     ix++;
+     *tmpc++  = mu;
+
+     /* setup size */
+     c->used = a->used + 1;
+  } else {
+     /* a was negative and |a| < b */
+     c->used  = 1;
+
+     /* the result is a single digit */
+     if (a->used == 1) {
+        *tmpc++  =  b - a->dp[0];
+     } else {
+        *tmpc++  =  b;
+     }
+
+     /* setup count so the clearing of oldused
+      * can fall through correctly
+      */
+     ix       = 1;
+  }
+
+  /* now zero to oldused */
+  while (ix++ < oldused) {
+     *tmpc++ = 0;
+  }
+  mp_clamp(c);
+
+  return MP_OKAY;
+}
+

bn_mp_addmod.c

+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+#include <tommath.h>
+
+/* d = a + b (mod c) */
+int
+mp_addmod (mp_int * a, mp_int * b, mp_int * c, mp_int * d)
+{
+  int     res;
+  mp_int  t;
+
+  if ((res = mp_init (&t)) != MP_OKAY) {
+    return res;
+  }
+
+  if ((res = mp_add (a, b, &t)) != MP_OKAY) {
+    mp_clear (&t);
+    return res;
+  }
+  res = mp_mod (&t, c, d);
+  mp_clear (&t);
+  return res;
+}

bn_mp_and.c

+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+#include <tommath.h>
+
+/* AND two ints together */
+int
+mp_and (mp_int * a, mp_int * b, mp_int * c)
+{
+  int     res, ix, px;
+  mp_int  t, *x;
+
+  if (a->used > b->used) {
+    if ((res = mp_init_copy (&t, a)) != MP_OKAY) {
+      return res;
+    }
+    px = b->used;
+    x = b;
+  } else {
+    if ((res = mp_init_copy (&t, b)) != MP_OKAY) {
+      return res;
+    }
+    px = a->used;
+    x = a;
+  }
+
+  for (ix = 0; ix < px; ix++) {
+    t.dp[ix] &= x->dp[ix];
+  }
+
+  /* zero digits above the last from the smallest mp_int */
+  for (; ix < t.used; ix++) {
+    t.dp[ix] = 0;
+  }
+
+  mp_clamp (&t);
+  mp_exch (c, &t);
+  mp_clear (&t);
+  return MP_OKAY;
+}

bn_mp_clamp.c

+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+#include <tommath.h>
+
+/* trim unused digits 
+ *
+ * This is used to ensure that leading zero digits are
+ * trimed and the leading "used" digit will be non-zero
+ * Typically very fast.  Also fixes the sign if there
+ * are no more leading digits
+ */
+void
+mp_clamp (mp_int * a)
+{
+  /* decrease used while the most significant digit is
+   * zero.
+   */
+  while (a->used > 0 && a->dp[a->used - 1] == 0) {
+    --(a->used);
+  }
+
+  /* reset the sign flag if used == 0 */
+  if (a->used == 0) {
+    a->sign = MP_ZPOS;
+  }
+}

bn_mp_clear.c

+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+#include <tommath.h>
+
+/* clear one (frees)  */
+void
+mp_clear (mp_int * a)
+{
+  /* only do anything if a hasn't been freed previously */
+  if (a->dp != NULL) {
+    /* first zero the digits */
+    memset (a->dp, 0, sizeof (mp_digit) * a->used);
+
+    /* free ram */
+    XFREE(a->dp);
+
+    /* reset members to make debugging easier */
+    a->dp    = NULL;
+    a->alloc = a->used = 0;
+    a->sign  = MP_ZPOS;
+  }
+}

bn_mp_clear_multi.c

+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+#include <tommath.h>
+#include <stdarg.h>
+
+void mp_clear_multi(mp_int *mp, ...) 
+{
+    mp_int* next_mp = mp;
+    va_list args;
+    va_start(args, mp);
+    while (next_mp != NULL) {
+        mp_clear(next_mp);
+        next_mp = va_arg(args, mp_int*);
+    }
+    va_end(args);
+}

bn_mp_cmp.c

+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+#include <tommath.h>
+
+/* compare two ints (signed)*/
+int
+mp_cmp (mp_int * a, mp_int * b)
+{
+  /* compare based on sign */
+  if (a->sign != b->sign) {
+     if (a->sign == MP_NEG) {
+        return MP_LT;
+     } else {
+        return MP_GT;
+     }
+  }
+  
+  /* compare digits */
+  if (a->sign == MP_NEG) {
+     /* if negative compare opposite direction */
+     return mp_cmp_mag(b, a);
+  } else {
+     return mp_cmp_mag(a, b);
+  }
+}

bn_mp_cmp_d.c

+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+#include <tommath.h>
+
+/* compare a digit */
+int mp_cmp_d(mp_int * a, mp_digit b)
+{
+  /* compare based on sign */
+  if (a->sign == MP_NEG) {
+    return MP_LT;
+  }
+
+  /* compare based on magnitude */
+  if (a->used > 1) {
+    return MP_GT;
+  }
+
+  /* compare the only digit of a to b */
+  if (a->dp[0] > b) {
+    return MP_GT;
+  } else if (a->dp[0] < b) {
+    return MP_LT;
+  } else {
+    return MP_EQ;
+  }
+}

bn_mp_cmp_mag.c

+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+#include <tommath.h>
+
+/* compare maginitude of two ints (unsigned) */
+int mp_cmp_mag (mp_int * a, mp_int * b)
+{
+  int     n;
+  mp_digit *tmpa, *tmpb;
+
+  /* compare based on # of non-zero digits */
+  if (a->used > b->used) {
+    return MP_GT;
+  }
+  
+  if (a->used < b->used) {
+    return MP_LT;
+  }
+
+  /* alias for a */
+  tmpa = a->dp + (a->used - 1);
+
+  /* alias for b */
+  tmpb = b->dp + (a->used - 1);
+
+  /* compare based on digits  */
+  for (n = 0; n < a->used; ++n, --tmpa, --tmpb) {
+    if (*tmpa > *tmpb) {
+      return MP_GT;
+    }
+
+    if (*tmpa < *tmpb) {
+      return MP_LT;
+    }
+  }
+  return MP_EQ;
+}

bn_mp_cnt_lsb.c

+/* LibTomMath, multiple-precision integer library -- Tom St Denis
+ *
+ * LibTomMath is a library that provides multiple-precision
+ * integer arithmetic as well as number theoretic functionality.
+ *
+ * The library was designed directly after the MPI library by
+ * Michael Fromberger but has been written from scratch with
+ * additional optimizations in place.
+ *
+ * The library is free for all purposes without any express
+ * guarantee it works.
+ *
+ * Tom St Denis, tomstdenis@iahu.ca, http://math.libtomcrypt.org
+ */
+#include <tommath.h>
+
+static const int lnz[16] = { 
+   4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0
+};
+
+/* Counts the number of lsbs which are zero before the first zero bit */
+int mp_cnt_lsb(mp_int *a)
+{
+   int x;
+   mp_digit q, qq;
+
+   /* easy out */
+   if (mp_iszero(a) == 1) {
+      return 0;
+   }
+
+   /* scan lower digits until non-zero */
+   for (x = 0; x < a->used && a->dp[x] == 0; x++);
+   q = a->dp[x];
+   x *= DIGIT_BIT;
+
+   /* now scan this digit until a 1 is found */
+   if ((q & 1) == 0) {
+      do {
+         qq  = q & 15;
+         x  += lnz[qq];
+         q >>= 4;
+      } while (qq == 0);
+   }
+   return x;
+}
+