mpi.c

常用的64位密码加密算法

{
  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;
}

/* End: bn_fast_s_mp_mul_high_digs.c */

/* Start: 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, [e-mail], http://math.libtomcrypt.org
 */
#include <ltc_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;
}

/* End: bn_fast_s_mp_sqr.c */

/* Start: 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, [e-mail], http://math.libtomcrypt.org
 */
#include <ltc_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;
}

/* End: bn_mp_2expt.c */

/* Start: 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, [e-mail], http://math.libtomcrypt.org
 */
#include <ltc_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;
}

/* End: bn_mp_abs.c */

/* Start: 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, [e-mail], http://math.libtomcrypt.org
 */
#include <ltc_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;
}


/* End: bn_mp_add.c */

/* Start: 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, [e-mail], http://math.libtomcrypt.org
 */
#include <ltc_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;
}


/* End: bn_mp_add_d.c */

/* Start: 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, [e-mail], http://math.libtomcrypt.org
 */
#include <ltc_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;
}

/* End: bn_mp_addmod.c */

/* Start: 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, [e-mail], http://math.libtomcrypt.org
 */
#include <ltc_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;