tommath/bn_mp_invmod_slow.c

#include <tommath_private.h>
#ifdef BN_MP_INVMOD_SLOW_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, tstdenis82@gmail.com, http://libtom.org
 */

/* hac 14.61, pp608 */
int mp_invmod_slow(mp_int *a, mp_int *b, mp_int *c)
{
  mp_int  x, y, u, v, A, B, C, D;
  int     res;

  /* b cannot be negative */
  if ((b->sign == MP_NEG) || (mp_iszero(b) == MP_YES)) {
    return MP_VAL;
  }

  /* init temps */
  if ((res = mp_init_multi(&x, &y, &u, &v,
                           &A, &B, &C, &D, NULL)) != MP_OKAY) {
     return res;
  }

  /* x = a, y = b */
  if ((res = mp_mod(a, b, &x)) != MP_OKAY) {
      goto LBL_ERR;
  }
  if ((res = mp_copy(b, &y)) != MP_OKAY) {
    goto LBL_ERR;
  }

  /* 2. [modified] if x,y are both even then return an error! */
  if ((mp_iseven(&x) == MP_YES) && (mp_iseven(&y) == MP_YES)) {
    res = MP_VAL;
    goto LBL_ERR;
  }

  /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */
  if ((res = mp_copy(&x, &u)) != MP_OKAY) {
    goto LBL_ERR;
  }
  if ((res = mp_copy(&y, &v)) != MP_OKAY) {
    goto LBL_ERR;
  }
  mp_set(&A, 1);
  mp_set(&D, 1);

top:
  /* 4.  while u is even do */
  while (mp_iseven(&u) == MP_YES) {
    /* 4.1 u = u/2 */
    if ((res = mp_div_2(&u, &u)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 4.2 if A or B is odd then */
    if ((mp_isodd(&A) == MP_YES) || (mp_isodd(&B) == MP_YES)) {
      /* A = (A+y)/2, B = (B-x)/2 */
      if ((res = mp_add(&A, &y, &A)) != MP_OKAY) {
         goto LBL_ERR;
      }
      if ((res = mp_sub(&B, &x, &B)) != MP_OKAY) {
         goto LBL_ERR;
      }
    }
    /* A = A/2, B = B/2 */
    if ((res = mp_div_2(&A, &A)) != MP_OKAY) {
      goto LBL_ERR;
    }
    if ((res = mp_div_2(&B, &B)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* 5.  while v is even do */
  while (mp_iseven(&v) == MP_YES) {
    /* 5.1 v = v/2 */
    if ((res = mp_div_2(&v, &v)) != MP_OKAY) {
      goto LBL_ERR;
    }
    /* 5.2 if C or D is odd then */
    if ((mp_isodd(&C) == MP_YES) || (mp_isodd(&D) == MP_YES)) {
      /* C = (C+y)/2, D = (D-x)/2 */
      if ((res = mp_add(&C, &y, &C)) != MP_OKAY) {
         goto LBL_ERR;
      }
      if ((res = mp_sub(&D, &x, &D)) != MP_OKAY) {
         goto LBL_ERR;
      }
    }
    /* C = C/2, D = D/2 */
    if ((res = mp_div_2(&C, &C)) != MP_OKAY) {
      goto LBL_ERR;
    }
    if ((res = mp_div_2(&D, &D)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* 6.  if u >= v then */
  if (mp_cmp(&u, &v) != MP_LT) {
    /* u = u - v, A = A - C, B = B - D */
    if ((res = mp_sub(&u, &v, &u)) != MP_OKAY) {
      goto LBL_ERR;
    }

    if ((res = mp_sub(&A, &C, &A)) != MP_OKAY) {
      goto LBL_ERR;
    }

    if ((res = mp_sub(&B, &D, &B)) != MP_OKAY) {
      goto LBL_ERR;
    }
  } else {
    /* v - v - u, C = C - A, D = D - B */
    if ((res = mp_sub(&v, &u, &v)) != MP_OKAY) {
      goto LBL_ERR;
    }

    if ((res = mp_sub(&C, &A, &C)) != MP_OKAY) {
      goto LBL_ERR;
    }

    if ((res = mp_sub(&D, &B, &D)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }

  /* if not zero goto step 4 */
  if (mp_iszero(&u) == MP_NO)
    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 LBL_ERR;
  }

  /* if its too low */
  while (mp_cmp_d(&C, 0) == MP_LT) {
      if ((res = mp_add(&C, b, &C)) != MP_OKAY) {
         goto LBL_ERR;
      }
  }

  /* too big */
  while (mp_cmp_mag(&C, b) != MP_LT) {
      if ((res = mp_sub(&C, b, &C)) != MP_OKAY) {
         goto LBL_ERR;
      }
  }

  /* C is now the inverse */
  mp_exch(&C, c);
  res = MP_OKAY;
LBL_ERR:
  mp_clear_multi(&x, &y, &u, &v, &A, &B, &C, &D, NULL);
  return res;
}
#endif

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