tommath/bn_fast_mp_invmod.c

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

/* computes the modular inverse via binary extended euclidean algorithm,
 * that is c = 1/a mod b
 *
 * Based on slow 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) == MP_YES) {
    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 LBL_ERR;
  }

  /* we need y = |a| */
  if ((res = mp_mod(a, b, &y)) != MP_OKAY) {
    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(&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 B is odd then */
    if (mp_isodd(&B) == MP_YES) {
      if ((res = mp_sub(&B, &x, &B)) != MP_OKAY) {
        goto LBL_ERR;
      }
    }
    /* B = B/2 */
    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 D is odd then */
    if (mp_isodd(&D) == MP_YES) {
      /* D = (D-x)/2 */
      if ((res = mp_sub(&D, &x, &D)) != MP_OKAY) {
        goto LBL_ERR;
      }
    }
    /* D = D/2 */
    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, B = B - D */
    if ((res = mp_sub(&u, &v, &u)) != MP_OKAY) {
      goto LBL_ERR;
    }

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

  /* b is now the inverse */
  neg = a->sign;
  while (D.sign == MP_NEG) {
    if ((res = mp_add(&D, b, &D)) != MP_OKAY) {
      goto LBL_ERR;
    }
  }
  mp_exch(&D, c);
  c->sign = neg;
  res = MP_OKAY;

LBL_ERR:
  mp_clear_multi(&x, &y, &u, &v, &B, &D, NULL);
  return res;
}
#endif

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