#include <tommath.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, tomstdenis@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) == 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 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) == 1) {
		/* 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) == 1) {
			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) == 1) {
		/* 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) == 1) {
			/* 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) == 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 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

/* $Source: /cvs/libtom/libtommath/bn_fast_mp_invmod.c,v $ */
/* $Revision: 1.4 $ */
/* $Date: 2006/12/28 01:25:13 $ */