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/* This Source Code Form is subject to the terms of the Mozilla Public
 * License, v. 2.0. If a copy of the MPL was not distributed with this
 * file, You can obtain one at http://mozilla.org/MPL/2.0/. */

#include "ec2.h"
#include "mplogic.h"
#include "mp_gf2m.h"
#include <stdlib.h>

/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery
 * projective coordinates. Uses algorithm Mdouble in appendix of Lopez, J. 
 * and Dahab, R.  "Fast multiplication on elliptic curves over GF(2^m)
 * without precomputation". modified to not require precomputation of
 * c=b^{2^{m-1}}. */
static mp_err
gf2m_Mdouble(mp_int *x, mp_int *z, const ECGroup *group)
{
	mp_err res = MP_OKAY;
	mp_int t1;

	MP_DIGITS(&t1) = 0;
	MP_CHECKOK(mp_init(&t1));

	MP_CHECKOK(group->meth->field_sqr(x, x, group->meth));
	MP_CHECKOK(group->meth->field_sqr(z, &t1, group->meth));
	MP_CHECKOK(group->meth->field_mul(x, &t1, z, group->meth));
	MP_CHECKOK(group->meth->field_sqr(x, x, group->meth));
	MP_CHECKOK(group->meth->field_sqr(&t1, &t1, group->meth));
	MP_CHECKOK(group->meth->
			   field_mul(&group->curveb, &t1, &t1, group->meth));
	MP_CHECKOK(group->meth->field_add(x, &t1, x, group->meth));

  CLEANUP:
	mp_clear(&t1);
	return res;
}

/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in
 * Montgomery projective coordinates. Uses algorithm Madd in appendix of
 * Lopex, J. and Dahab, R.  "Fast multiplication on elliptic curves over
 * GF(2^m) without precomputation". */
static mp_err
gf2m_Madd(const mp_int *x, mp_int *x1, mp_int *z1, mp_int *x2, mp_int *z2,
		  const ECGroup *group)
{
	mp_err res = MP_OKAY;
	mp_int t1, t2;

	MP_DIGITS(&t1) = 0;
	MP_DIGITS(&t2) = 0;
	MP_CHECKOK(mp_init(&t1));
	MP_CHECKOK(mp_init(&t2));

	MP_CHECKOK(mp_copy(x, &t1));
	MP_CHECKOK(group->meth->field_mul(x1, z2, x1, group->meth));
	MP_CHECKOK(group->meth->field_mul(z1, x2, z1, group->meth));
	MP_CHECKOK(group->meth->field_mul(x1, z1, &t2, group->meth));
	MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth));
	MP_CHECKOK(group->meth->field_sqr(z1, z1, group->meth));
	MP_CHECKOK(group->meth->field_mul(z1, &t1, x1, group->meth));
	MP_CHECKOK(group->meth->field_add(x1, &t2, x1, group->meth));

  CLEANUP:
	mp_clear(&t1);
	mp_clear(&t2);
	return res;
}

/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
 * using Montgomery point multiplication algorithm Mxy() in appendix of
 * Lopex, J. and Dahab, R.  "Fast multiplication on elliptic curves over
 * GF(2^m) without precomputation". Returns: 0 on error 1 if return value
 * should be the point at infinity 2 otherwise */
static int
gf2m_Mxy(const mp_int *x, const mp_int *y, mp_int *x1, mp_int *z1,
		 mp_int *x2, mp_int *z2, const ECGroup *group)
{
	mp_err res = MP_OKAY;
	int ret = 0;
	mp_int t3, t4, t5;

	MP_DIGITS(&t3) = 0;
	MP_DIGITS(&t4) = 0;
	MP_DIGITS(&t5) = 0;
	MP_CHECKOK(mp_init(&t3));
	MP_CHECKOK(mp_init(&t4));
	MP_CHECKOK(mp_init(&t5));

	if (mp_cmp_z(z1) == 0) {
		mp_zero(x2);
		mp_zero(z2);
		ret = 1;
		goto CLEANUP;
	}

	if (mp_cmp_z(z2) == 0) {
		MP_CHECKOK(mp_copy(x, x2));
		MP_CHECKOK(group->meth->field_add(x, y, z2, group->meth));
		ret = 2;
		goto CLEANUP;
	}

	MP_CHECKOK(mp_set_int(&t5, 1));
	if (group->meth->field_enc) {
		MP_CHECKOK(group->meth->field_enc(&t5, &t5, group->meth));
	}

	MP_CHECKOK(group->meth->field_mul(z1, z2, &t3, group->meth));

	MP_CHECKOK(group->meth->field_mul(z1, x, z1, group->meth));
	MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth));
	MP_CHECKOK(group->meth->field_mul(z2, x, z2, group->meth));
	MP_CHECKOK(group->meth->field_mul(z2, x1, x1, group->meth));
	MP_CHECKOK(group->meth->field_add(z2, x2, z2, group->meth));

	MP_CHECKOK(group->meth->field_mul(z2, z1, z2, group->meth));
	MP_CHECKOK(group->meth->field_sqr(x, &t4, group->meth));
	MP_CHECKOK(group->meth->field_add(&t4, y, &t4, group->meth));
	MP_CHECKOK(group->meth->field_mul(&t4, &t3, &t4, group->meth));
	MP_CHECKOK(group->meth->field_add(&t4, z2, &t4, group->meth));

	MP_CHECKOK(group->meth->field_mul(&t3, x, &t3, group->meth));
	MP_CHECKOK(group->meth->field_div(&t5, &t3, &t3, group->meth));
	MP_CHECKOK(group->meth->field_mul(&t3, &t4, &t4, group->meth));
	MP_CHECKOK(group->meth->field_mul(x1, &t3, x2, group->meth));
	MP_CHECKOK(group->meth->field_add(x2, x, z2, group->meth));

	MP_CHECKOK(group->meth->field_mul(z2, &t4, z2, group->meth));
	MP_CHECKOK(group->meth->field_add(z2, y, z2, group->meth));

	ret = 2;

  CLEANUP:
	mp_clear(&t3);
	mp_clear(&t4);
	mp_clear(&t5);
	if (res == MP_OKAY) {
		return ret;
	} else {
		return 0;
	}
}

/* Computes R = nP based on algorithm 2P of Lopex, J. and Dahab, R.  "Fast 
 * multiplication on elliptic curves over GF(2^m) without
 * precomputation". Elliptic curve points P and R can be identical. Uses
 * Montgomery projective coordinates. */
mp_err
ec_GF2m_pt_mul_mont(const mp_int *n, const mp_int *px, const mp_int *py,
					mp_int *rx, mp_int *ry, const ECGroup *group)
{
	mp_err res = MP_OKAY;
	mp_int x1, x2, z1, z2;
	int i, j;
	mp_digit top_bit, mask;

	MP_DIGITS(&x1) = 0;
	MP_DIGITS(&x2) = 0;
	MP_DIGITS(&z1) = 0;
	MP_DIGITS(&z2) = 0;
	MP_CHECKOK(mp_init(&x1));
	MP_CHECKOK(mp_init(&x2));
	MP_CHECKOK(mp_init(&z1));
	MP_CHECKOK(mp_init(&z2));

	/* if result should be point at infinity */
	if ((mp_cmp_z(n) == 0) || (ec_GF2m_pt_is_inf_aff(px, py) == MP_YES)) {
		MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry));
		goto CLEANUP;
	}

	MP_CHECKOK(mp_copy(px, &x1));	/* x1 = px */
	MP_CHECKOK(mp_set_int(&z1, 1));	/* z1 = 1 */
	MP_CHECKOK(group->meth->field_sqr(&x1, &z2, group->meth));	/* z2 =
																 * x1^2 =
																 * px^2 */
	MP_CHECKOK(group->meth->field_sqr(&z2, &x2, group->meth));
	MP_CHECKOK(group->meth->field_add(&x2, &group->curveb, &x2, group->meth));	/* x2 
																				 * = 
																				 * px^4 
																				 * + 
																				 * b 
																				 */

	/* find top-most bit and go one past it */
	i = MP_USED(n) - 1;
	j = MP_DIGIT_BIT - 1;
	top_bit = 1;
	top_bit <<= MP_DIGIT_BIT - 1;
	mask = top_bit;
	while (!(MP_DIGITS(n)[i] & mask)) {
		mask >>= 1;
		j--;
	}
	mask >>= 1;
	j--;

	/* if top most bit was at word break, go to next word */
	if (!mask) {
		i--;
		j = MP_DIGIT_BIT - 1;
		mask = top_bit;
	}

	for (; i >= 0; i--) {
		for (; j >= 0; j--) {
			if (MP_DIGITS(n)[i] & mask) {
				MP_CHECKOK(gf2m_Madd(px, &x1, &z1, &x2, &z2, group));
				MP_CHECKOK(gf2m_Mdouble(&x2, &z2, group));
			} else {
				MP_CHECKOK(gf2m_Madd(px, &x2, &z2, &x1, &z1, group));
				MP_CHECKOK(gf2m_Mdouble(&x1, &z1, group));
			}
			mask >>= 1;
		}
		j = MP_DIGIT_BIT - 1;
		mask = top_bit;
	}

	/* convert out of "projective" coordinates */
	i = gf2m_Mxy(px, py, &x1, &z1, &x2, &z2, group);
	if (i == 0) {
		res = MP_BADARG;
		goto CLEANUP;
	} else if (i == 1) {
		MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry));
	} else {
		MP_CHECKOK(mp_copy(&x2, rx));
		MP_CHECKOK(mp_copy(&z2, ry));
	}

  CLEANUP:
	mp_clear(&x1);
	mp_clear(&x2);
	mp_clear(&z1);
	mp_clear(&z2);
	return res;
}