michael@0: /* This Source Code Form is subject to the terms of the Mozilla Public
michael@0:  * License, v. 2.0. If a copy of the MPL was not distributed with this
michael@0:  * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
michael@0: 
michael@0: #include "ec2.h"
michael@0: #include "mplogic.h"
michael@0: #include "mp_gf2m.h"
michael@0: #include <stdlib.h>
michael@0: 
michael@0: /* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery
michael@0:  * projective coordinates. Uses algorithm Mdouble in appendix of Lopez, J. 
michael@0:  * and Dahab, R.  "Fast multiplication on elliptic curves over GF(2^m)
michael@0:  * without precomputation". modified to not require precomputation of
michael@0:  * c=b^{2^{m-1}}. */
michael@0: static mp_err
michael@0: gf2m_Mdouble(mp_int *x, mp_int *z, const ECGroup *group)
michael@0: {
michael@0: 	mp_err res = MP_OKAY;
michael@0: 	mp_int t1;
michael@0: 
michael@0: 	MP_DIGITS(&t1) = 0;
michael@0: 	MP_CHECKOK(mp_init(&t1));
michael@0: 
michael@0: 	MP_CHECKOK(group->meth->field_sqr(x, x, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_sqr(z, &t1, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_mul(x, &t1, z, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_sqr(x, x, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_sqr(&t1, &t1, group->meth));
michael@0: 	MP_CHECKOK(group->meth->
michael@0: 			   field_mul(&group->curveb, &t1, &t1, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_add(x, &t1, x, group->meth));
michael@0: 
michael@0:   CLEANUP:
michael@0: 	mp_clear(&t1);
michael@0: 	return res;
michael@0: }
michael@0: 
michael@0: /* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in
michael@0:  * Montgomery projective coordinates. Uses algorithm Madd in appendix of
michael@0:  * Lopex, J. and Dahab, R.  "Fast multiplication on elliptic curves over
michael@0:  * GF(2^m) without precomputation". */
michael@0: static mp_err
michael@0: gf2m_Madd(const mp_int *x, mp_int *x1, mp_int *z1, mp_int *x2, mp_int *z2,
michael@0: 		  const ECGroup *group)
michael@0: {
michael@0: 	mp_err res = MP_OKAY;
michael@0: 	mp_int t1, t2;
michael@0: 
michael@0: 	MP_DIGITS(&t1) = 0;
michael@0: 	MP_DIGITS(&t2) = 0;
michael@0: 	MP_CHECKOK(mp_init(&t1));
michael@0: 	MP_CHECKOK(mp_init(&t2));
michael@0: 
michael@0: 	MP_CHECKOK(mp_copy(x, &t1));
michael@0: 	MP_CHECKOK(group->meth->field_mul(x1, z2, x1, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_mul(z1, x2, z1, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_mul(x1, z1, &t2, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_sqr(z1, z1, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_mul(z1, &t1, x1, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_add(x1, &t2, x1, group->meth));
michael@0: 
michael@0:   CLEANUP:
michael@0: 	mp_clear(&t1);
michael@0: 	mp_clear(&t2);
michael@0: 	return res;
michael@0: }
michael@0: 
michael@0: /* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
michael@0:  * using Montgomery point multiplication algorithm Mxy() in appendix of
michael@0:  * Lopex, J. and Dahab, R.  "Fast multiplication on elliptic curves over
michael@0:  * GF(2^m) without precomputation". Returns: 0 on error 1 if return value
michael@0:  * should be the point at infinity 2 otherwise */
michael@0: static int
michael@0: gf2m_Mxy(const mp_int *x, const mp_int *y, mp_int *x1, mp_int *z1,
michael@0: 		 mp_int *x2, mp_int *z2, const ECGroup *group)
michael@0: {
michael@0: 	mp_err res = MP_OKAY;
michael@0: 	int ret = 0;
michael@0: 	mp_int t3, t4, t5;
michael@0: 
michael@0: 	MP_DIGITS(&t3) = 0;
michael@0: 	MP_DIGITS(&t4) = 0;
michael@0: 	MP_DIGITS(&t5) = 0;
michael@0: 	MP_CHECKOK(mp_init(&t3));
michael@0: 	MP_CHECKOK(mp_init(&t4));
michael@0: 	MP_CHECKOK(mp_init(&t5));
michael@0: 
michael@0: 	if (mp_cmp_z(z1) == 0) {
michael@0: 		mp_zero(x2);
michael@0: 		mp_zero(z2);
michael@0: 		ret = 1;
michael@0: 		goto CLEANUP;
michael@0: 	}
michael@0: 
michael@0: 	if (mp_cmp_z(z2) == 0) {
michael@0: 		MP_CHECKOK(mp_copy(x, x2));
michael@0: 		MP_CHECKOK(group->meth->field_add(x, y, z2, group->meth));
michael@0: 		ret = 2;
michael@0: 		goto CLEANUP;
michael@0: 	}
michael@0: 
michael@0: 	MP_CHECKOK(mp_set_int(&t5, 1));
michael@0: 	if (group->meth->field_enc) {
michael@0: 		MP_CHECKOK(group->meth->field_enc(&t5, &t5, group->meth));
michael@0: 	}
michael@0: 
michael@0: 	MP_CHECKOK(group->meth->field_mul(z1, z2, &t3, group->meth));
michael@0: 
michael@0: 	MP_CHECKOK(group->meth->field_mul(z1, x, z1, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_mul(z2, x, z2, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_mul(z2, x1, x1, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_add(z2, x2, z2, group->meth));
michael@0: 
michael@0: 	MP_CHECKOK(group->meth->field_mul(z2, z1, z2, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_sqr(x, &t4, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_add(&t4, y, &t4, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_mul(&t4, &t3, &t4, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_add(&t4, z2, &t4, group->meth));
michael@0: 
michael@0: 	MP_CHECKOK(group->meth->field_mul(&t3, x, &t3, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_div(&t5, &t3, &t3, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_mul(&t3, &t4, &t4, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_mul(x1, &t3, x2, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_add(x2, x, z2, group->meth));
michael@0: 
michael@0: 	MP_CHECKOK(group->meth->field_mul(z2, &t4, z2, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_add(z2, y, z2, group->meth));
michael@0: 
michael@0: 	ret = 2;
michael@0: 
michael@0:   CLEANUP:
michael@0: 	mp_clear(&t3);
michael@0: 	mp_clear(&t4);
michael@0: 	mp_clear(&t5);
michael@0: 	if (res == MP_OKAY) {
michael@0: 		return ret;
michael@0: 	} else {
michael@0: 		return 0;
michael@0: 	}
michael@0: }
michael@0: 
michael@0: /* Computes R = nP based on algorithm 2P of Lopex, J. and Dahab, R.  "Fast 
michael@0:  * multiplication on elliptic curves over GF(2^m) without
michael@0:  * precomputation". Elliptic curve points P and R can be identical. Uses
michael@0:  * Montgomery projective coordinates. */
michael@0: mp_err
michael@0: ec_GF2m_pt_mul_mont(const mp_int *n, const mp_int *px, const mp_int *py,
michael@0: 					mp_int *rx, mp_int *ry, const ECGroup *group)
michael@0: {
michael@0: 	mp_err res = MP_OKAY;
michael@0: 	mp_int x1, x2, z1, z2;
michael@0: 	int i, j;
michael@0: 	mp_digit top_bit, mask;
michael@0: 
michael@0: 	MP_DIGITS(&x1) = 0;
michael@0: 	MP_DIGITS(&x2) = 0;
michael@0: 	MP_DIGITS(&z1) = 0;
michael@0: 	MP_DIGITS(&z2) = 0;
michael@0: 	MP_CHECKOK(mp_init(&x1));
michael@0: 	MP_CHECKOK(mp_init(&x2));
michael@0: 	MP_CHECKOK(mp_init(&z1));
michael@0: 	MP_CHECKOK(mp_init(&z2));
michael@0: 
michael@0: 	/* if result should be point at infinity */
michael@0: 	if ((mp_cmp_z(n) == 0) || (ec_GF2m_pt_is_inf_aff(px, py) == MP_YES)) {
michael@0: 		MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry));
michael@0: 		goto CLEANUP;
michael@0: 	}
michael@0: 
michael@0: 	MP_CHECKOK(mp_copy(px, &x1));	/* x1 = px */
michael@0: 	MP_CHECKOK(mp_set_int(&z1, 1));	/* z1 = 1 */
michael@0: 	MP_CHECKOK(group->meth->field_sqr(&x1, &z2, group->meth));	/* z2 =
michael@0: 																 * x1^2 =
michael@0: 																 * px^2 */
michael@0: 	MP_CHECKOK(group->meth->field_sqr(&z2, &x2, group->meth));
michael@0: 	MP_CHECKOK(group->meth->field_add(&x2, &group->curveb, &x2, group->meth));	/* x2 
michael@0: 																				 * = 
michael@0: 																				 * px^4 
michael@0: 																				 * + 
michael@0: 																				 * b 
michael@0: 																				 */
michael@0: 
michael@0: 	/* find top-most bit and go one past it */
michael@0: 	i = MP_USED(n) - 1;
michael@0: 	j = MP_DIGIT_BIT - 1;
michael@0: 	top_bit = 1;
michael@0: 	top_bit <<= MP_DIGIT_BIT - 1;
michael@0: 	mask = top_bit;
michael@0: 	while (!(MP_DIGITS(n)[i] & mask)) {
michael@0: 		mask >>= 1;
michael@0: 		j--;
michael@0: 	}
michael@0: 	mask >>= 1;
michael@0: 	j--;
michael@0: 
michael@0: 	/* if top most bit was at word break, go to next word */
michael@0: 	if (!mask) {
michael@0: 		i--;
michael@0: 		j = MP_DIGIT_BIT - 1;
michael@0: 		mask = top_bit;
michael@0: 	}
michael@0: 
michael@0: 	for (; i >= 0; i--) {
michael@0: 		for (; j >= 0; j--) {
michael@0: 			if (MP_DIGITS(n)[i] & mask) {
michael@0: 				MP_CHECKOK(gf2m_Madd(px, &x1, &z1, &x2, &z2, group));
michael@0: 				MP_CHECKOK(gf2m_Mdouble(&x2, &z2, group));
michael@0: 			} else {
michael@0: 				MP_CHECKOK(gf2m_Madd(px, &x2, &z2, &x1, &z1, group));
michael@0: 				MP_CHECKOK(gf2m_Mdouble(&x1, &z1, group));
michael@0: 			}
michael@0: 			mask >>= 1;
michael@0: 		}
michael@0: 		j = MP_DIGIT_BIT - 1;
michael@0: 		mask = top_bit;
michael@0: 	}
michael@0: 
michael@0: 	/* convert out of "projective" coordinates */
michael@0: 	i = gf2m_Mxy(px, py, &x1, &z1, &x2, &z2, group);
michael@0: 	if (i == 0) {
michael@0: 		res = MP_BADARG;
michael@0: 		goto CLEANUP;
michael@0: 	} else if (i == 1) {
michael@0: 		MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry));
michael@0: 	} else {
michael@0: 		MP_CHECKOK(mp_copy(&x2, rx));
michael@0: 		MP_CHECKOK(mp_copy(&z2, ry));
michael@0: 	}
michael@0: 
michael@0:   CLEANUP:
michael@0: 	mp_clear(&x1);
michael@0: 	mp_clear(&x2);
michael@0: 	mp_clear(&z1);
michael@0: 	mp_clear(&z2);
michael@0: 	return res;
michael@0: }