andre@0: /* This Source Code Form is subject to the terms of the Mozilla Public
andre@0:  * License, v. 2.0. If a copy of the MPL was not distributed with this
andre@0:  * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
andre@0: 
andre@0: #include "mpi.h"
andre@0: #include "mplogic.h"
andre@0: #include "ecl.h"
andre@0: #include "ecl-priv.h"
andre@0: #include <stdlib.h>
andre@0: 
andre@0: /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k * P(x, 
andre@0:  * y).  If x, y = NULL, then P is assumed to be the generator (base point) 
andre@0:  * of the group of points on the elliptic curve. Input and output values
andre@0:  * are assumed to be NOT field-encoded. */
andre@0: mp_err
andre@0: ECPoint_mul(const ECGroup *group, const mp_int *k, const mp_int *px,
andre@0: 			const mp_int *py, mp_int *rx, mp_int *ry)
andre@0: {
andre@0: 	mp_err res = MP_OKAY;
andre@0: 	mp_int kt;
andre@0: 
andre@0: 	ARGCHK((k != NULL) && (group != NULL), MP_BADARG);
andre@0: 	MP_DIGITS(&kt) = 0;
andre@0: 
andre@0: 	/* want scalar to be less than or equal to group order */
andre@0: 	if (mp_cmp(k, &group->order) > 0) {
andre@0: 		MP_CHECKOK(mp_init(&kt));
andre@0: 		MP_CHECKOK(mp_mod(k, &group->order, &kt));
andre@0: 	} else {
andre@0: 		MP_SIGN(&kt) = MP_ZPOS;
andre@0: 		MP_USED(&kt) = MP_USED(k);
andre@0: 		MP_ALLOC(&kt) = MP_ALLOC(k);
andre@0: 		MP_DIGITS(&kt) = MP_DIGITS(k);
andre@0: 	}
andre@0: 
andre@0: 	if ((px == NULL) || (py == NULL)) {
andre@0: 		if (group->base_point_mul) {
andre@0: 			MP_CHECKOK(group->base_point_mul(&kt, rx, ry, group));
andre@0: 		} else {
andre@0: 			MP_CHECKOK(group->
andre@0: 					   point_mul(&kt, &group->genx, &group->geny, rx, ry,
andre@0: 								 group));
andre@0: 		}
andre@0: 	} else {
andre@0: 		if (group->meth->field_enc) {
andre@0: 			MP_CHECKOK(group->meth->field_enc(px, rx, group->meth));
andre@0: 			MP_CHECKOK(group->meth->field_enc(py, ry, group->meth));
andre@0: 			MP_CHECKOK(group->point_mul(&kt, rx, ry, rx, ry, group));
andre@0: 		} else {
andre@0: 			MP_CHECKOK(group->point_mul(&kt, px, py, rx, ry, group));
andre@0: 		}
andre@0: 	}
andre@0: 	if (group->meth->field_dec) {
andre@0: 		MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
andre@0: 		MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
andre@0: 	}
andre@0: 
andre@0:   CLEANUP:
andre@0: 	if (MP_DIGITS(&kt) != MP_DIGITS(k)) {
andre@0: 		mp_clear(&kt);
andre@0: 	}
andre@0: 	return res;
andre@0: }
andre@0: 
andre@0: /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G + 
andre@0:  * k2 * P(x, y), where G is the generator (base point) of the group of
andre@0:  * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
andre@0:  * Input and output values are assumed to be NOT field-encoded. */
andre@0: mp_err
andre@0: ec_pts_mul_basic(const mp_int *k1, const mp_int *k2, const mp_int *px,
andre@0: 				 const mp_int *py, mp_int *rx, mp_int *ry,
andre@0: 				 const ECGroup *group)
andre@0: {
andre@0: 	mp_err res = MP_OKAY;
andre@0: 	mp_int sx, sy;
andre@0: 
andre@0: 	ARGCHK(group != NULL, MP_BADARG);
andre@0: 	ARGCHK(!((k1 == NULL)
andre@0: 			 && ((k2 == NULL) || (px == NULL)
andre@0: 				 || (py == NULL))), MP_BADARG);
andre@0: 
andre@0: 	/* if some arguments are not defined used ECPoint_mul */
andre@0: 	if (k1 == NULL) {
andre@0: 		return ECPoint_mul(group, k2, px, py, rx, ry);
andre@0: 	} else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
andre@0: 		return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
andre@0: 	}
andre@0: 
andre@0: 	MP_DIGITS(&sx) = 0;
andre@0: 	MP_DIGITS(&sy) = 0;
andre@0: 	MP_CHECKOK(mp_init(&sx));
andre@0: 	MP_CHECKOK(mp_init(&sy));
andre@0: 
andre@0: 	MP_CHECKOK(ECPoint_mul(group, k1, NULL, NULL, &sx, &sy));
andre@0: 	MP_CHECKOK(ECPoint_mul(group, k2, px, py, rx, ry));
andre@0: 
andre@0: 	if (group->meth->field_enc) {
andre@0: 		MP_CHECKOK(group->meth->field_enc(&sx, &sx, group->meth));
andre@0: 		MP_CHECKOK(group->meth->field_enc(&sy, &sy, group->meth));
andre@0: 		MP_CHECKOK(group->meth->field_enc(rx, rx, group->meth));
andre@0: 		MP_CHECKOK(group->meth->field_enc(ry, ry, group->meth));
andre@0: 	}
andre@0: 
andre@0: 	MP_CHECKOK(group->point_add(&sx, &sy, rx, ry, rx, ry, group));
andre@0: 
andre@0: 	if (group->meth->field_dec) {
andre@0: 		MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
andre@0: 		MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
andre@0: 	}
andre@0: 
andre@0:   CLEANUP:
andre@0: 	mp_clear(&sx);
andre@0: 	mp_clear(&sy);
andre@0: 	return res;
andre@0: }
andre@0: 
andre@0: /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G + 
andre@0:  * k2 * P(x, y), where G is the generator (base point) of the group of
andre@0:  * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
andre@0:  * Input and output values are assumed to be NOT field-encoded. Uses
andre@0:  * algorithm 15 (simultaneous multiple point multiplication) from Brown,
andre@0:  * Hankerson, Lopez, Menezes. Software Implementation of the NIST
andre@0:  * Elliptic Curves over Prime Fields. */
andre@0: mp_err
andre@0: ec_pts_mul_simul_w2(const mp_int *k1, const mp_int *k2, const mp_int *px,
andre@0: 					const mp_int *py, mp_int *rx, mp_int *ry,
andre@0: 					const ECGroup *group)
andre@0: {
andre@0: 	mp_err res = MP_OKAY;
andre@0: 	mp_int precomp[4][4][2];
andre@0: 	const mp_int *a, *b;
andre@0: 	int i, j;
andre@0: 	int ai, bi, d;
andre@0: 
andre@0: 	ARGCHK(group != NULL, MP_BADARG);
andre@0: 	ARGCHK(!((k1 == NULL)
andre@0: 			 && ((k2 == NULL) || (px == NULL)
andre@0: 				 || (py == NULL))), MP_BADARG);
andre@0: 
andre@0: 	/* if some arguments are not defined used ECPoint_mul */
andre@0: 	if (k1 == NULL) {
andre@0: 		return ECPoint_mul(group, k2, px, py, rx, ry);
andre@0: 	} else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
andre@0: 		return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
andre@0: 	}
andre@0: 
andre@0: 	/* initialize precomputation table */
andre@0: 	for (i = 0; i < 4; i++) {
andre@0: 		for (j = 0; j < 4; j++) {
andre@0: 			MP_DIGITS(&precomp[i][j][0]) = 0;
andre@0: 			MP_DIGITS(&precomp[i][j][1]) = 0;
andre@0: 		}
andre@0: 	}
andre@0: 	for (i = 0; i < 4; i++) {
andre@0: 		for (j = 0; j < 4; j++) {
andre@0: 			 MP_CHECKOK( mp_init_size(&precomp[i][j][0],
andre@0: 						 ECL_MAX_FIELD_SIZE_DIGITS) );
andre@0: 			 MP_CHECKOK( mp_init_size(&precomp[i][j][1],
andre@0: 						 ECL_MAX_FIELD_SIZE_DIGITS) );
andre@0: 		}
andre@0: 	}
andre@0: 
andre@0: 	/* fill precomputation table */
andre@0: 	/* assign {k1, k2} = {a, b} such that len(a) >= len(b) */
andre@0: 	if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) {
andre@0: 		a = k2;
andre@0: 		b = k1;
andre@0: 		if (group->meth->field_enc) {
andre@0: 			MP_CHECKOK(group->meth->
andre@0: 					   field_enc(px, &precomp[1][0][0], group->meth));
andre@0: 			MP_CHECKOK(group->meth->
andre@0: 					   field_enc(py, &precomp[1][0][1], group->meth));
andre@0: 		} else {
andre@0: 			MP_CHECKOK(mp_copy(px, &precomp[1][0][0]));
andre@0: 			MP_CHECKOK(mp_copy(py, &precomp[1][0][1]));
andre@0: 		}
andre@0: 		MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0]));
andre@0: 		MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1]));
andre@0: 	} else {
andre@0: 		a = k1;
andre@0: 		b = k2;
andre@0: 		MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0]));
andre@0: 		MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1]));
andre@0: 		if (group->meth->field_enc) {
andre@0: 			MP_CHECKOK(group->meth->
andre@0: 					   field_enc(px, &precomp[0][1][0], group->meth));
andre@0: 			MP_CHECKOK(group->meth->
andre@0: 					   field_enc(py, &precomp[0][1][1], group->meth));
andre@0: 		} else {
andre@0: 			MP_CHECKOK(mp_copy(px, &precomp[0][1][0]));
andre@0: 			MP_CHECKOK(mp_copy(py, &precomp[0][1][1]));
andre@0: 		}
andre@0: 	}
andre@0: 	/* precompute [*][0][*] */
andre@0: 	mp_zero(&precomp[0][0][0]);
andre@0: 	mp_zero(&precomp[0][0][1]);
andre@0: 	MP_CHECKOK(group->
andre@0: 			   point_dbl(&precomp[1][0][0], &precomp[1][0][1],
andre@0: 						 &precomp[2][0][0], &precomp[2][0][1], group));
andre@0: 	MP_CHECKOK(group->
andre@0: 			   point_add(&precomp[1][0][0], &precomp[1][0][1],
andre@0: 						 &precomp[2][0][0], &precomp[2][0][1],
andre@0: 						 &precomp[3][0][0], &precomp[3][0][1], group));
andre@0: 	/* precompute [*][1][*] */
andre@0: 	for (i = 1; i < 4; i++) {
andre@0: 		MP_CHECKOK(group->
andre@0: 				   point_add(&precomp[0][1][0], &precomp[0][1][1],
andre@0: 							 &precomp[i][0][0], &precomp[i][0][1],
andre@0: 							 &precomp[i][1][0], &precomp[i][1][1], group));
andre@0: 	}
andre@0: 	/* precompute [*][2][*] */
andre@0: 	MP_CHECKOK(group->
andre@0: 			   point_dbl(&precomp[0][1][0], &precomp[0][1][1],
andre@0: 						 &precomp[0][2][0], &precomp[0][2][1], group));
andre@0: 	for (i = 1; i < 4; i++) {
andre@0: 		MP_CHECKOK(group->
andre@0: 				   point_add(&precomp[0][2][0], &precomp[0][2][1],
andre@0: 							 &precomp[i][0][0], &precomp[i][0][1],
andre@0: 							 &precomp[i][2][0], &precomp[i][2][1], group));
andre@0: 	}
andre@0: 	/* precompute [*][3][*] */
andre@0: 	MP_CHECKOK(group->
andre@0: 			   point_add(&precomp[0][1][0], &precomp[0][1][1],
andre@0: 						 &precomp[0][2][0], &precomp[0][2][1],
andre@0: 						 &precomp[0][3][0], &precomp[0][3][1], group));
andre@0: 	for (i = 1; i < 4; i++) {
andre@0: 		MP_CHECKOK(group->
andre@0: 				   point_add(&precomp[0][3][0], &precomp[0][3][1],
andre@0: 							 &precomp[i][0][0], &precomp[i][0][1],
andre@0: 							 &precomp[i][3][0], &precomp[i][3][1], group));
andre@0: 	}
andre@0: 
andre@0: 	d = (mpl_significant_bits(a) + 1) / 2;
andre@0: 
andre@0: 	/* R = inf */
andre@0: 	mp_zero(rx);
andre@0: 	mp_zero(ry);
andre@0: 
andre@0: 	for (i = d - 1; i >= 0; i--) {
andre@0: 		ai = MP_GET_BIT(a, 2 * i + 1);
andre@0: 		ai <<= 1;
andre@0: 		ai |= MP_GET_BIT(a, 2 * i);
andre@0: 		bi = MP_GET_BIT(b, 2 * i + 1);
andre@0: 		bi <<= 1;
andre@0: 		bi |= MP_GET_BIT(b, 2 * i);
andre@0: 		/* R = 2^2 * R */
andre@0: 		MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group));
andre@0: 		MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group));
andre@0: 		/* R = R + (ai * A + bi * B) */
andre@0: 		MP_CHECKOK(group->
andre@0: 				   point_add(rx, ry, &precomp[ai][bi][0],
andre@0: 							 &precomp[ai][bi][1], rx, ry, group));
andre@0: 	}
andre@0: 
andre@0: 	if (group->meth->field_dec) {
andre@0: 		MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
andre@0: 		MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
andre@0: 	}
andre@0: 
andre@0:   CLEANUP:
andre@0: 	for (i = 0; i < 4; i++) {
andre@0: 		for (j = 0; j < 4; j++) {
andre@0: 			mp_clear(&precomp[i][j][0]);
andre@0: 			mp_clear(&precomp[i][j][1]);
andre@0: 		}
andre@0: 	}
andre@0: 	return res;
andre@0: }
andre@0: 
andre@0: /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G + 
andre@0:  * k2 * P(x, y), where G is the generator (base point) of the group of
andre@0:  * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
andre@0:  * Input and output values are assumed to be NOT field-encoded. */
andre@0: mp_err
andre@0: ECPoints_mul(const ECGroup *group, const mp_int *k1, const mp_int *k2,
andre@0: 			 const mp_int *px, const mp_int *py, mp_int *rx, mp_int *ry)
andre@0: {
andre@0: 	mp_err res = MP_OKAY;
andre@0: 	mp_int k1t, k2t;
andre@0: 	const mp_int *k1p, *k2p;
andre@0: 
andre@0: 	MP_DIGITS(&k1t) = 0;
andre@0: 	MP_DIGITS(&k2t) = 0;
andre@0: 
andre@0: 	ARGCHK(group != NULL, MP_BADARG);
andre@0: 
andre@0: 	/* want scalar to be less than or equal to group order */
andre@0: 	if (k1 != NULL) {
andre@0: 		if (mp_cmp(k1, &group->order) >= 0) {
andre@0: 			MP_CHECKOK(mp_init(&k1t));
andre@0: 			MP_CHECKOK(mp_mod(k1, &group->order, &k1t));
andre@0: 			k1p = &k1t;
andre@0: 		} else {
andre@0: 			k1p = k1;
andre@0: 		}
andre@0: 	} else {
andre@0: 		k1p = k1;
andre@0: 	}
andre@0: 	if (k2 != NULL) {
andre@0: 		if (mp_cmp(k2, &group->order) >= 0) {
andre@0: 			MP_CHECKOK(mp_init(&k2t));
andre@0: 			MP_CHECKOK(mp_mod(k2, &group->order, &k2t));
andre@0: 			k2p = &k2t;
andre@0: 		} else {
andre@0: 			k2p = k2;
andre@0: 		}
andre@0: 	} else {
andre@0: 		k2p = k2;
andre@0: 	}
andre@0: 
andre@0: 	/* if points_mul is defined, then use it */
andre@0: 	if (group->points_mul) {
andre@0: 		res = group->points_mul(k1p, k2p, px, py, rx, ry, group);
andre@0: 	} else {
andre@0: 		res = ec_pts_mul_simul_w2(k1p, k2p, px, py, rx, ry, group);
andre@0: 	}
andre@0: 
andre@0:   CLEANUP:
andre@0: 	mp_clear(&k1t);
andre@0: 	mp_clear(&k2t);
andre@0: 	return res;
andre@0: }