xref: /illumos-gate/usr/src/common/crypto/ecc/ecl_mult.c (revision c40a6cd7)

/*
 * ***** BEGIN LICENSE BLOCK *****
 * Version: MPL 1.1/GPL 2.0/LGPL 2.1
 *
 * The contents of this file are subject to the Mozilla Public License Version
 * 1.1 (the "License"); you may not use this file except in compliance with
 * the License. You may obtain a copy of the License at
 * http://www.mozilla.org/MPL/
 *
 * Software distributed under the License is distributed on an "AS IS" basis,
 * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
 * for the specific language governing rights and limitations under the
 * License.
 *
 * The Original Code is the elliptic curve math library.
 *
 * The Initial Developer of the Original Code is
 * Sun Microsystems, Inc.
 * Portions created by the Initial Developer are Copyright (C) 2003
 * the Initial Developer. All Rights Reserved.
 *
 * Contributor(s):
 *   Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories
 *
 * Alternatively, the contents of this file may be used under the terms of
 * either the GNU General Public License Version 2 or later (the "GPL"), or
 * the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
 * in which case the provisions of the GPL or the LGPL are applicable instead
 * of those above. If you wish to allow use of your version of this file only
 * under the terms of either the GPL or the LGPL, and not to allow others to
 * use your version of this file under the terms of the MPL, indicate your
 * decision by deleting the provisions above and replace them with the notice
 * and other provisions required by the GPL or the LGPL. If you do not delete
 * the provisions above, a recipient may use your version of this file under
 * the terms of any one of the MPL, the GPL or the LGPL.
 *
 * ***** END LICENSE BLOCK ***** */
/*
 * Copyright 2007 Sun Microsystems, Inc.  All rights reserved.
 * Use is subject to license terms.
 *
 * Sun elects to use this software under the MPL license.
 */

#include "mpi.h"
#include "mplogic.h"
#include "ecl.h"
#include "ecl-priv.h"
#ifndef _KERNEL
#include <stdlib.h>
#endif

/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k * P(x,
 * y).  If x, y = NULL, then P is assumed to be the generator (base point)
 * of the group of points on the elliptic curve. Input and output values
 * are assumed to be NOT field-encoded. */
mp_err
ECPoint_mul(const ECGroup *group, const mp_int *k, const mp_int *px,
			const mp_int *py, mp_int *rx, mp_int *ry)
{
	mp_err res = MP_OKAY;
	mp_int kt;

	ARGCHK((k != NULL) && (group != NULL), MP_BADARG);
	MP_DIGITS(&kt) = 0;

	/* want scalar to be less than or equal to group order */
	if (mp_cmp(k, &group->order) > 0) {
		MP_CHECKOK(mp_init(&kt, FLAG(k)));
		MP_CHECKOK(mp_mod(k, &group->order, &kt));
	} else {
		MP_SIGN(&kt) = MP_ZPOS;
		MP_USED(&kt) = MP_USED(k);
		MP_ALLOC(&kt) = MP_ALLOC(k);
		MP_DIGITS(&kt) = MP_DIGITS(k);
	}

	if ((px == NULL) || (py == NULL)) {
		if (group->base_point_mul) {
			MP_CHECKOK(group->base_point_mul(&kt, rx, ry, group));
		} else {
			MP_CHECKOK(group->
					   point_mul(&kt, &group->genx, &group->geny, rx, ry,
								 group));
		}
	} else {
		if (group->meth->field_enc) {
			MP_CHECKOK(group->meth->field_enc(px, rx, group->meth));
			MP_CHECKOK(group->meth->field_enc(py, ry, group->meth));
			MP_CHECKOK(group->point_mul(&kt, rx, ry, rx, ry, group));
		} else {
			MP_CHECKOK(group->point_mul(&kt, px, py, rx, ry, group));
		}
	}
	if (group->meth->field_dec) {
		MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
		MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
	}

  CLEANUP:
	if (MP_DIGITS(&kt) != MP_DIGITS(k)) {
		mp_clear(&kt);
	}
	return res;
}

/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
 * k2 * P(x, y), where G is the generator (base point) of the group of
 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
 * Input and output values are assumed to be NOT field-encoded. */
mp_err
ec_pts_mul_basic(const mp_int *k1, const mp_int *k2, const mp_int *px,
				 const mp_int *py, mp_int *rx, mp_int *ry,
				 const ECGroup *group)
{
	mp_err res = MP_OKAY;
	mp_int sx, sy;

	ARGCHK(group != NULL, MP_BADARG);
	ARGCHK(!((k1 == NULL)
			 && ((k2 == NULL) || (px == NULL)
				 || (py == NULL))), MP_BADARG);

	/* if some arguments are not defined used ECPoint_mul */
	if (k1 == NULL) {
		return ECPoint_mul(group, k2, px, py, rx, ry);
	} else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
		return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
	}

	MP_DIGITS(&sx) = 0;
	MP_DIGITS(&sy) = 0;
	MP_CHECKOK(mp_init(&sx, FLAG(k1)));
	MP_CHECKOK(mp_init(&sy, FLAG(k1)));

	MP_CHECKOK(ECPoint_mul(group, k1, NULL, NULL, &sx, &sy));
	MP_CHECKOK(ECPoint_mul(group, k2, px, py, rx, ry));

	if (group->meth->field_enc) {
		MP_CHECKOK(group->meth->field_enc(&sx, &sx, group->meth));
		MP_CHECKOK(group->meth->field_enc(&sy, &sy, group->meth));
		MP_CHECKOK(group->meth->field_enc(rx, rx, group->meth));
		MP_CHECKOK(group->meth->field_enc(ry, ry, group->meth));
	}

	MP_CHECKOK(group->point_add(&sx, &sy, rx, ry, rx, ry, group));

	if (group->meth->field_dec) {
		MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
		MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
	}

  CLEANUP:
	mp_clear(&sx);
	mp_clear(&sy);
	return res;
}

/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
 * k2 * P(x, y), where G is the generator (base point) of the group of
 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
 * Input and output values are assumed to be NOT field-encoded. Uses
 * algorithm 15 (simultaneous multiple point multiplication) from Brown,
 * Hankerson, Lopez, Menezes. Software Implementation of the NIST
 * Elliptic Curves over Prime Fields. */
mp_err
ec_pts_mul_simul_w2(const mp_int *k1, const mp_int *k2, const mp_int *px,
					const mp_int *py, mp_int *rx, mp_int *ry,
					const ECGroup *group)
{
	mp_err res = MP_OKAY;
	mp_int precomp[4][4][2];
	const mp_int *a, *b;
	int i, j;
	int ai, bi, d;

	ARGCHK(group != NULL, MP_BADARG);
	ARGCHK(!((k1 == NULL)
			 && ((k2 == NULL) || (px == NULL)
				 || (py == NULL))), MP_BADARG);

	/* if some arguments are not defined used ECPoint_mul */
	if (k1 == NULL) {
		return ECPoint_mul(group, k2, px, py, rx, ry);
	} else if ((k2 == NULL) || (px == NULL) || (py == NULL)) {
		return ECPoint_mul(group, k1, NULL, NULL, rx, ry);
	}

	/* initialize precomputation table */
	for (i = 0; i < 4; i++) {
		for (j = 0; j < 4; j++) {
			MP_DIGITS(&precomp[i][j][0]) = 0;
			MP_DIGITS(&precomp[i][j][1]) = 0;
		}
	}
	for (i = 0; i < 4; i++) {
		for (j = 0; j < 4; j++) {
			 MP_CHECKOK( mp_init_size(&precomp[i][j][0],
					 ECL_MAX_FIELD_SIZE_DIGITS, FLAG(k1)) );
			 MP_CHECKOK( mp_init_size(&precomp[i][j][1],
					 ECL_MAX_FIELD_SIZE_DIGITS, FLAG(k1)) );
		}
	}

	/* fill precomputation table */
	/* assign {k1, k2} = {a, b} such that len(a) >= len(b) */
	if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) {
		a = k2;
		b = k1;
		if (group->meth->field_enc) {
			MP_CHECKOK(group->meth->
					   field_enc(px, &precomp[1][0][0], group->meth));
			MP_CHECKOK(group->meth->
					   field_enc(py, &precomp[1][0][1], group->meth));
		} else {
			MP_CHECKOK(mp_copy(px, &precomp[1][0][0]));
			MP_CHECKOK(mp_copy(py, &precomp[1][0][1]));
		}
		MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0]));
		MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1]));
	} else {
		a = k1;
		b = k2;
		MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0]));
		MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1]));
		if (group->meth->field_enc) {
			MP_CHECKOK(group->meth->
					   field_enc(px, &precomp[0][1][0], group->meth));
			MP_CHECKOK(group->meth->
					   field_enc(py, &precomp[0][1][1], group->meth));
		} else {
			MP_CHECKOK(mp_copy(px, &precomp[0][1][0]));
			MP_CHECKOK(mp_copy(py, &precomp[0][1][1]));
		}
	}
	/* precompute [*][0][*] */
	mp_zero(&precomp[0][0][0]);
	mp_zero(&precomp[0][0][1]);
	MP_CHECKOK(group->
			   point_dbl(&precomp[1][0][0], &precomp[1][0][1],
						 &precomp[2][0][0], &precomp[2][0][1], group));
	MP_CHECKOK(group->
			   point_add(&precomp[1][0][0], &precomp[1][0][1],
						 &precomp[2][0][0], &precomp[2][0][1],
						 &precomp[3][0][0], &precomp[3][0][1], group));
	/* precompute [*][1][*] */
	for (i = 1; i < 4; i++) {
		MP_CHECKOK(group->
				   point_add(&precomp[0][1][0], &precomp[0][1][1],
							 &precomp[i][0][0], &precomp[i][0][1],
							 &precomp[i][1][0], &precomp[i][1][1], group));
	}
	/* precompute [*][2][*] */
	MP_CHECKOK(group->
			   point_dbl(&precomp[0][1][0], &precomp[0][1][1],
						 &precomp[0][2][0], &precomp[0][2][1], group));
	for (i = 1; i < 4; i++) {
		MP_CHECKOK(group->
				   point_add(&precomp[0][2][0], &precomp[0][2][1],
							 &precomp[i][0][0], &precomp[i][0][1],
							 &precomp[i][2][0], &precomp[i][2][1], group));
	}
	/* precompute [*][3][*] */
	MP_CHECKOK(group->
			   point_add(&precomp[0][1][0], &precomp[0][1][1],
						 &precomp[0][2][0], &precomp[0][2][1],
						 &precomp[0][3][0], &precomp[0][3][1], group));
	for (i = 1; i < 4; i++) {
		MP_CHECKOK(group->
				   point_add(&precomp[0][3][0], &precomp[0][3][1],
							 &precomp[i][0][0], &precomp[i][0][1],
							 &precomp[i][3][0], &precomp[i][3][1], group));
	}

	d = (mpl_significant_bits(a) + 1) / 2;

	/* R = inf */
	mp_zero(rx);
	mp_zero(ry);

	for (i = d - 1; i >= 0; i--) {
		ai = MP_GET_BIT(a, 2 * i + 1);
		ai <<= 1;
		ai |= MP_GET_BIT(a, 2 * i);
		bi = MP_GET_BIT(b, 2 * i + 1);
		bi <<= 1;
		bi |= MP_GET_BIT(b, 2 * i);
		/* R = 2^2 * R */
		MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group));
		MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group));
		/* R = R + (ai * A + bi * B) */
		MP_CHECKOK(group->
				   point_add(rx, ry, &precomp[ai][bi][0],
							 &precomp[ai][bi][1], rx, ry, group));
	}

	if (group->meth->field_dec) {
		MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth));
		MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth));
	}

  CLEANUP:
	for (i = 0; i < 4; i++) {
		for (j = 0; j < 4; j++) {
			mp_clear(&precomp[i][j][0]);
			mp_clear(&precomp[i][j][1]);
		}
	}
	return res;
}

/* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G +
 * k2 * P(x, y), where G is the generator (base point) of the group of
 * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL.
 * Input and output values are assumed to be NOT field-encoded. */
mp_err
ECPoints_mul(const ECGroup *group, const mp_int *k1, const mp_int *k2,
			 const mp_int *px, const mp_int *py, mp_int *rx, mp_int *ry)
{
	mp_err res = MP_OKAY;
	mp_int k1t, k2t;
	const mp_int *k1p, *k2p;

	MP_DIGITS(&k1t) = 0;
	MP_DIGITS(&k2t) = 0;

	ARGCHK(group != NULL, MP_BADARG);

	/* want scalar to be less than or equal to group order */
	if (k1 != NULL) {
		if (mp_cmp(k1, &group->order) >= 0) {
			MP_CHECKOK(mp_init(&k1t, FLAG(k1)));
			MP_CHECKOK(mp_mod(k1, &group->order, &k1t));
			k1p = &k1t;
		} else {
			k1p = k1;
		}
	} else {
		k1p = k1;
	}
	if (k2 != NULL) {
		if (mp_cmp(k2, &group->order) >= 0) {
			MP_CHECKOK(mp_init(&k2t, FLAG(k2)));
			MP_CHECKOK(mp_mod(k2, &group->order, &k2t));
			k2p = &k2t;
		} else {
			k2p = k2;
		}
	} else {
		k2p = k2;
	}

	/* if points_mul is defined, then use it */
	if (group->points_mul) {
		res = group->points_mul(k1p, k2p, px, py, rx, ry, group);
	} else {
		res = ec_pts_mul_simul_w2(k1p, k2p, px, py, rx, ry, group);
	}

  CLEANUP:
	mp_clear(&k1t);
	mp_clear(&k2t);
	return res;
}