xref: /illumos-gate/usr/src/common/crypto/ecc/ec2_mont.c (revision c40a6cd785e883b3f052b122c332e21174fc1871)

/*
 * ***** 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 for binary polynomial field curves.
 *
 * 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):
 *   Sheueling Chang-Shantz <sheueling.chang@sun.com>,
 *   Stephen Fung <fungstep@hotmail.com>, and
 *   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 "ec2.h"
#include "mplogic.h"
#include "mp_gf2m.h"
#ifndef _KERNEL
#include <stdlib.h>
#endif

/* 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, int kmflag)
{
	mp_err res = MP_OKAY;
	mp_int t1;

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

	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, int kmflag)
{
	mp_err res = MP_OKAY;
	mp_int t1, t2;

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

	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, FLAG(x2)));
	MP_CHECKOK(mp_init(&t4, FLAG(x2)));
	MP_CHECKOK(mp_init(&t5, FLAG(x2)));

	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, FLAG(n)));
	MP_CHECKOK(mp_init(&x2, FLAG(n)));
	MP_CHECKOK(mp_init(&z1, FLAG(n)));
	MP_CHECKOK(mp_init(&z2, FLAG(n)));

	/* 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, FLAG(n)));
				MP_CHECKOK(gf2m_Mdouble(&x2, &z2, group, FLAG(n)));
			} else {
				MP_CHECKOK(gf2m_Madd(px, &x2, &z2, &x1, &z1, group, FLAG(n)));
				MP_CHECKOK(gf2m_Mdouble(&x1, &z1, group, FLAG(n)));
			}
			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;
}