xref: /titanic_51/usr/src/common/crypto/ecc/ecp_224.c (revision f9fbec18f5b458b560ecf45d3db8e8bd56bf6942)

/*
 * ***** 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 prime 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):
 *   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.
 */

#pragma ident	"%Z%%M%	%I%	%E% SMI"

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

#define ECP224_DIGITS ECL_CURVE_DIGITS(224)

/* Fast modular reduction for p224 = 2^224 - 2^96 + 1.  a can be r. Uses
 * algorithm 7 from Brown, Hankerson, Lopez, Menezes. Software
 * Implementation of the NIST Elliptic Curves over Prime Fields. */
mp_err
ec_GFp_nistp224_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
{
	mp_err res = MP_OKAY;
	mp_size a_used = MP_USED(a);

	int    r3b;
	mp_digit carry;
#ifdef ECL_THIRTY_TWO_BIT
        mp_digit a6a = 0, a6b = 0,
                a5a = 0, a5b = 0, a4a = 0, a4b = 0, a3a = 0, a3b = 0;
        mp_digit r0a, r0b, r1a, r1b, r2a, r2b, r3a;
#else
	mp_digit a6 = 0, a5 = 0, a4 = 0, a3b = 0, a5a = 0;
        mp_digit a6b = 0, a6a_a5b = 0, a5b = 0, a5a_a4b = 0, a4a_a3b = 0;
        mp_digit r0, r1, r2, r3;
#endif

	/* reduction not needed if a is not larger than field size */
	if (a_used < ECP224_DIGITS) {
		if (a == r) return MP_OKAY;
		return mp_copy(a, r);
	}
	/* for polynomials larger than twice the field size, use regular
	 * reduction */
	if (a_used > ECL_CURVE_DIGITS(224*2)) {
		MP_CHECKOK(mp_mod(a, &meth->irr, r));
	} else {
#ifdef ECL_THIRTY_TWO_BIT
		/* copy out upper words of a */
		switch (a_used) {
		case 14:
			a6b = MP_DIGIT(a, 13);
		case 13:
			a6a = MP_DIGIT(a, 12);
		case 12:
			a5b = MP_DIGIT(a, 11);
		case 11:
			a5a = MP_DIGIT(a, 10);
		case 10:
			a4b = MP_DIGIT(a, 9);
		case 9:
			a4a = MP_DIGIT(a, 8);
		case 8:
			a3b = MP_DIGIT(a, 7);
		}
		r3a = MP_DIGIT(a, 6);
		r2b= MP_DIGIT(a, 5);
		r2a= MP_DIGIT(a, 4);
		r1b = MP_DIGIT(a, 3);
		r1a = MP_DIGIT(a, 2);
		r0b = MP_DIGIT(a, 1);
		r0a = MP_DIGIT(a, 0);


		/* implement r = (a3a,a2,a1,a0)
			+(a5a, a4,a3b,  0)
			+(  0, a6,a5b,  0)
			-(  0	 0,    0|a6b, a6a|a5b )
			-(  a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */
		MP_ADD_CARRY (r1b, a3b, r1b, 0,     carry);
		MP_ADD_CARRY (r2a, a4a, r2a, carry, carry);
		MP_ADD_CARRY (r2b, a4b, r2b, carry, carry);
		MP_ADD_CARRY (r3a, a5a, r3a, carry, carry);
		r3b = carry;
		MP_ADD_CARRY (r1b, a5b, r1b, 0,     carry);
		MP_ADD_CARRY (r2a, a6a, r2a, carry, carry);
		MP_ADD_CARRY (r2b, a6b, r2b, carry, carry);
		MP_ADD_CARRY (r3a,   0, r3a, carry, carry);
		r3b += carry;
		MP_SUB_BORROW(r0a, a3b, r0a, 0,     carry);
		MP_SUB_BORROW(r0b, a4a, r0b, carry, carry);
		MP_SUB_BORROW(r1a, a4b, r1a, carry, carry);
		MP_SUB_BORROW(r1b, a5a, r1b, carry, carry);
		MP_SUB_BORROW(r2a, a5b, r2a, carry, carry);
		MP_SUB_BORROW(r2b, a6a, r2b, carry, carry);
		MP_SUB_BORROW(r3a, a6b, r3a, carry, carry);
		r3b -= carry;
		MP_SUB_BORROW(r0a, a5b, r0a, 0,     carry);
		MP_SUB_BORROW(r0b, a6a, r0b, carry, carry);
		MP_SUB_BORROW(r1a, a6b, r1a, carry, carry);
		if (carry) {
			MP_SUB_BORROW(r1b, 0, r1b, carry, carry);
			MP_SUB_BORROW(r2a, 0, r2a, carry, carry);
			MP_SUB_BORROW(r2b, 0, r2b, carry, carry);
			MP_SUB_BORROW(r3a, 0, r3a, carry, carry);
			r3b -= carry;
		}

		while (r3b > 0) {
			int tmp;
			MP_ADD_CARRY(r1b, r3b, r1b, 0,     carry);
			if (carry) {
				MP_ADD_CARRY(r2a,  0, r2a, carry, carry);
				MP_ADD_CARRY(r2b,  0, r2b, carry, carry);
				MP_ADD_CARRY(r3a,  0, r3a, carry, carry);
			}
			tmp = carry;
			MP_SUB_BORROW(r0a, r3b, r0a, 0,     carry);
			if (carry) {
				MP_SUB_BORROW(r0b, 0, r0b, carry, carry);
				MP_SUB_BORROW(r1a, 0, r1a, carry, carry);
				MP_SUB_BORROW(r1b, 0, r1b, carry, carry);
				MP_SUB_BORROW(r2a, 0, r2a, carry, carry);
				MP_SUB_BORROW(r2b, 0, r2b, carry, carry);
				MP_SUB_BORROW(r3a, 0, r3a, carry, carry);
				tmp -= carry;
			}
			r3b = tmp;
		}

		while (r3b < 0) {
			mp_digit maxInt = MP_DIGIT_MAX;
                	MP_ADD_CARRY (r0a, 1, r0a, 0,     carry);
                	MP_ADD_CARRY (r0b, 0, r0b, carry, carry);
                	MP_ADD_CARRY (r1a, 0, r1a, carry, carry);
                	MP_ADD_CARRY (r1b, maxInt, r1b, carry, carry);
                	MP_ADD_CARRY (r2a, maxInt, r2a, carry, carry);
                	MP_ADD_CARRY (r2b, maxInt, r2b, carry, carry);
                	MP_ADD_CARRY (r3a, maxInt, r3a, carry, carry);
			r3b += carry;
		}
		/* check for final reduction */
		/* now the only way we are over is if the top 4 words are all ones */
		if ((r3a == MP_DIGIT_MAX) && (r2b == MP_DIGIT_MAX)
			&& (r2a == MP_DIGIT_MAX) && (r1b == MP_DIGIT_MAX) &&
			 ((r1a != 0) || (r0b != 0) || (r0a != 0)) ) {
			/* one last subraction */
			MP_SUB_BORROW(r0a, 1, r0a, 0,     carry);
			MP_SUB_BORROW(r0b, 0, r0b, carry, carry);
			MP_SUB_BORROW(r1a, 0, r1a, carry, carry);
			r1b = r2a = r2b = r3a = 0;
		}


		if (a != r) {
			MP_CHECKOK(s_mp_pad(r, 7));
		}
		/* set the lower words of r */
		MP_SIGN(r) = MP_ZPOS;
		MP_USED(r) = 7;
		MP_DIGIT(r, 6) = r3a;
		MP_DIGIT(r, 5) = r2b;
		MP_DIGIT(r, 4) = r2a;
		MP_DIGIT(r, 3) = r1b;
		MP_DIGIT(r, 2) = r1a;
		MP_DIGIT(r, 1) = r0b;
		MP_DIGIT(r, 0) = r0a;
#else
		/* copy out upper words of a */
		switch (a_used) {
		case 7:
			a6 = MP_DIGIT(a, 6);
			a6b = a6 >> 32;
			a6a_a5b = a6 << 32;
		case 6:
			a5 = MP_DIGIT(a, 5);
			a5b = a5 >> 32;
			a6a_a5b |= a5b;
			a5b = a5b << 32;
			a5a_a4b = a5 << 32;
			a5a = a5 & 0xffffffff;
		case 5:
			a4 = MP_DIGIT(a, 4);
			a5a_a4b |= a4 >> 32;
			a4a_a3b = a4 << 32;
		case 4:
			a3b = MP_DIGIT(a, 3) >> 32;
			a4a_a3b |= a3b;
			a3b = a3b << 32;
		}

		r3 = MP_DIGIT(a, 3) & 0xffffffff;
		r2 = MP_DIGIT(a, 2);
		r1 = MP_DIGIT(a, 1);
		r0 = MP_DIGIT(a, 0);

		/* implement r = (a3a,a2,a1,a0)
			+(a5a, a4,a3b,  0)
			+(  0, a6,a5b,  0)
			-(  0	 0,    0|a6b, a6a|a5b )
			-(  a6b, a6a|a5b, a5a|a4b, a4a|a3b ) */
		MP_ADD_CARRY (r1, a3b, r1, 0,     carry);
		MP_ADD_CARRY (r2, a4 , r2, carry, carry);
		MP_ADD_CARRY (r3, a5a, r3, carry, carry);
		MP_ADD_CARRY (r1, a5b, r1, 0,     carry);
		MP_ADD_CARRY (r2, a6 , r2, carry, carry);
		MP_ADD_CARRY (r3,   0, r3, carry, carry);

		MP_SUB_BORROW(r0, a4a_a3b, r0, 0,     carry);
		MP_SUB_BORROW(r1, a5a_a4b, r1, carry, carry);
		MP_SUB_BORROW(r2, a6a_a5b, r2, carry, carry);
		MP_SUB_BORROW(r3, a6b    , r3, carry, carry);
		MP_SUB_BORROW(r0, a6a_a5b, r0, 0,     carry);
		MP_SUB_BORROW(r1, a6b    , r1, carry, carry);
		if (carry) {
			MP_SUB_BORROW(r2, 0, r2, carry, carry);
			MP_SUB_BORROW(r3, 0, r3, carry, carry);
		}


		/* if the value is negative, r3 has a 2's complement
		 * high value */
		r3b = (int)(r3 >>32);
		while (r3b > 0) {
			r3 &= 0xffffffff;
			MP_ADD_CARRY(r1,((mp_digit)r3b) << 32, r1, 0, carry);
			if (carry) {
				MP_ADD_CARRY(r2,  0, r2, carry, carry);
				MP_ADD_CARRY(r3,  0, r3, carry, carry);
			}
			MP_SUB_BORROW(r0, r3b, r0, 0, carry);
			if (carry) {
				MP_SUB_BORROW(r1, 0, r1, carry, carry);
				MP_SUB_BORROW(r2, 0, r2, carry, carry);
				MP_SUB_BORROW(r3, 0, r3, carry, carry);
			}
			r3b = (int)(r3 >>32);
		}

		while (r3b < 0) {
                	MP_ADD_CARRY (r0, 1, r0, 0,     carry);
                	MP_ADD_CARRY (r1, MP_DIGIT_MAX <<32, r1, carry, carry);
                	MP_ADD_CARRY (r2, MP_DIGIT_MAX, r2, carry, carry);
                	MP_ADD_CARRY (r3, MP_DIGIT_MAX >> 32, r3, carry, carry);
			r3b = (int)(r3 >>32);
		}
		/* check for final reduction */
		/* now the only way we are over is if the top 4 words are all ones */
		if ((r3 == (MP_DIGIT_MAX >> 32)) && (r2 == MP_DIGIT_MAX)
			&& ((r1 & MP_DIGIT_MAX << 32)== MP_DIGIT_MAX << 32) &&
			 ((r1 != MP_DIGIT_MAX << 32 ) || (r0 != 0)) ) {
			/* one last subraction */
			MP_SUB_BORROW(r0, 1, r0, 0,     carry);
			MP_SUB_BORROW(r1, 0, r1, carry, carry);
			r2 = r3 = 0;
		}


		if (a != r) {
			MP_CHECKOK(s_mp_pad(r, 4));
		}
		/* set the lower words of r */
		MP_SIGN(r) = MP_ZPOS;
		MP_USED(r) = 4;
		MP_DIGIT(r, 3) = r3;
		MP_DIGIT(r, 2) = r2;
		MP_DIGIT(r, 1) = r1;
		MP_DIGIT(r, 0) = r0;
#endif
	}

  CLEANUP:
	return res;
}

/* Compute the square of polynomial a, reduce modulo p224. Store the
 * result in r.  r could be a.  Uses optimized modular reduction for p224.
 */
mp_err
ec_GFp_nistp224_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
{
	mp_err res = MP_OKAY;

	MP_CHECKOK(mp_sqr(a, r));
	MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth));
  CLEANUP:
	return res;
}

/* Compute the product of two polynomials a and b, reduce modulo p224.
 * Store the result in r.  r could be a or b; a could be b.  Uses
 * optimized modular reduction for p224. */
mp_err
ec_GFp_nistp224_mul(const mp_int *a, const mp_int *b, mp_int *r,
					const GFMethod *meth)
{
	mp_err res = MP_OKAY;

	MP_CHECKOK(mp_mul(a, b, r));
	MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth));
  CLEANUP:
	return res;
}

/* Divides two field elements. If a is NULL, then returns the inverse of
 * b. */
mp_err
ec_GFp_nistp224_div(const mp_int *a, const mp_int *b, mp_int *r,
		   const GFMethod *meth)
{
	mp_err res = MP_OKAY;
	mp_int t;

	/* If a is NULL, then return the inverse of b, otherwise return a/b. */
	if (a == NULL) {
		return  mp_invmod(b, &meth->irr, r);
	} else {
		/* MPI doesn't support divmod, so we implement it using invmod and
		 * mulmod. */
		MP_CHECKOK(mp_init(&t, FLAG(b)));
		MP_CHECKOK(mp_invmod(b, &meth->irr, &t));
		MP_CHECKOK(mp_mul(a, &t, r));
		MP_CHECKOK(ec_GFp_nistp224_mod(r, r, meth));
	  CLEANUP:
		mp_clear(&t);
		return res;
	}
}

/* Wire in fast field arithmetic and precomputation of base point for
 * named curves. */
mp_err
ec_group_set_gfp224(ECGroup *group, ECCurveName name)
{
	if (name == ECCurve_NIST_P224) {
		group->meth->field_mod = &ec_GFp_nistp224_mod;
		group->meth->field_mul = &ec_GFp_nistp224_mul;
		group->meth->field_sqr = &ec_GFp_nistp224_sqr;
		group->meth->field_div = &ec_GFp_nistp224_div;
	}
	return MP_OKAY;
}