xref: /titanic_51/usr/src/common/crypto/ecc/ecp_256.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>
 *
 * 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

/* Fast modular reduction for p256 = 2^256 - 2^224 + 2^192+ 2^96 - 1.  a can be r.
 * Uses algorithm 2.29 from Hankerson, Menezes, Vanstone. Guide to
 * Elliptic Curve Cryptography. */
mp_err
ec_GFp_nistp256_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
{
	mp_err res = MP_OKAY;
	mp_size a_used = MP_USED(a);
	int a_bits = mpl_significant_bits(a);
	mp_digit carry;

#ifdef ECL_THIRTY_TWO_BIT
	mp_digit a8=0, a9=0, a10=0, a11=0, a12=0, a13=0, a14=0, a15=0;
	mp_digit r0, r1, r2, r3, r4, r5, r6, r7;
	int r8; /* must be a signed value ! */
#else
	mp_digit a4=0, a5=0, a6=0, a7=0;
	mp_digit a4h, a4l, a5h, a5l, a6h, a6l, a7h, a7l;
	mp_digit r0, r1, r2, r3;
	int r4; /* must be a signed value ! */
#endif
	/* for polynomials larger than twice the field size
	 * use regular reduction */
	if (a_bits < 256) {
		if (a == r) return MP_OKAY;
		return mp_copy(a,r);
	}
	if (a_bits > 512)  {
		MP_CHECKOK(mp_mod(a, &meth->irr, r));
	} else {

#ifdef ECL_THIRTY_TWO_BIT
		switch (a_used) {
		case 16:
			a15 = MP_DIGIT(a,15);
		case 15:
			a14 = MP_DIGIT(a,14);
		case 14:
			a13 = MP_DIGIT(a,13);
		case 13:
			a12 = MP_DIGIT(a,12);
		case 12:
			a11 = MP_DIGIT(a,11);
		case 11:
			a10 = MP_DIGIT(a,10);
		case 10:
			a9 = MP_DIGIT(a,9);
		case 9:
			a8 = MP_DIGIT(a,8);
		}

		r0 = MP_DIGIT(a,0);
		r1 = MP_DIGIT(a,1);
		r2 = MP_DIGIT(a,2);
		r3 = MP_DIGIT(a,3);
		r4 = MP_DIGIT(a,4);
		r5 = MP_DIGIT(a,5);
		r6 = MP_DIGIT(a,6);
		r7 = MP_DIGIT(a,7);

		/* sum 1 */
		MP_ADD_CARRY(r3, a11, r3, 0,     carry);
		MP_ADD_CARRY(r4, a12, r4, carry, carry);
		MP_ADD_CARRY(r5, a13, r5, carry, carry);
		MP_ADD_CARRY(r6, a14, r6, carry, carry);
		MP_ADD_CARRY(r7, a15, r7, carry, carry);
		r8 = carry;
		MP_ADD_CARRY(r3, a11, r3, 0,     carry);
		MP_ADD_CARRY(r4, a12, r4, carry, carry);
		MP_ADD_CARRY(r5, a13, r5, carry, carry);
		MP_ADD_CARRY(r6, a14, r6, carry, carry);
		MP_ADD_CARRY(r7, a15, r7, carry, carry);
		r8 += carry;
		/* sum 2 */
		MP_ADD_CARRY(r3, a12, r3, 0,     carry);
		MP_ADD_CARRY(r4, a13, r4, carry, carry);
		MP_ADD_CARRY(r5, a14, r5, carry, carry);
		MP_ADD_CARRY(r6, a15, r6, carry, carry);
		MP_ADD_CARRY(r7,   0, r7, carry, carry);
		r8 += carry;
		/* combine last bottom of sum 3 with second sum 2 */
		MP_ADD_CARRY(r0, a8,  r0, 0,     carry);
		MP_ADD_CARRY(r1, a9,  r1, carry, carry);
		MP_ADD_CARRY(r2, a10, r2, carry, carry);
		MP_ADD_CARRY(r3, a12, r3, carry, carry);
		MP_ADD_CARRY(r4, a13, r4, carry, carry);
		MP_ADD_CARRY(r5, a14, r5, carry, carry);
		MP_ADD_CARRY(r6, a15, r6, carry, carry);
		MP_ADD_CARRY(r7, a15, r7, carry, carry); /* from sum 3 */
		r8 += carry;
		/* sum 3 (rest of it)*/
		MP_ADD_CARRY(r6, a14, r6, 0,     carry);
		MP_ADD_CARRY(r7,   0, r7, carry, carry);
		r8 += carry;
		/* sum 4 (rest of it)*/
		MP_ADD_CARRY(r0, a9,  r0, 0,     carry);
		MP_ADD_CARRY(r1, a10, r1, carry, carry);
		MP_ADD_CARRY(r2, a11, r2, carry, carry);
		MP_ADD_CARRY(r3, a13, r3, carry, carry);
		MP_ADD_CARRY(r4, a14, r4, carry, carry);
		MP_ADD_CARRY(r5, a15, r5, carry, carry);
		MP_ADD_CARRY(r6, a13, r6, carry, carry);
		MP_ADD_CARRY(r7, a8,  r7, carry, carry);
		r8 += carry;
		/* diff 5 */
		MP_SUB_BORROW(r0, a11, r0, 0,     carry);
		MP_SUB_BORROW(r1, a12, r1, carry, carry);
		MP_SUB_BORROW(r2, a13, r2, carry, carry);
		MP_SUB_BORROW(r3,   0, r3, carry, carry);
		MP_SUB_BORROW(r4,   0, r4, carry, carry);
		MP_SUB_BORROW(r5,   0, r5, carry, carry);
		MP_SUB_BORROW(r6, a8,  r6, carry, carry);
		MP_SUB_BORROW(r7, a10, r7, carry, carry);
		r8 -= carry;
		/* diff 6 */
		MP_SUB_BORROW(r0, a12, r0, 0,     carry);
		MP_SUB_BORROW(r1, a13, r1, carry, carry);
		MP_SUB_BORROW(r2, a14, r2, carry, carry);
		MP_SUB_BORROW(r3, a15, r3, carry, carry);
		MP_SUB_BORROW(r4,   0, r4, carry, carry);
		MP_SUB_BORROW(r5,   0, r5, carry, carry);
		MP_SUB_BORROW(r6, a9,  r6, carry, carry);
		MP_SUB_BORROW(r7, a11, r7, carry, carry);
		r8 -= carry;
		/* diff 7 */
		MP_SUB_BORROW(r0, a13, r0, 0,     carry);
		MP_SUB_BORROW(r1, a14, r1, carry, carry);
		MP_SUB_BORROW(r2, a15, r2, carry, carry);
		MP_SUB_BORROW(r3, a8,  r3, carry, carry);
		MP_SUB_BORROW(r4, a9,  r4, carry, carry);
		MP_SUB_BORROW(r5, a10, r5, carry, carry);
		MP_SUB_BORROW(r6, 0,   r6, carry, carry);
		MP_SUB_BORROW(r7, a12, r7, carry, carry);
		r8 -= carry;
		/* diff 8 */
		MP_SUB_BORROW(r0, a14, r0, 0,     carry);
		MP_SUB_BORROW(r1, a15, r1, carry, carry);
		MP_SUB_BORROW(r2, 0,   r2, carry, carry);
		MP_SUB_BORROW(r3, a9,  r3, carry, carry);
		MP_SUB_BORROW(r4, a10, r4, carry, carry);
		MP_SUB_BORROW(r5, a11, r5, carry, carry);
		MP_SUB_BORROW(r6, 0,   r6, carry, carry);
		MP_SUB_BORROW(r7, a13, r7, carry, carry);
		r8 -= carry;

		/* reduce the overflows */
		while (r8 > 0) {
			mp_digit r8_d = r8;
			MP_ADD_CARRY(r0, r8_d,         r0, 0,     carry);
			MP_ADD_CARRY(r1, 0,            r1, carry, carry);
			MP_ADD_CARRY(r2, 0,            r2, carry, carry);
			MP_ADD_CARRY(r3, -r8_d,        r3, carry, carry);
			MP_ADD_CARRY(r4, MP_DIGIT_MAX, r4, carry, carry);
			MP_ADD_CARRY(r5, MP_DIGIT_MAX, r5, carry, carry);
			MP_ADD_CARRY(r6, -(r8_d+1),    r6, carry, carry);
			MP_ADD_CARRY(r7, (r8_d-1),     r7, carry, carry);
			r8 = carry;
		}

		/* reduce the underflows */
		while (r8 < 0) {
			mp_digit r8_d = -r8;
			MP_SUB_BORROW(r0, r8_d,         r0, 0,     carry);
			MP_SUB_BORROW(r1, 0,            r1, carry, carry);
			MP_SUB_BORROW(r2, 0,            r2, carry, carry);
			MP_SUB_BORROW(r3, -r8_d,        r3, carry, carry);
			MP_SUB_BORROW(r4, MP_DIGIT_MAX, r4, carry, carry);
			MP_SUB_BORROW(r5, MP_DIGIT_MAX, r5, carry, carry);
			MP_SUB_BORROW(r6, -(r8_d+1),    r6, carry, carry);
			MP_SUB_BORROW(r7, (r8_d-1),     r7, carry, carry);
			r8 = -carry;
		}
		if (a != r) {
			MP_CHECKOK(s_mp_pad(r,8));
		}
		MP_SIGN(r) = MP_ZPOS;
		MP_USED(r) = 8;

		MP_DIGIT(r,7) = r7;
		MP_DIGIT(r,6) = r6;
		MP_DIGIT(r,5) = r5;
		MP_DIGIT(r,4) = r4;
		MP_DIGIT(r,3) = r3;
		MP_DIGIT(r,2) = r2;
		MP_DIGIT(r,1) = r1;
		MP_DIGIT(r,0) = r0;

		/* final reduction if necessary */
		if ((r7 == MP_DIGIT_MAX) &&
			((r6 > 1) || ((r6 == 1) &&
			(r5 || r4 || r3 ||
				((r2 == MP_DIGIT_MAX) && (r1 == MP_DIGIT_MAX)
				  && (r0 == MP_DIGIT_MAX)))))) {
			MP_CHECKOK(mp_sub(r, &meth->irr, r));
		}
#ifdef notdef


		/* smooth the negatives */
		while (MP_SIGN(r) != MP_ZPOS) {
			MP_CHECKOK(mp_add(r, &meth->irr, r));
		}
		while (MP_USED(r) > 8) {
			MP_CHECKOK(mp_sub(r, &meth->irr, r));
		}

		/* final reduction if necessary */
		if (MP_DIGIT(r,7) >= MP_DIGIT(&meth->irr,7)) {
		    if (mp_cmp(r,&meth->irr) != MP_LT) {
			MP_CHECKOK(mp_sub(r, &meth->irr, r));
		    }
		}
#endif
		s_mp_clamp(r);
#else
		switch (a_used) {
		case 8:
			a7 = MP_DIGIT(a,7);
		case 7:
			a6 = MP_DIGIT(a,6);
		case 6:
			a5 = MP_DIGIT(a,5);
		case 5:
			a4 = MP_DIGIT(a,4);
		}
		a7l = a7 << 32;
		a7h = a7 >> 32;
		a6l = a6 << 32;
		a6h = a6 >> 32;
		a5l = a5 << 32;
		a5h = a5 >> 32;
		a4l = a4 << 32;
		a4h = a4 >> 32;
		r3 = MP_DIGIT(a,3);
		r2 = MP_DIGIT(a,2);
		r1 = MP_DIGIT(a,1);
		r0 = MP_DIGIT(a,0);

		/* sum 1 */
		MP_ADD_CARRY(r1, a5h << 32, r1, 0,     carry);
		MP_ADD_CARRY(r2, a6,        r2, carry, carry);
		MP_ADD_CARRY(r3, a7,        r3, carry, carry);
		r4 = carry;
		MP_ADD_CARRY(r1, a5h << 32, r1, 0,     carry);
		MP_ADD_CARRY(r2, a6,        r2, carry, carry);
		MP_ADD_CARRY(r3, a7,        r3, carry, carry);
		r4 += carry;
		/* sum 2 */
		MP_ADD_CARRY(r1, a6l,       r1, 0,     carry);
		MP_ADD_CARRY(r2, a6h | a7l, r2, carry, carry);
		MP_ADD_CARRY(r3, a7h,       r3, carry, carry);
		r4 += carry;
		MP_ADD_CARRY(r1, a6l,       r1, 0,     carry);
		MP_ADD_CARRY(r2, a6h | a7l, r2, carry, carry);
		MP_ADD_CARRY(r3, a7h,       r3, carry, carry);
		r4 += carry;

		/* sum 3 */
		MP_ADD_CARRY(r0, a4,        r0, 0,     carry);
		MP_ADD_CARRY(r1, a5l >> 32, r1, carry, carry);
		MP_ADD_CARRY(r2, 0,         r2, carry, carry);
		MP_ADD_CARRY(r3, a7,        r3, carry, carry);
		r4 += carry;
		/* sum 4 */
		MP_ADD_CARRY(r0, a4h | a5l,     r0, 0,     carry);
		MP_ADD_CARRY(r1, a5h|(a6h<<32), r1, carry, carry);
		MP_ADD_CARRY(r2, a7,            r2, carry, carry);
		MP_ADD_CARRY(r3, a6h | a4l,     r3, carry, carry);
		r4 += carry;
		/* diff 5 */
		MP_SUB_BORROW(r0, a5h | a6l,    r0, 0,     carry);
		MP_SUB_BORROW(r1, a6h,          r1, carry, carry);
		MP_SUB_BORROW(r2, 0,            r2, carry, carry);
		MP_SUB_BORROW(r3, (a4l>>32)|a5l,r3, carry, carry);
		r4 -= carry;
		/* diff 6 */
		MP_SUB_BORROW(r0, a6,  		r0, 0,     carry);
		MP_SUB_BORROW(r1, a7,           r1, carry, carry);
		MP_SUB_BORROW(r2, 0,            r2, carry, carry);
		MP_SUB_BORROW(r3, a4h|(a5h<<32),r3, carry, carry);
		r4 -= carry;
		/* diff 7 */
		MP_SUB_BORROW(r0, a6h|a7l,	r0, 0,     carry);
		MP_SUB_BORROW(r1, a7h|a4l,      r1, carry, carry);
		MP_SUB_BORROW(r2, a4h|a5l,      r2, carry, carry);
		MP_SUB_BORROW(r3, a6l,          r3, carry, carry);
		r4 -= carry;
		/* diff 8 */
		MP_SUB_BORROW(r0, a7,	        r0, 0,     carry);
		MP_SUB_BORROW(r1, a4h<<32,      r1, carry, carry);
		MP_SUB_BORROW(r2, a5,           r2, carry, carry);
		MP_SUB_BORROW(r3, a6h<<32,      r3, carry, carry);
		r4 -= carry;

		/* reduce the overflows */
		while (r4 > 0) {
			mp_digit r4_long = r4;
			mp_digit r4l = (r4_long << 32);
			MP_ADD_CARRY(r0, r4_long,      r0, 0,     carry);
			MP_ADD_CARRY(r1, -r4l,         r1, carry, carry);
			MP_ADD_CARRY(r2, MP_DIGIT_MAX, r2, carry, carry);
			MP_ADD_CARRY(r3, r4l-r4_long-1,r3, carry, carry);
			r4 = carry;
		}

		/* reduce the underflows */
		while (r4 < 0) {
			mp_digit r4_long = -r4;
			mp_digit r4l = (r4_long << 32);
			MP_SUB_BORROW(r0, r4_long,      r0, 0,     carry);
			MP_SUB_BORROW(r1, -r4l,         r1, carry, carry);
			MP_SUB_BORROW(r2, MP_DIGIT_MAX, r2, carry, carry);
			MP_SUB_BORROW(r3, r4l-r4_long-1,r3, carry, carry);
			r4 = -carry;
		}

		if (a != r) {
			MP_CHECKOK(s_mp_pad(r,4));
		}
		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;

		/* final reduction if necessary */
		if ((r3 > 0xFFFFFFFF00000001ULL) ||
			((r3 == 0xFFFFFFFF00000001ULL) &&
			(r2 || (r1 >> 32)||
			       (r1 == 0xFFFFFFFFULL && r0 == MP_DIGIT_MAX)))) {
			/* very rare, just use mp_sub */
			MP_CHECKOK(mp_sub(r, &meth->irr, r));
		}

		s_mp_clamp(r);
#endif
	}

  CLEANUP:
	return res;
}

/* Compute the square of polynomial a, reduce modulo p256. Store the
 * result in r.  r could be a.  Uses optimized modular reduction for p256.
 */
mp_err
ec_GFp_nistp256_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_nistp256_mod(r, r, meth));
  CLEANUP:
	return res;
}

/* Compute the product of two polynomials a and b, reduce modulo p256.
 * Store the result in r.  r could be a or b; a could be b.  Uses
 * optimized modular reduction for p256. */
mp_err
ec_GFp_nistp256_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_nistp256_mod(r, r, meth));
  CLEANUP:
	return res;
}

/* Wire in fast field arithmetic and precomputation of base point for
 * named curves. */
mp_err
ec_group_set_gfp256(ECGroup *group, ECCurveName name)
{
	if (name == ECCurve_NIST_P256) {
		group->meth->field_mod = &ec_GFp_nistp256_mod;
		group->meth->field_mul = &ec_GFp_nistp256_mul;
		group->meth->field_sqr = &ec_GFp_nistp256_sqr;
	}
	return MP_OKAY;
}