xref: /onnv-gate/usr/src/common/crypto/ecc/ecl_gf.c (revision 5697:324be5104707)

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

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

#include "mpi.h"
#include "mp_gf2m.h"
#include "ecl-priv.h"
#include "mpi-priv.h"
#ifndef _KERNEL
#include <stdlib.h>
#endif

/* Allocate memory for a new GFMethod object. */
GFMethod *
GFMethod_new(int kmflag)
{
	mp_err res = MP_OKAY;
	GFMethod *meth;
#ifdef _KERNEL
	meth = (GFMethod *) kmem_alloc(sizeof(GFMethod), kmflag);
#else
	meth = (GFMethod *) malloc(sizeof(GFMethod));
	if (meth == NULL)
		return NULL;
#endif
	meth->constructed = MP_YES;
	MP_DIGITS(&meth->irr) = 0;
	meth->extra_free = NULL;
	MP_CHECKOK(mp_init(&meth->irr, kmflag));

  CLEANUP:
	if (res != MP_OKAY) {
		GFMethod_free(meth);
		return NULL;
	}
	return meth;
}

/* Construct a generic GFMethod for arithmetic over prime fields with
 * irreducible irr. */
GFMethod *
GFMethod_consGFp(const mp_int *irr)
{
	mp_err res = MP_OKAY;
	GFMethod *meth = NULL;

	meth = GFMethod_new(FLAG(irr));
	if (meth == NULL)
		return NULL;

	MP_CHECKOK(mp_copy(irr, &meth->irr));
	meth->irr_arr[0] = mpl_significant_bits(irr);
	meth->irr_arr[1] = meth->irr_arr[2] = meth->irr_arr[3] =
		meth->irr_arr[4] = 0;
	switch(MP_USED(&meth->irr)) {
	/* maybe we need 1 and 2 words here as well?*/
	case 3:
		meth->field_add = &ec_GFp_add_3;
		meth->field_sub = &ec_GFp_sub_3;
		break;
	case 4:
		meth->field_add = &ec_GFp_add_4;
		meth->field_sub = &ec_GFp_sub_4;
		break;
	case 5:
		meth->field_add = &ec_GFp_add_5;
		meth->field_sub = &ec_GFp_sub_5;
		break;
	case 6:
		meth->field_add = &ec_GFp_add_6;
		meth->field_sub = &ec_GFp_sub_6;
		break;
	default:
		meth->field_add = &ec_GFp_add;
		meth->field_sub = &ec_GFp_sub;
	}
	meth->field_neg = &ec_GFp_neg;
	meth->field_mod = &ec_GFp_mod;
	meth->field_mul = &ec_GFp_mul;
	meth->field_sqr = &ec_GFp_sqr;
	meth->field_div = &ec_GFp_div;
	meth->field_enc = NULL;
	meth->field_dec = NULL;
	meth->extra1 = NULL;
	meth->extra2 = NULL;
	meth->extra_free = NULL;

  CLEANUP:
	if (res != MP_OKAY) {
		GFMethod_free(meth);
		return NULL;
	}
	return meth;
}

/* Construct a generic GFMethod for arithmetic over binary polynomial
 * fields with irreducible irr that has array representation irr_arr (see
 * ecl-priv.h for description of the representation).  If irr_arr is NULL,
 * then it is constructed from the bitstring representation. */
GFMethod *
GFMethod_consGF2m(const mp_int *irr, const unsigned int irr_arr[5])
{
	mp_err res = MP_OKAY;
	int ret;
	GFMethod *meth = NULL;

	meth = GFMethod_new(FLAG(irr));
	if (meth == NULL)
		return NULL;

	MP_CHECKOK(mp_copy(irr, &meth->irr));
	if (irr_arr != NULL) {
		/* Irreducible polynomials are either trinomials or pentanomials. */
		meth->irr_arr[0] = irr_arr[0];
		meth->irr_arr[1] = irr_arr[1];
		meth->irr_arr[2] = irr_arr[2];
		if (irr_arr[2] > 0) {
			meth->irr_arr[3] = irr_arr[3];
			meth->irr_arr[4] = irr_arr[4];
		} else {
			meth->irr_arr[3] = meth->irr_arr[4] = 0;
		}
	} else {
		ret = mp_bpoly2arr(irr, meth->irr_arr, 5);
		/* Irreducible polynomials are either trinomials or pentanomials. */
		if ((ret != 5) && (ret != 3)) {
			res = MP_UNDEF;
			goto CLEANUP;
		}
	}
	meth->field_add = &ec_GF2m_add;
	meth->field_neg = &ec_GF2m_neg;
	meth->field_sub = &ec_GF2m_add;
	meth->field_mod = &ec_GF2m_mod;
	meth->field_mul = &ec_GF2m_mul;
	meth->field_sqr = &ec_GF2m_sqr;
	meth->field_div = &ec_GF2m_div;
	meth->field_enc = NULL;
	meth->field_dec = NULL;
	meth->extra1 = NULL;
	meth->extra2 = NULL;
	meth->extra_free = NULL;

  CLEANUP:
	if (res != MP_OKAY) {
		GFMethod_free(meth);
		return NULL;
	}
	return meth;
}

/* Free the memory allocated (if any) to a GFMethod object. */
void
GFMethod_free(GFMethod *meth)
{
	if (meth == NULL)
		return;
	if (meth->constructed == MP_NO)
		return;
	mp_clear(&meth->irr);
	if (meth->extra_free != NULL)
		meth->extra_free(meth);
#ifdef _KERNEL
	kmem_free(meth, sizeof(GFMethod));
#else
	free(meth);
#endif
}

/* Wrapper functions for generic prime field arithmetic. */

/* Add two field elements.  Assumes that 0 <= a, b < meth->irr */
mp_err
ec_GFp_add(const mp_int *a, const mp_int *b, mp_int *r,
		   const GFMethod *meth)
{
	/* PRE: 0 <= a, b < p = meth->irr POST: 0 <= r < p, r = a + b (mod p) */
	mp_err res;

	if ((res = mp_add(a, b, r)) != MP_OKAY) {
		return res;
	}
	if (mp_cmp(r, &meth->irr) >= 0) {
		return mp_sub(r, &meth->irr, r);
	}
	return res;
}

/* Negates a field element.  Assumes that 0 <= a < meth->irr */
mp_err
ec_GFp_neg(const mp_int *a, mp_int *r, const GFMethod *meth)
{
	/* PRE: 0 <= a < p = meth->irr POST: 0 <= r < p, r = -a (mod p) */

	if (mp_cmp_z(a) == 0) {
		mp_zero(r);
		return MP_OKAY;
	}
	return mp_sub(&meth->irr, a, r);
}

/* Subtracts two field elements.  Assumes that 0 <= a, b < meth->irr */
mp_err
ec_GFp_sub(const mp_int *a, const mp_int *b, mp_int *r,
		   const GFMethod *meth)
{
	mp_err res = MP_OKAY;

	/* PRE: 0 <= a, b < p = meth->irr POST: 0 <= r < p, r = a - b (mod p) */
	res = mp_sub(a, b, r);
	if (res == MP_RANGE) {
		MP_CHECKOK(mp_sub(b, a, r));
		if (mp_cmp_z(r) < 0) {
			MP_CHECKOK(mp_add(r, &meth->irr, r));
		}
		MP_CHECKOK(ec_GFp_neg(r, r, meth));
	}
	if (mp_cmp_z(r) < 0) {
		MP_CHECKOK(mp_add(r, &meth->irr, r));
	}
  CLEANUP:
	return res;
}
/*
 * Inline adds for small curve lengths.
 */
/* 3 words */
mp_err
ec_GFp_add_3(const mp_int *a, const mp_int *b, mp_int *r,
			const GFMethod *meth)
{
	mp_err res = MP_OKAY;
	mp_digit a0 = 0, a1 = 0, a2 = 0;
	mp_digit r0 = 0, r1 = 0, r2 = 0;
	mp_digit carry;

	switch(MP_USED(a)) {
	case 3:
		a2 = MP_DIGIT(a,2);
	case 2:
		a1 = MP_DIGIT(a,1);
	case 1:
		a0 = MP_DIGIT(a,0);
	}
	switch(MP_USED(b)) {
	case 3:
		r2 = MP_DIGIT(b,2);
	case 2:
		r1 = MP_DIGIT(b,1);
	case 1:
		r0 = MP_DIGIT(b,0);
	}

#ifndef MPI_AMD64_ADD
	MP_ADD_CARRY(a0, r0, r0, 0,     carry);
	MP_ADD_CARRY(a1, r1, r1, carry, carry);
	MP_ADD_CARRY(a2, r2, r2, carry, carry);
#else
	__asm__ (
                "xorq   %3,%3           \n\t"
                "addq   %4,%0           \n\t"
                "adcq   %5,%1           \n\t"
                "adcq   %6,%2           \n\t"
                "adcq   $0,%3           \n\t"
                : "=r"(r0), "=r"(r1), "=r"(r2), "=r"(carry)
                : "r" (a0), "r" (a1), "r" (a2),
		  "0" (r0), "1" (r1), "2" (r2)
                : "%cc" );
#endif

	MP_CHECKOK(s_mp_pad(r, 3));
	MP_DIGIT(r, 2) = r2;
	MP_DIGIT(r, 1) = r1;
	MP_DIGIT(r, 0) = r0;
	MP_SIGN(r) = MP_ZPOS;
	MP_USED(r) = 3;

	/* Do quick 'subract' if we've gone over
	 * (add the 2's complement of the curve field) */
	 a2 = MP_DIGIT(&meth->irr,2);
	if (carry ||  r2 >  a2 ||
		((r2 == a2) && mp_cmp(r,&meth->irr) != MP_LT)) {
		a1 = MP_DIGIT(&meth->irr,1);
		a0 = MP_DIGIT(&meth->irr,0);
#ifndef MPI_AMD64_ADD
		MP_SUB_BORROW(r0, a0, r0, 0,     carry);
		MP_SUB_BORROW(r1, a1, r1, carry, carry);
		MP_SUB_BORROW(r2, a2, r2, carry, carry);
#else
		__asm__ (
			"subq   %3,%0           \n\t"
			"sbbq   %4,%1           \n\t"
			"sbbq   %5,%2           \n\t"
			: "=r"(r0), "=r"(r1), "=r"(r2)
			: "r" (a0), "r" (a1), "r" (a2),
			  "0" (r0), "1" (r1), "2" (r2)
			: "%cc" );
#endif
		MP_DIGIT(r, 2) = r2;
		MP_DIGIT(r, 1) = r1;
		MP_DIGIT(r, 0) = r0;
	}

	s_mp_clamp(r);

  CLEANUP:
	return res;
}

/* 4 words */
mp_err
ec_GFp_add_4(const mp_int *a, const mp_int *b, mp_int *r,
			const GFMethod *meth)
{
	mp_err res = MP_OKAY;
	mp_digit a0 = 0, a1 = 0, a2 = 0, a3 = 0;
	mp_digit r0 = 0, r1 = 0, r2 = 0, r3 = 0;
	mp_digit carry;

	switch(MP_USED(a)) {
	case 4:
		a3 = MP_DIGIT(a,3);
	case 3:
		a2 = MP_DIGIT(a,2);
	case 2:
		a1 = MP_DIGIT(a,1);
	case 1:
		a0 = MP_DIGIT(a,0);
	}
	switch(MP_USED(b)) {
	case 4:
		r3 = MP_DIGIT(b,3);
	case 3:
		r2 = MP_DIGIT(b,2);
	case 2:
		r1 = MP_DIGIT(b,1);
	case 1:
		r0 = MP_DIGIT(b,0);
	}

#ifndef MPI_AMD64_ADD
	MP_ADD_CARRY(a0, r0, r0, 0,     carry);
	MP_ADD_CARRY(a1, r1, r1, carry, carry);
	MP_ADD_CARRY(a2, r2, r2, carry, carry);
	MP_ADD_CARRY(a3, r3, r3, carry, carry);
#else
	__asm__ (
                "xorq   %4,%4           \n\t"
                "addq   %5,%0           \n\t"
                "adcq   %6,%1           \n\t"
                "adcq   %7,%2           \n\t"
                "adcq   %8,%3           \n\t"
                "adcq   $0,%4           \n\t"
                : "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3), "=r"(carry)
                : "r" (a0), "r" (a1), "r" (a2), "r" (a3),
		  "0" (r0), "1" (r1), "2" (r2), "3" (r3)
                : "%cc" );
#endif

	MP_CHECKOK(s_mp_pad(r, 4));
	MP_DIGIT(r, 3) = r3;
	MP_DIGIT(r, 2) = r2;
	MP_DIGIT(r, 1) = r1;
	MP_DIGIT(r, 0) = r0;
	MP_SIGN(r) = MP_ZPOS;
	MP_USED(r) = 4;

	/* Do quick 'subract' if we've gone over
	 * (add the 2's complement of the curve field) */
	 a3 = MP_DIGIT(&meth->irr,3);
	if (carry ||  r3 >  a3 ||
		((r3 == a3) && mp_cmp(r,&meth->irr) != MP_LT)) {
		a2 = MP_DIGIT(&meth->irr,2);
		a1 = MP_DIGIT(&meth->irr,1);
		a0 = MP_DIGIT(&meth->irr,0);
#ifndef MPI_AMD64_ADD
		MP_SUB_BORROW(r0, a0, r0, 0,     carry);
		MP_SUB_BORROW(r1, a1, r1, carry, carry);
		MP_SUB_BORROW(r2, a2, r2, carry, carry);
		MP_SUB_BORROW(r3, a3, r3, carry, carry);
#else
		__asm__ (
			"subq   %4,%0           \n\t"
			"sbbq   %5,%1           \n\t"
			"sbbq   %6,%2           \n\t"
			"sbbq   %7,%3           \n\t"
			: "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3)
			: "r" (a0), "r" (a1), "r" (a2), "r" (a3),
			  "0" (r0), "1" (r1), "2" (r2), "3" (r3)
			: "%cc" );
#endif
		MP_DIGIT(r, 3) = r3;
		MP_DIGIT(r, 2) = r2;
		MP_DIGIT(r, 1) = r1;
		MP_DIGIT(r, 0) = r0;
	}

	s_mp_clamp(r);

  CLEANUP:
	return res;
}

/* 5 words */
mp_err
ec_GFp_add_5(const mp_int *a, const mp_int *b, mp_int *r,
			const GFMethod *meth)
{
	mp_err res = MP_OKAY;
	mp_digit a0 = 0, a1 = 0, a2 = 0, a3 = 0, a4 = 0;
	mp_digit r0 = 0, r1 = 0, r2 = 0, r3 = 0, r4 = 0;
	mp_digit carry;

	switch(MP_USED(a)) {
	case 5:
		a4 = MP_DIGIT(a,4);
	case 4:
		a3 = MP_DIGIT(a,3);
	case 3:
		a2 = MP_DIGIT(a,2);
	case 2:
		a1 = MP_DIGIT(a,1);
	case 1:
		a0 = MP_DIGIT(a,0);
	}
	switch(MP_USED(b)) {
	case 5:
		r4 = MP_DIGIT(b,4);
	case 4:
		r3 = MP_DIGIT(b,3);
	case 3:
		r2 = MP_DIGIT(b,2);
	case 2:
		r1 = MP_DIGIT(b,1);
	case 1:
		r0 = MP_DIGIT(b,0);
	}

	MP_ADD_CARRY(a0, r0, r0, 0,     carry);
	MP_ADD_CARRY(a1, r1, r1, carry, carry);
	MP_ADD_CARRY(a2, r2, r2, carry, carry);
	MP_ADD_CARRY(a3, r3, r3, carry, carry);
	MP_ADD_CARRY(a4, r4, r4, carry, carry);

	MP_CHECKOK(s_mp_pad(r, 5));
	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;
	MP_SIGN(r) = MP_ZPOS;
	MP_USED(r) = 5;

	/* Do quick 'subract' if we've gone over
	 * (add the 2's complement of the curve field) */
	 a4 = MP_DIGIT(&meth->irr,4);
	if (carry ||  r4 >  a4 ||
		((r4 == a4) && mp_cmp(r,&meth->irr) != MP_LT)) {
		a3 = MP_DIGIT(&meth->irr,3);
		a2 = MP_DIGIT(&meth->irr,2);
		a1 = MP_DIGIT(&meth->irr,1);
		a0 = MP_DIGIT(&meth->irr,0);
		MP_SUB_BORROW(r0, a0, r0, 0,     carry);
		MP_SUB_BORROW(r1, a1, r1, carry, carry);
		MP_SUB_BORROW(r2, a2, r2, carry, carry);
		MP_SUB_BORROW(r3, a3, r3, carry, carry);
		MP_SUB_BORROW(r4, a4, r4, carry, carry);
		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;
	}

	s_mp_clamp(r);

  CLEANUP:
	return res;
}

/* 6 words */
mp_err
ec_GFp_add_6(const mp_int *a, const mp_int *b, mp_int *r,
			const GFMethod *meth)
{
	mp_err res = MP_OKAY;
	mp_digit a0 = 0, a1 = 0, a2 = 0, a3 = 0, a4 = 0, a5 = 0;
	mp_digit r0 = 0, r1 = 0, r2 = 0, r3 = 0, r4 = 0, r5 = 0;
	mp_digit carry;

	switch(MP_USED(a)) {
	case 6:
		a5 = MP_DIGIT(a,5);
	case 5:
		a4 = MP_DIGIT(a,4);
	case 4:
		a3 = MP_DIGIT(a,3);
	case 3:
		a2 = MP_DIGIT(a,2);
	case 2:
		a1 = MP_DIGIT(a,1);
	case 1:
		a0 = MP_DIGIT(a,0);
	}
	switch(MP_USED(b)) {
	case 6:
		r5 = MP_DIGIT(b,5);
	case 5:
		r4 = MP_DIGIT(b,4);
	case 4:
		r3 = MP_DIGIT(b,3);
	case 3:
		r2 = MP_DIGIT(b,2);
	case 2:
		r1 = MP_DIGIT(b,1);
	case 1:
		r0 = MP_DIGIT(b,0);
	}

	MP_ADD_CARRY(a0, r0, r0, 0,     carry);
	MP_ADD_CARRY(a1, r1, r1, carry, carry);
	MP_ADD_CARRY(a2, r2, r2, carry, carry);
	MP_ADD_CARRY(a3, r3, r3, carry, carry);
	MP_ADD_CARRY(a4, r4, r4, carry, carry);
	MP_ADD_CARRY(a5, r5, r5, carry, carry);

	MP_CHECKOK(s_mp_pad(r, 6));
	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;
	MP_SIGN(r) = MP_ZPOS;
	MP_USED(r) = 6;

	/* Do quick 'subract' if we've gone over
	 * (add the 2's complement of the curve field) */
	a5 = MP_DIGIT(&meth->irr,5);
	if (carry ||  r5 >  a5 ||
		((r5 == a5) && mp_cmp(r,&meth->irr) != MP_LT)) {
		a4 = MP_DIGIT(&meth->irr,4);
		a3 = MP_DIGIT(&meth->irr,3);
		a2 = MP_DIGIT(&meth->irr,2);
		a1 = MP_DIGIT(&meth->irr,1);
		a0 = MP_DIGIT(&meth->irr,0);
		MP_SUB_BORROW(r0, a0, r0, 0,     carry);
		MP_SUB_BORROW(r1, a1, r1, carry, carry);
		MP_SUB_BORROW(r2, a2, r2, carry, carry);
		MP_SUB_BORROW(r3, a3, r3, carry, carry);
		MP_SUB_BORROW(r4, a4, r4, carry, carry);
		MP_SUB_BORROW(r5, a5, r5, carry, carry);
		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;
	}

	s_mp_clamp(r);

  CLEANUP:
	return res;
}

/*
 * The following subraction functions do in-line subractions based
 * on our curve size.
 *
 * ... 3 words
 */
mp_err
ec_GFp_sub_3(const mp_int *a, const mp_int *b, mp_int *r,
			const GFMethod *meth)
{
	mp_err res = MP_OKAY;
	mp_digit b0 = 0, b1 = 0, b2 = 0;
	mp_digit r0 = 0, r1 = 0, r2 = 0;
	mp_digit borrow;

	switch(MP_USED(a)) {
	case 3:
		r2 = MP_DIGIT(a,2);
	case 2:
		r1 = MP_DIGIT(a,1);
	case 1:
		r0 = MP_DIGIT(a,0);
	}
	switch(MP_USED(b)) {
	case 3:
		b2 = MP_DIGIT(b,2);
	case 2:
		b1 = MP_DIGIT(b,1);
	case 1:
		b0 = MP_DIGIT(b,0);
	}

#ifndef MPI_AMD64_ADD
	MP_SUB_BORROW(r0, b0, r0, 0,     borrow);
	MP_SUB_BORROW(r1, b1, r1, borrow, borrow);
	MP_SUB_BORROW(r2, b2, r2, borrow, borrow);
#else
	__asm__ (
                "xorq   %3,%3           \n\t"
                "subq   %4,%0           \n\t"
                "sbbq   %5,%1           \n\t"
                "sbbq   %6,%2           \n\t"
                "adcq   $0,%3           \n\t"
                : "=r"(r0), "=r"(r1), "=r"(r2), "=r" (borrow)
                : "r" (b0), "r" (b1), "r" (b2),
		  "0" (r0), "1" (r1), "2" (r2)
                : "%cc" );
#endif

	/* Do quick 'add' if we've gone under 0
	 * (subtract the 2's complement of the curve field) */
	if (borrow) {
	 	b2 = MP_DIGIT(&meth->irr,2);
		b1 = MP_DIGIT(&meth->irr,1);
		b0 = MP_DIGIT(&meth->irr,0);
#ifndef MPI_AMD64_ADD
		MP_ADD_CARRY(b0, r0, r0, 0,      borrow);
		MP_ADD_CARRY(b1, r1, r1, borrow, borrow);
		MP_ADD_CARRY(b2, r2, r2, borrow, borrow);
#else
		__asm__ (
			"addq   %3,%0           \n\t"
			"adcq   %4,%1           \n\t"
			"adcq   %5,%2           \n\t"
			: "=r"(r0), "=r"(r1), "=r"(r2)
			: "r" (b0), "r" (b1), "r" (b2),
  			  "0" (r0), "1" (r1), "2" (r2)
			: "%cc" );
#endif
	}

#ifdef MPI_AMD64_ADD
	/* compiler fakeout? */
	if ((r2 == b0) && (r1 == b0) && (r0 == b0)) {
		MP_CHECKOK(s_mp_pad(r, 4));
	}
#endif
	MP_CHECKOK(s_mp_pad(r, 3));
	MP_DIGIT(r, 2) = r2;
	MP_DIGIT(r, 1) = r1;
	MP_DIGIT(r, 0) = r0;
	MP_SIGN(r) = MP_ZPOS;
	MP_USED(r) = 3;
	s_mp_clamp(r);

  CLEANUP:
	return res;
}

/* 4 words */
mp_err
ec_GFp_sub_4(const mp_int *a, const mp_int *b, mp_int *r,
			const GFMethod *meth)
{
	mp_err res = MP_OKAY;
	mp_digit b0 = 0, b1 = 0, b2 = 0, b3 = 0;
	mp_digit r0 = 0, r1 = 0, r2 = 0, r3 = 0;
	mp_digit borrow;

	switch(MP_USED(a)) {
	case 4:
		r3 = MP_DIGIT(a,3);
	case 3:
		r2 = MP_DIGIT(a,2);
	case 2:
		r1 = MP_DIGIT(a,1);
	case 1:
		r0 = MP_DIGIT(a,0);
	}
	switch(MP_USED(b)) {
	case 4:
		b3 = MP_DIGIT(b,3);
	case 3:
		b2 = MP_DIGIT(b,2);
	case 2:
		b1 = MP_DIGIT(b,1);
	case 1:
		b0 = MP_DIGIT(b,0);
	}

#ifndef MPI_AMD64_ADD
	MP_SUB_BORROW(r0, b0, r0, 0,     borrow);
	MP_SUB_BORROW(r1, b1, r1, borrow, borrow);
	MP_SUB_BORROW(r2, b2, r2, borrow, borrow);
	MP_SUB_BORROW(r3, b3, r3, borrow, borrow);
#else
	__asm__ (
                "xorq   %4,%4           \n\t"
                "subq   %5,%0           \n\t"
                "sbbq   %6,%1           \n\t"
                "sbbq   %7,%2           \n\t"
                "sbbq   %8,%3           \n\t"
                "adcq   $0,%4           \n\t"
                : "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3), "=r" (borrow)
                : "r" (b0), "r" (b1), "r" (b2), "r" (b3),
		  "0" (r0), "1" (r1), "2" (r2), "3" (r3)
                : "%cc" );
#endif

	/* Do quick 'add' if we've gone under 0
	 * (subtract the 2's complement of the curve field) */
	if (borrow) {
	 	b3 = MP_DIGIT(&meth->irr,3);
	 	b2 = MP_DIGIT(&meth->irr,2);
		b1 = MP_DIGIT(&meth->irr,1);
		b0 = MP_DIGIT(&meth->irr,0);
#ifndef MPI_AMD64_ADD
		MP_ADD_CARRY(b0, r0, r0, 0,      borrow);
		MP_ADD_CARRY(b1, r1, r1, borrow, borrow);
		MP_ADD_CARRY(b2, r2, r2, borrow, borrow);
		MP_ADD_CARRY(b3, r3, r3, borrow, borrow);
#else
		__asm__ (
			"addq   %4,%0           \n\t"
			"adcq   %5,%1           \n\t"
			"adcq   %6,%2           \n\t"
			"adcq   %7,%3           \n\t"
			: "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3)
			: "r" (b0), "r" (b1), "r" (b2), "r" (b3),
  			  "0" (r0), "1" (r1), "2" (r2), "3" (r3)
			: "%cc" );
#endif
	}
#ifdef MPI_AMD64_ADD
	/* compiler fakeout? */
	if ((r3 == b0) && (r1 == b0) && (r0 == b0)) {
		MP_CHECKOK(s_mp_pad(r, 4));
	}
#endif
	MP_CHECKOK(s_mp_pad(r, 4));
	MP_DIGIT(r, 3) = r3;
	MP_DIGIT(r, 2) = r2;
	MP_DIGIT(r, 1) = r1;
	MP_DIGIT(r, 0) = r0;
	MP_SIGN(r) = MP_ZPOS;
	MP_USED(r) = 4;
	s_mp_clamp(r);

  CLEANUP:
	return res;
}

/* 5 words */
mp_err
ec_GFp_sub_5(const mp_int *a, const mp_int *b, mp_int *r,
			const GFMethod *meth)
{
	mp_err res = MP_OKAY;
	mp_digit b0 = 0, b1 = 0, b2 = 0, b3 = 0, b4 = 0;
	mp_digit r0 = 0, r1 = 0, r2 = 0, r3 = 0, r4 = 0;
	mp_digit borrow;

	switch(MP_USED(a)) {
	case 5:
		r4 = MP_DIGIT(a,4);
	case 4:
		r3 = MP_DIGIT(a,3);
	case 3:
		r2 = MP_DIGIT(a,2);
	case 2:
		r1 = MP_DIGIT(a,1);
	case 1:
		r0 = MP_DIGIT(a,0);
	}
	switch(MP_USED(b)) {
	case 5:
		b4 = MP_DIGIT(b,4);
	case 4:
		b3 = MP_DIGIT(b,3);
	case 3:
		b2 = MP_DIGIT(b,2);
	case 2:
		b1 = MP_DIGIT(b,1);
	case 1:
		b0 = MP_DIGIT(b,0);
	}

	MP_SUB_BORROW(r0, b0, r0, 0,     borrow);
	MP_SUB_BORROW(r1, b1, r1, borrow, borrow);
	MP_SUB_BORROW(r2, b2, r2, borrow, borrow);
	MP_SUB_BORROW(r3, b3, r3, borrow, borrow);
	MP_SUB_BORROW(r4, b4, r4, borrow, borrow);

	/* Do quick 'add' if we've gone under 0
	 * (subtract the 2's complement of the curve field) */
	if (borrow) {
	 	b4 = MP_DIGIT(&meth->irr,4);
	 	b3 = MP_DIGIT(&meth->irr,3);
	 	b2 = MP_DIGIT(&meth->irr,2);
		b1 = MP_DIGIT(&meth->irr,1);
		b0 = MP_DIGIT(&meth->irr,0);
		MP_ADD_CARRY(b0, r0, r0, 0,      borrow);
		MP_ADD_CARRY(b1, r1, r1, borrow, borrow);
		MP_ADD_CARRY(b2, r2, r2, borrow, borrow);
		MP_ADD_CARRY(b3, r3, r3, borrow, borrow);
	}
	MP_CHECKOK(s_mp_pad(r, 5));
	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;
	MP_SIGN(r) = MP_ZPOS;
	MP_USED(r) = 5;
	s_mp_clamp(r);

  CLEANUP:
	return res;
}

/* 6 words */
mp_err
ec_GFp_sub_6(const mp_int *a, const mp_int *b, mp_int *r,
			const GFMethod *meth)
{
	mp_err res = MP_OKAY;
	mp_digit b0 = 0, b1 = 0, b2 = 0, b3 = 0, b4 = 0, b5 = 0;
	mp_digit r0 = 0, r1 = 0, r2 = 0, r3 = 0, r4 = 0, r5 = 0;
	mp_digit borrow;

	switch(MP_USED(a)) {
	case 6:
		r5 = MP_DIGIT(a,5);
	case 5:
		r4 = MP_DIGIT(a,4);
	case 4:
		r3 = MP_DIGIT(a,3);
	case 3:
		r2 = MP_DIGIT(a,2);
	case 2:
		r1 = MP_DIGIT(a,1);
	case 1:
		r0 = MP_DIGIT(a,0);
	}
	switch(MP_USED(b)) {
	case 6:
		b5 = MP_DIGIT(b,5);
	case 5:
		b4 = MP_DIGIT(b,4);
	case 4:
		b3 = MP_DIGIT(b,3);
	case 3:
		b2 = MP_DIGIT(b,2);
	case 2:
		b1 = MP_DIGIT(b,1);
	case 1:
		b0 = MP_DIGIT(b,0);
	}

	MP_SUB_BORROW(r0, b0, r0, 0,     borrow);
	MP_SUB_BORROW(r1, b1, r1, borrow, borrow);
	MP_SUB_BORROW(r2, b2, r2, borrow, borrow);
	MP_SUB_BORROW(r3, b3, r3, borrow, borrow);
	MP_SUB_BORROW(r4, b4, r4, borrow, borrow);
	MP_SUB_BORROW(r5, b5, r5, borrow, borrow);

	/* Do quick 'add' if we've gone under 0
	 * (subtract the 2's complement of the curve field) */
	if (borrow) {
	 	b5 = MP_DIGIT(&meth->irr,5);
	 	b4 = MP_DIGIT(&meth->irr,4);
	 	b3 = MP_DIGIT(&meth->irr,3);
	 	b2 = MP_DIGIT(&meth->irr,2);
		b1 = MP_DIGIT(&meth->irr,1);
		b0 = MP_DIGIT(&meth->irr,0);
		MP_ADD_CARRY(b0, r0, r0, 0,      borrow);
		MP_ADD_CARRY(b1, r1, r1, borrow, borrow);
		MP_ADD_CARRY(b2, r2, r2, borrow, borrow);
		MP_ADD_CARRY(b3, r3, r3, borrow, borrow);
		MP_ADD_CARRY(b4, r4, r4, borrow, borrow);
	}

	MP_CHECKOK(s_mp_pad(r, 6));
	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;
	MP_SIGN(r) = MP_ZPOS;
	MP_USED(r) = 6;
	s_mp_clamp(r);

  CLEANUP:
	return res;
}


/* Reduces an integer to a field element. */
mp_err
ec_GFp_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
{
	return mp_mod(a, &meth->irr, r);
}

/* Multiplies two field elements. */
mp_err
ec_GFp_mul(const mp_int *a, const mp_int *b, mp_int *r,
		   const GFMethod *meth)
{
	return mp_mulmod(a, b, &meth->irr, r);
}

/* Squares a field element. */
mp_err
ec_GFp_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
{
	return mp_sqrmod(a, &meth->irr, r);
}

/* Divides two field elements. If a is NULL, then returns the inverse of
 * b. */
mp_err
ec_GFp_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_mulmod(a, &t, &meth->irr, r));
	  CLEANUP:
		mp_clear(&t);
		return res;
	}
}

/* Wrapper functions for generic binary polynomial field arithmetic. */

/* Adds two field elements. */
mp_err
ec_GF2m_add(const mp_int *a, const mp_int *b, mp_int *r,
			const GFMethod *meth)
{
	return mp_badd(a, b, r);
}

/* Negates a field element. Note that for binary polynomial fields, the
 * negation of a field element is the field element itself. */
mp_err
ec_GF2m_neg(const mp_int *a, mp_int *r, const GFMethod *meth)
{
	if (a == r) {
		return MP_OKAY;
	} else {
		return mp_copy(a, r);
	}
}

/* Reduces a binary polynomial to a field element. */
mp_err
ec_GF2m_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
{
	return mp_bmod(a, meth->irr_arr, r);
}

/* Multiplies two field elements. */
mp_err
ec_GF2m_mul(const mp_int *a, const mp_int *b, mp_int *r,
			const GFMethod *meth)
{
	return mp_bmulmod(a, b, meth->irr_arr, r);
}

/* Squares a field element. */
mp_err
ec_GF2m_sqr(const mp_int *a, mp_int *r, const GFMethod *meth)
{
	return mp_bsqrmod(a, meth->irr_arr, r);
}

/* Divides two field elements. If a is NULL, then returns the inverse of
 * b. */
mp_err
ec_GF2m_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) {
		/* The GF(2^m) portion of MPI doesn't support invmod, so we
		 * compute 1/b. */
		MP_CHECKOK(mp_init(&t, FLAG(b)));
		MP_CHECKOK(mp_set_int(&t, 1));
		MP_CHECKOK(mp_bdivmod(&t, b, &meth->irr, meth->irr_arr, r));
	  CLEANUP:
		mp_clear(&t);
		return res;
	} else {
		return mp_bdivmod(a, b, &meth->irr, meth->irr_arr, r);
	}
}