jdk/src/share/native/sun/security/ec/ecl_gf.c
changeset 3492 e549cea58864
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/jdk/src/share/native/sun/security/ec/ecl_gf.c	Tue Aug 11 16:52:26 2009 +0100
@@ -0,0 +1,1062 @@
+/* *********************************************************************
+ *
+ * Sun elects to have this file available under and governed by the
+ * Mozilla Public License Version 1.1 ("MPL") (see
+ * http://www.mozilla.org/MPL/ for full license text). For the avoidance
+ * of doubt and subject to the following, Sun also elects to allow
+ * licensees to use this file under the MPL, the GNU General Public
+ * License version 2 only or the Lesser General Public License version
+ * 2.1 only. Any references to the "GNU General Public License version 2
+ * or later" or "GPL" in the following shall be construed to mean the
+ * GNU General Public License version 2 only. Any references to the "GNU
+ * Lesser General Public License version 2.1 or later" or "LGPL" in the
+ * following shall be construed to mean the GNU Lesser General Public
+ * License version 2.1 only. However, the following notice accompanied
+ * the original version of this file:
+ *
+ * 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.
+ *
+ *********************************************************************** */
+/*
+ * Copyright 2007 Sun Microsystems, Inc.  All rights reserved.
+ * Use is subject to license terms.
+ */
+
+#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);
+        }
+}