/*
* Copyright (c) 2007, 2011, Oracle and/or its affiliates. All rights reserved.
* Use is subject to license terms.
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with this library; if not, write to the Free Software Foundation,
* Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*/
/* *********************************************************************
*
* 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
*
*********************************************************************** */
#include "ecp.h"
#include "mpi.h"
#include "mplogic.h"
#include "mpi-priv.h"
#ifndef _KERNEL
#include <stdlib.h>
#endif
#define ECP192_DIGITS ECL_CURVE_DIGITS(192)
/* Fast modular reduction for p192 = 2^192 - 2^64 - 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_nistp192_mod(const mp_int *a, mp_int *r, const GFMethod *meth)
{
mp_err res = MP_OKAY;
mp_size a_used = MP_USED(a);
mp_digit r3;
#ifndef MPI_AMD64_ADD
mp_digit carry;
#endif
#ifdef ECL_THIRTY_TWO_BIT
mp_digit a5a = 0, a5b = 0, a4a = 0, a4b = 0, a3a = 0, a3b = 0;
mp_digit r0a, r0b, r1a, r1b, r2a, r2b;
#else
mp_digit a5 = 0, a4 = 0, a3 = 0;
mp_digit r0, r1, r2;
#endif
/* reduction not needed if a is not larger than field size */
if (a_used < ECP192_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 > ECP192_DIGITS*2) {
MP_CHECKOK(mp_mod(a, &meth->irr, r));
} else {
/* copy out upper words of a */
#ifdef ECL_THIRTY_TWO_BIT
/* in all the math below,
* nXb is most signifiant, nXa is least significant */
switch (a_used) {
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);
case 7:
a3a = 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 = (a2,a1,a0)+(a5,a5,a5)+(a4,a4,0)+(0,a3,a3) */
MP_ADD_CARRY(r0a, a3a, r0a, 0, carry);
MP_ADD_CARRY(r0b, a3b, r0b, carry, carry);
MP_ADD_CARRY(r1a, a3a, r1a, carry, carry);
MP_ADD_CARRY(r1b, a3b, r1b, carry, carry);
MP_ADD_CARRY(r2a, a4a, r2a, carry, carry);
MP_ADD_CARRY(r2b, a4b, r2b, carry, carry);
r3 = carry; carry = 0;
MP_ADD_CARRY(r0a, a5a, r0a, 0, carry);
MP_ADD_CARRY(r0b, a5b, r0b, carry, carry);
MP_ADD_CARRY(r1a, a5a, r1a, carry, carry);
MP_ADD_CARRY(r1b, a5b, r1b, carry, carry);
MP_ADD_CARRY(r2a, a5a, r2a, carry, carry);
MP_ADD_CARRY(r2b, a5b, r2b, carry, carry);
r3 += carry;
MP_ADD_CARRY(r1a, a4a, r1a, 0, carry);
MP_ADD_CARRY(r1b, a4b, r1b, carry, carry);
MP_ADD_CARRY(r2a, 0, r2a, carry, carry);
MP_ADD_CARRY(r2b, 0, r2b, carry, carry);
r3 += carry;
/* reduce out the carry */
while (r3) {
MP_ADD_CARRY(r0a, r3, r0a, 0, carry);
MP_ADD_CARRY(r0b, 0, r0b, carry, carry);
MP_ADD_CARRY(r1a, r3, r1a, carry, carry);
MP_ADD_CARRY(r1b, 0, r1b, carry, carry);
MP_ADD_CARRY(r2a, 0, r2a, carry, carry);
MP_ADD_CARRY(r2b, 0, r2b, carry, carry);
r3 = carry;
}
/* check for final reduction */
/*
* our field is 0xffffffffffffffff, 0xfffffffffffffffe,
* 0xffffffffffffffff. That means we can only be over and need
* one more reduction
* if r2 == 0xffffffffffffffffff (same as r2+1 == 0)
* and
* r1 == 0xffffffffffffffffff or
* r1 == 0xfffffffffffffffffe and r0 = 0xfffffffffffffffff
* In all cases, we subtract the field (or add the 2's
* complement value (1,1,0)). (r0, r1, r2)
*/
if (((r2b == 0xffffffff) && (r2a == 0xffffffff)
&& (r1b == 0xffffffff) ) &&
((r1a == 0xffffffff) ||
(r1a == 0xfffffffe) && (r0a == 0xffffffff) &&
(r0b == 0xffffffff)) ) {
/* do a quick subtract */
MP_ADD_CARRY(r0a, 1, r0a, 0, carry);
r0b += carry;
r1a = r1b = r2a = r2b = 0;
}
/* set the lower words of r */
if (a != r) {
MP_CHECKOK(s_mp_pad(r, 6));
}
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;
MP_USED(r) = 6;
#else
switch (a_used) {
case 6:
a5 = MP_DIGIT(a, 5);
case 5:
a4 = MP_DIGIT(a, 4);
case 4:
a3 = MP_DIGIT(a, 3);
}
r2 = MP_DIGIT(a, 2);
r1 = MP_DIGIT(a, 1);
r0 = MP_DIGIT(a, 0);
/* implement r = (a2,a1,a0)+(a5,a5,a5)+(a4,a4,0)+(0,a3,a3) */
#ifndef MPI_AMD64_ADD
MP_ADD_CARRY_ZERO(r0, a3, r0, carry);
MP_ADD_CARRY(r1, a3, r1, carry, carry);
MP_ADD_CARRY(r2, a4, r2, carry, carry);
r3 = carry;
MP_ADD_CARRY_ZERO(r0, a5, r0, carry);
MP_ADD_CARRY(r1, a5, r1, carry, carry);
MP_ADD_CARRY(r2, a5, r2, carry, carry);
r3 += carry;
MP_ADD_CARRY_ZERO(r1, a4, r1, carry);
MP_ADD_CARRY(r2, 0, r2, carry, carry);
r3 += carry;
#else
r2 = MP_DIGIT(a, 2);
r1 = MP_DIGIT(a, 1);
r0 = MP_DIGIT(a, 0);
/* set the lower words of r */
__asm__ (
"xorq %3,%3 \n\t"
"addq %4,%0 \n\t"
"adcq %4,%1 \n\t"
"adcq %5,%2 \n\t"
"adcq $0,%3 \n\t"
"addq %6,%0 \n\t"
"adcq %6,%1 \n\t"
"adcq %6,%2 \n\t"
"adcq $0,%3 \n\t"
"addq %5,%1 \n\t"
"adcq $0,%2 \n\t"
"adcq $0,%3 \n\t"
: "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3), "=r"(a3),
"=r"(a4), "=r"(a5)
: "0" (r0), "1" (r1), "2" (r2), "3" (r3),
"4" (a3), "5" (a4), "6"(a5)
: "%cc" );
#endif
/* reduce out the carry */
while (r3) {
#ifndef MPI_AMD64_ADD
MP_ADD_CARRY_ZERO(r0, r3, r0, carry);
MP_ADD_CARRY(r1, r3, r1, carry, carry);
MP_ADD_CARRY(r2, 0, r2, carry, carry);
r3 = carry;
#else
a3=r3;
__asm__ (
"xorq %3,%3 \n\t"
"addq %4,%0 \n\t"
"adcq %4,%1 \n\t"
"adcq $0,%2 \n\t"
"adcq $0,%3 \n\t"
: "=r"(r0), "=r"(r1), "=r"(r2), "=r"(r3), "=r"(a3)
: "0" (r0), "1" (r1), "2" (r2), "3" (r3), "4"(a3)
: "%cc" );
#endif
}
/* check for final reduction */
/*
* our field is 0xffffffffffffffff, 0xfffffffffffffffe,
* 0xffffffffffffffff. That means we can only be over and need
* one more reduction
* if r2 == 0xffffffffffffffffff (same as r2+1 == 0)
* and
* r1 == 0xffffffffffffffffff or
* r1 == 0xfffffffffffffffffe and r0 = 0xfffffffffffffffff
* In all cases, we subtract the field (or add the 2's
* complement value (1,1,0)). (r0, r1, r2)
*/
if (r3 || ((r2 == MP_DIGIT_MAX) &&
((r1 == MP_DIGIT_MAX) ||
((r1 == (MP_DIGIT_MAX-1)) && (r0 == MP_DIGIT_MAX))))) {
/* do a quick subtract */
r0++;
r1 = r2 = 0;
}
/* set the lower words of r */
if (a != r) {
MP_CHECKOK(s_mp_pad(r, 3));
}
MP_DIGIT(r, 2) = r2;
MP_DIGIT(r, 1) = r1;
MP_DIGIT(r, 0) = r0;
MP_USED(r) = 3;
#endif
}
CLEANUP:
return res;
}
#ifndef ECL_THIRTY_TWO_BIT
/* Compute the sum of 192 bit curves. Do the work in-line since the
* number of words are so small, we don't want to overhead of mp function
* calls. Uses optimized modular reduction for p192.
*/
mp_err
ec_GFp_nistp192_add(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_ZERO(a0, r0, r0, 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
/* Do quick 'subract' if we've gone over
* (add the 2's complement of the curve field) */
if (carry || ((r2 == MP_DIGIT_MAX) &&
((r1 == MP_DIGIT_MAX) ||
((r1 == (MP_DIGIT_MAX-1)) && (r0 == MP_DIGIT_MAX))))) {
#ifndef MPI_AMD64_ADD
MP_ADD_CARRY_ZERO(r0, 1, r0, carry);
MP_ADD_CARRY(r1, 1, r1, carry, carry);
MP_ADD_CARRY(r2, 0, r2, carry, carry);
#else
__asm__ (
"addq $1,%0 \n\t"
"adcq $1,%1 \n\t"
"adcq $0,%2 \n\t"
: "=r"(r0), "=r"(r1), "=r"(r2)
: "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;
s_mp_clamp(r);
CLEANUP:
return res;
}
/* Compute the diff of 192 bit curves. Do the work in-line since the
* number of words are so small, we don't want to overhead of mp function
* calls. Uses optimized modular reduction for p192.
*/
mp_err
ec_GFp_nistp192_sub(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) {
#ifndef MPI_AMD64_ADD
MP_SUB_BORROW(r0, 1, r0, 0, borrow);
MP_SUB_BORROW(r1, 1, r1, borrow, borrow);
MP_SUB_BORROW(r2, 0, r2, borrow, borrow);
#else
__asm__ (
"subq $1,%0 \n\t"
"sbbq $1,%1 \n\t"
"sbbq $0,%2 \n\t"
: "=r"(r0), "=r"(r1), "=r"(r2)
: "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;
s_mp_clamp(r);
CLEANUP:
return res;
}
#endif
/* Compute the square of polynomial a, reduce modulo p192. Store the
* result in r. r could be a. Uses optimized modular reduction for p192.
*/
mp_err
ec_GFp_nistp192_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_nistp192_mod(r, r, meth));
CLEANUP:
return res;
}
/* Compute the product of two polynomials a and b, reduce modulo p192.
* Store the result in r. r could be a or b; a could be b. Uses
* optimized modular reduction for p192. */
mp_err
ec_GFp_nistp192_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_nistp192_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_nistp192_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_nistp192_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_gfp192(ECGroup *group, ECCurveName name)
{
if (name == ECCurve_NIST_P192) {
group->meth->field_mod = &ec_GFp_nistp192_mod;
group->meth->field_mul = &ec_GFp_nistp192_mul;
group->meth->field_sqr = &ec_GFp_nistp192_sqr;
group->meth->field_div = &ec_GFp_nistp192_div;
#ifndef ECL_THIRTY_TWO_BIT
group->meth->field_add = &ec_GFp_nistp192_add;
group->meth->field_sub = &ec_GFp_nistp192_sub;
#endif
}
return MP_OKAY;
}