/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
#include "ecp.h"
#include "mpi.h"
#include "mplogic.h"
#include "mpi-priv.h"
#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. */
static 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. Subtract the curve. (curve is 2^224 - 2^96 +1)
*/
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, MP_DIGIT_MAX << 32, 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
}
s_mp_clamp(r);
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.
*/
static 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. */
static 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. */
static 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));
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;
}