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/* 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 "ec2.h"
#include "mplogic.h"
#include "mp_gf2m.h"
#include <stdlib.h>
/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery
* projective coordinates. Uses algorithm Mdouble in appendix of Lopez, J.
* and Dahab, R. "Fast multiplication on elliptic curves over GF(2^m)
* without precomputation". modified to not require precomputation of
* c=b^{2^{m-1}}. */
static mp_err
gf2m_Mdouble(mp_int *x, mp_int *z, const ECGroup *group)
{
mp_err res = MP_OKAY;
mp_int t1;
MP_DIGITS(&t1) = 0;
MP_CHECKOK(mp_init(&t1));
MP_CHECKOK(group->meth->field_sqr(x, x, group->meth));
MP_CHECKOK(group->meth->field_sqr(z, &t1, group->meth));
MP_CHECKOK(group->meth->field_mul(x, &t1, z, group->meth));
MP_CHECKOK(group->meth->field_sqr(x, x, group->meth));
MP_CHECKOK(group->meth->field_sqr(&t1, &t1, group->meth));
MP_CHECKOK(group->meth->
field_mul(&group->curveb, &t1, &t1, group->meth));
MP_CHECKOK(group->meth->field_add(x, &t1, x, group->meth));
CLEANUP:
mp_clear(&t1);
return res;
}
/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in
* Montgomery projective coordinates. Uses algorithm Madd in appendix of
* Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over
* GF(2^m) without precomputation". */
static mp_err
gf2m_Madd(const mp_int *x, mp_int *x1, mp_int *z1, mp_int *x2, mp_int *z2,
const ECGroup *group)
{
mp_err res = MP_OKAY;
mp_int t1, t2;
MP_DIGITS(&t1) = 0;
MP_DIGITS(&t2) = 0;
MP_CHECKOK(mp_init(&t1));
MP_CHECKOK(mp_init(&t2));
MP_CHECKOK(mp_copy(x, &t1));
MP_CHECKOK(group->meth->field_mul(x1, z2, x1, group->meth));
MP_CHECKOK(group->meth->field_mul(z1, x2, z1, group->meth));
MP_CHECKOK(group->meth->field_mul(x1, z1, &t2, group->meth));
MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth));
MP_CHECKOK(group->meth->field_sqr(z1, z1, group->meth));
MP_CHECKOK(group->meth->field_mul(z1, &t1, x1, group->meth));
MP_CHECKOK(group->meth->field_add(x1, &t2, x1, group->meth));
CLEANUP:
mp_clear(&t1);
mp_clear(&t2);
return res;
}
/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
* using Montgomery point multiplication algorithm Mxy() in appendix of
* Lopex, J. and Dahab, R. "Fast multiplication on elliptic curves over
* GF(2^m) without precomputation". Returns: 0 on error 1 if return value
* should be the point at infinity 2 otherwise */
static int
gf2m_Mxy(const mp_int *x, const mp_int *y, mp_int *x1, mp_int *z1,
mp_int *x2, mp_int *z2, const ECGroup *group)
{
mp_err res = MP_OKAY;
int ret = 0;
mp_int t3, t4, t5;
MP_DIGITS(&t3) = 0;
MP_DIGITS(&t4) = 0;
MP_DIGITS(&t5) = 0;
MP_CHECKOK(mp_init(&t3));
MP_CHECKOK(mp_init(&t4));
MP_CHECKOK(mp_init(&t5));
if (mp_cmp_z(z1) == 0) {
mp_zero(x2);
mp_zero(z2);
ret = 1;
goto CLEANUP;
}
if (mp_cmp_z(z2) == 0) {
MP_CHECKOK(mp_copy(x, x2));
MP_CHECKOK(group->meth->field_add(x, y, z2, group->meth));
ret = 2;
goto CLEANUP;
}
MP_CHECKOK(mp_set_int(&t5, 1));
if (group->meth->field_enc) {
MP_CHECKOK(group->meth->field_enc(&t5, &t5, group->meth));
}
MP_CHECKOK(group->meth->field_mul(z1, z2, &t3, group->meth));
MP_CHECKOK(group->meth->field_mul(z1, x, z1, group->meth));
MP_CHECKOK(group->meth->field_add(z1, x1, z1, group->meth));
MP_CHECKOK(group->meth->field_mul(z2, x, z2, group->meth));
MP_CHECKOK(group->meth->field_mul(z2, x1, x1, group->meth));
MP_CHECKOK(group->meth->field_add(z2, x2, z2, group->meth));
MP_CHECKOK(group->meth->field_mul(z2, z1, z2, group->meth));
MP_CHECKOK(group->meth->field_sqr(x, &t4, group->meth));
MP_CHECKOK(group->meth->field_add(&t4, y, &t4, group->meth));
MP_CHECKOK(group->meth->field_mul(&t4, &t3, &t4, group->meth));
MP_CHECKOK(group->meth->field_add(&t4, z2, &t4, group->meth));
MP_CHECKOK(group->meth->field_mul(&t3, x, &t3, group->meth));
MP_CHECKOK(group->meth->field_div(&t5, &t3, &t3, group->meth));
MP_CHECKOK(group->meth->field_mul(&t3, &t4, &t4, group->meth));
MP_CHECKOK(group->meth->field_mul(x1, &t3, x2, group->meth));
MP_CHECKOK(group->meth->field_add(x2, x, z2, group->meth));
MP_CHECKOK(group->meth->field_mul(z2, &t4, z2, group->meth));
MP_CHECKOK(group->meth->field_add(z2, y, z2, group->meth));
ret = 2;
CLEANUP:
mp_clear(&t3);
mp_clear(&t4);
mp_clear(&t5);
if (res == MP_OKAY) {
return ret;
} else {
return 0;
}
}
/* Computes R = nP based on algorithm 2P of Lopex, J. and Dahab, R. "Fast
* multiplication on elliptic curves over GF(2^m) without
* precomputation". Elliptic curve points P and R can be identical. Uses
* Montgomery projective coordinates. */
mp_err
ec_GF2m_pt_mul_mont(const mp_int *n, const mp_int *px, const mp_int *py,
mp_int *rx, mp_int *ry, const ECGroup *group)
{
mp_err res = MP_OKAY;
mp_int x1, x2, z1, z2;
int i, j;
mp_digit top_bit, mask;
MP_DIGITS(&x1) = 0;
MP_DIGITS(&x2) = 0;
MP_DIGITS(&z1) = 0;
MP_DIGITS(&z2) = 0;
MP_CHECKOK(mp_init(&x1));
MP_CHECKOK(mp_init(&x2));
MP_CHECKOK(mp_init(&z1));
MP_CHECKOK(mp_init(&z2));
/* if result should be point at infinity */
if ((mp_cmp_z(n) == 0) || (ec_GF2m_pt_is_inf_aff(px, py) == MP_YES)) {
MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry));
goto CLEANUP;
}
MP_CHECKOK(mp_copy(px, &x1)); /* x1 = px */
MP_CHECKOK(mp_set_int(&z1, 1)); /* z1 = 1 */
MP_CHECKOK(group->meth->field_sqr(&x1, &z2, group->meth)); /* z2 =
* x1^2 =
* px^2 */
MP_CHECKOK(group->meth->field_sqr(&z2, &x2, group->meth));
MP_CHECKOK(group->meth->field_add(&x2, &group->curveb, &x2, group->meth)); /* x2
* =
* px^4
* +
* b
*/
/* find top-most bit and go one past it */
i = MP_USED(n) - 1;
j = MP_DIGIT_BIT - 1;
top_bit = 1;
top_bit <<= MP_DIGIT_BIT - 1;
mask = top_bit;
while (!(MP_DIGITS(n)[i] & mask)) {
mask >>= 1;
j--;
}
mask >>= 1;
j--;
/* if top most bit was at word break, go to next word */
if (!mask) {
i--;
j = MP_DIGIT_BIT - 1;
mask = top_bit;
}
for (; i >= 0; i--) {
for (; j >= 0; j--) {
if (MP_DIGITS(n)[i] & mask) {
MP_CHECKOK(gf2m_Madd(px, &x1, &z1, &x2, &z2, group));
MP_CHECKOK(gf2m_Mdouble(&x2, &z2, group));
} else {
MP_CHECKOK(gf2m_Madd(px, &x2, &z2, &x1, &z1, group));
MP_CHECKOK(gf2m_Mdouble(&x1, &z1, group));
}
mask >>= 1;
}
j = MP_DIGIT_BIT - 1;
mask = top_bit;
}
/* convert out of "projective" coordinates */
i = gf2m_Mxy(px, py, &x1, &z1, &x2, &z2, group);
if (i == 0) {
res = MP_BADARG;
goto CLEANUP;
} else if (i == 1) {
MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry));
} else {
MP_CHECKOK(mp_copy(&x2, rx));
MP_CHECKOK(mp_copy(&z2, ry));
}
CLEANUP:
mp_clear(&x1);
mp_clear(&x2);
mp_clear(&z1);
mp_clear(&z2);
return res;
}
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