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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>
/* Checks if point P(px, py) is at infinity. Uses affine coordinates. */
mp_err
ec_GF2m_pt_is_inf_aff(const mp_int *px, const mp_int *py)
{
if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) {
return MP_YES;
} else {
return MP_NO;
}
}
/* Sets P(px, py) to be the point at infinity. Uses affine coordinates. */
mp_err
ec_GF2m_pt_set_inf_aff(mp_int *px, mp_int *py)
{
mp_zero(px);
mp_zero(py);
return MP_OKAY;
}
/* Computes R = P + Q based on IEEE P1363 A.10.2. Elliptic curve points P,
* Q, and R can all be identical. Uses affine coordinates. */
mp_err
ec_GF2m_pt_add_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
const mp_int *qy, mp_int *rx, mp_int *ry,
const ECGroup *group)
{
mp_err res = MP_OKAY;
mp_int lambda, tempx, tempy;
MP_DIGITS(&lambda) = 0;
MP_DIGITS(&tempx) = 0;
MP_DIGITS(&tempy) = 0;
MP_CHECKOK(mp_init(&lambda));
MP_CHECKOK(mp_init(&tempx));
MP_CHECKOK(mp_init(&tempy));
/* if P = inf, then R = Q */
if (ec_GF2m_pt_is_inf_aff(px, py) == 0) {
MP_CHECKOK(mp_copy(qx, rx));
MP_CHECKOK(mp_copy(qy, ry));
res = MP_OKAY;
goto CLEANUP;
}
/* if Q = inf, then R = P */
if (ec_GF2m_pt_is_inf_aff(qx, qy) == 0) {
MP_CHECKOK(mp_copy(px, rx));
MP_CHECKOK(mp_copy(py, ry));
res = MP_OKAY;
goto CLEANUP;
}
/* if px != qx, then lambda = (py+qy) / (px+qx), tempx = a + lambda^2
* + lambda + px + qx */
if (mp_cmp(px, qx) != 0) {
MP_CHECKOK(group->meth->field_add(py, qy, &tempy, group->meth));
MP_CHECKOK(group->meth->field_add(px, qx, &tempx, group->meth));
MP_CHECKOK(group->meth->
field_div(&tempy, &tempx, &lambda, group->meth));
MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
MP_CHECKOK(group->meth->
field_add(&tempx, &lambda, &tempx, group->meth));
MP_CHECKOK(group->meth->
field_add(&tempx, &group->curvea, &tempx, group->meth));
MP_CHECKOK(group->meth->
field_add(&tempx, px, &tempx, group->meth));
MP_CHECKOK(group->meth->
field_add(&tempx, qx, &tempx, group->meth));
} else {
/* if py != qy or qx = 0, then R = inf */
if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qx) == 0)) {
mp_zero(rx);
mp_zero(ry);
res = MP_OKAY;
goto CLEANUP;
}
/* lambda = qx + qy / qx */
MP_CHECKOK(group->meth->field_div(qy, qx, &lambda, group->meth));
MP_CHECKOK(group->meth->
field_add(&lambda, qx, &lambda, group->meth));
/* tempx = a + lambda^2 + lambda */
MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
MP_CHECKOK(group->meth->
field_add(&tempx, &lambda, &tempx, group->meth));
MP_CHECKOK(group->meth->
field_add(&tempx, &group->curvea, &tempx, group->meth));
}
/* ry = (qx + tempx) * lambda + tempx + qy */
MP_CHECKOK(group->meth->field_add(qx, &tempx, &tempy, group->meth));
MP_CHECKOK(group->meth->
field_mul(&tempy, &lambda, &tempy, group->meth));
MP_CHECKOK(group->meth->
field_add(&tempy, &tempx, &tempy, group->meth));
MP_CHECKOK(group->meth->field_add(&tempy, qy, ry, group->meth));
/* rx = tempx */
MP_CHECKOK(mp_copy(&tempx, rx));
CLEANUP:
mp_clear(&lambda);
mp_clear(&tempx);
mp_clear(&tempy);
return res;
}
/* Computes R = P - Q. Elliptic curve points P, Q, and R can all be
* identical. Uses affine coordinates. */
mp_err
ec_GF2m_pt_sub_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
const mp_int *qy, mp_int *rx, mp_int *ry,
const ECGroup *group)
{
mp_err res = MP_OKAY;
mp_int nqy;
MP_DIGITS(&nqy) = 0;
MP_CHECKOK(mp_init(&nqy));
/* nqy = qx+qy */
MP_CHECKOK(group->meth->field_add(qx, qy, &nqy, group->meth));
MP_CHECKOK(group->point_add(px, py, qx, &nqy, rx, ry, group));
CLEANUP:
mp_clear(&nqy);
return res;
}
/* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
* affine coordinates. */
mp_err
ec_GF2m_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx,
mp_int *ry, const ECGroup *group)
{
return group->point_add(px, py, px, py, rx, ry, group);
}
/* by default, this routine is unused and thus doesn't need to be compiled */
#ifdef ECL_ENABLE_GF2M_PT_MUL_AFF
/* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and
* R can be identical. Uses affine coordinates. */
mp_err
ec_GF2m_pt_mul_aff(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 k, k3, qx, qy, sx, sy;
int b1, b3, i, l;
MP_DIGITS(&k) = 0;
MP_DIGITS(&k3) = 0;
MP_DIGITS(&qx) = 0;
MP_DIGITS(&qy) = 0;
MP_DIGITS(&sx) = 0;
MP_DIGITS(&sy) = 0;
MP_CHECKOK(mp_init(&k));
MP_CHECKOK(mp_init(&k3));
MP_CHECKOK(mp_init(&qx));
MP_CHECKOK(mp_init(&qy));
MP_CHECKOK(mp_init(&sx));
MP_CHECKOK(mp_init(&sy));
/* if n = 0 then r = inf */
if (mp_cmp_z(n) == 0) {
mp_zero(rx);
mp_zero(ry);
res = MP_OKAY;
goto CLEANUP;
}
/* Q = P, k = n */
MP_CHECKOK(mp_copy(px, &qx));
MP_CHECKOK(mp_copy(py, &qy));
MP_CHECKOK(mp_copy(n, &k));
/* if n < 0 then Q = -Q, k = -k */
if (mp_cmp_z(n) < 0) {
MP_CHECKOK(group->meth->field_add(&qx, &qy, &qy, group->meth));
MP_CHECKOK(mp_neg(&k, &k));
}
#ifdef ECL_DEBUG /* basic double and add method */
l = mpl_significant_bits(&k) - 1;
MP_CHECKOK(mp_copy(&qx, &sx));
MP_CHECKOK(mp_copy(&qy, &sy));
for (i = l - 1; i >= 0; i--) {
/* S = 2S */
MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
/* if k_i = 1, then S = S + Q */
if (mpl_get_bit(&k, i) != 0) {
MP_CHECKOK(group->
point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
}
}
#else /* double and add/subtract method from
* standard */
/* k3 = 3 * k */
MP_CHECKOK(mp_set_int(&k3, 3));
MP_CHECKOK(mp_mul(&k, &k3, &k3));
/* S = Q */
MP_CHECKOK(mp_copy(&qx, &sx));
MP_CHECKOK(mp_copy(&qy, &sy));
/* l = index of high order bit in binary representation of 3*k */
l = mpl_significant_bits(&k3) - 1;
/* for i = l-1 downto 1 */
for (i = l - 1; i >= 1; i--) {
/* S = 2S */
MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
b3 = MP_GET_BIT(&k3, i);
b1 = MP_GET_BIT(&k, i);
/* if k3_i = 1 and k_i = 0, then S = S + Q */
if ((b3 == 1) && (b1 == 0)) {
MP_CHECKOK(group->
point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
/* if k3_i = 0 and k_i = 1, then S = S - Q */
} else if ((b3 == 0) && (b1 == 1)) {
MP_CHECKOK(group->
point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group));
}
}
#endif
/* output S */
MP_CHECKOK(mp_copy(&sx, rx));
MP_CHECKOK(mp_copy(&sy, ry));
CLEANUP:
mp_clear(&k);
mp_clear(&k3);
mp_clear(&qx);
mp_clear(&qy);
mp_clear(&sx);
mp_clear(&sy);
return res;
}
#endif
/* Validates a point on a GF2m curve. */
mp_err
ec_GF2m_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group)
{
mp_err res = MP_NO;
mp_int accl, accr, tmp, pxt, pyt;
MP_DIGITS(&accl) = 0;
MP_DIGITS(&accr) = 0;
MP_DIGITS(&tmp) = 0;
MP_DIGITS(&pxt) = 0;
MP_DIGITS(&pyt) = 0;
MP_CHECKOK(mp_init(&accl));
MP_CHECKOK(mp_init(&accr));
MP_CHECKOK(mp_init(&tmp));
MP_CHECKOK(mp_init(&pxt));
MP_CHECKOK(mp_init(&pyt));
/* 1: Verify that publicValue is not the point at infinity */
if (ec_GF2m_pt_is_inf_aff(px, py) == MP_YES) {
res = MP_NO;
goto CLEANUP;
}
/* 2: Verify that the coordinates of publicValue are elements
* of the field.
*/
if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) ||
(MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) {
res = MP_NO;
goto CLEANUP;
}
/* 3: Verify that publicValue is on the curve. */
if (group->meth->field_enc) {
group->meth->field_enc(px, &pxt, group->meth);
group->meth->field_enc(py, &pyt, group->meth);
} else {
mp_copy(px, &pxt);
mp_copy(py, &pyt);
}
/* left-hand side: y^2 + x*y */
MP_CHECKOK( group->meth->field_sqr(&pyt, &accl, group->meth) );
MP_CHECKOK( group->meth->field_mul(&pxt, &pyt, &tmp, group->meth) );
MP_CHECKOK( group->meth->field_add(&accl, &tmp, &accl, group->meth) );
/* right-hand side: x^3 + a*x^2 + b */
MP_CHECKOK( group->meth->field_sqr(&pxt, &tmp, group->meth) );
MP_CHECKOK( group->meth->field_mul(&pxt, &tmp, &accr, group->meth) );
MP_CHECKOK( group->meth->field_mul(&group->curvea, &tmp, &tmp, group->meth) );
MP_CHECKOK( group->meth->field_add(&tmp, &accr, &accr, group->meth) );
MP_CHECKOK( group->meth->field_add(&accr, &group->curveb, &accr, group->meth) );
/* check LHS - RHS == 0 */
MP_CHECKOK( group->meth->field_add(&accl, &accr, &accr, group->meth) );
if (mp_cmp_z(&accr) != 0) {
res = MP_NO;
goto CLEANUP;
}
/* 4: Verify that the order of the curve times the publicValue
* is the point at infinity.
*/
MP_CHECKOK( ECPoint_mul(group, &group->order, px, py, &pxt, &pyt) );
if (ec_GF2m_pt_is_inf_aff(&pxt, &pyt) != MP_YES) {
res = MP_NO;
goto CLEANUP;
}
res = MP_YES;
CLEANUP:
mp_clear(&accl);
mp_clear(&accr);
mp_clear(&tmp);
mp_clear(&pxt);
mp_clear(&pyt);
return res;
}
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