/* Converts a point P(px, py, pz) from Jacobian projective coordinates to
* affine coordinates R(rx, ry). P and R can share x and y coordinates.
* Assumes input is already field-encoded using field_enc, and returns
* output that is still field-encoded. */
mp_err
ec_GFp_pt_jac2aff(const mp_int *px, const mp_int *py, const mp_int *pz,
mp_int *rx, mp_int *ry, const ECGroup *group)
{
mp_err res = MP_OKAY;
mp_int z1, z2, z3;
MP_DIGITS(&z1) = 0;
MP_DIGITS(&z2) = 0;
MP_DIGITS(&z3) = 0;
MP_CHECKOK(mp_init(&z1));
MP_CHECKOK(mp_init(&z2));
MP_CHECKOK(mp_init(&z3));
/* if point at infinity, then set point at infinity and exit */
if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
MP_CHECKOK(ec_GFp_pt_set_inf_aff(rx, ry));
goto CLEANUP;
}
/* transform (px, py, pz) into (px / pz^2, py / pz^3) */
if (mp_cmp_d(pz, 1) == 0) {
MP_CHECKOK(mp_copy(px, rx));
MP_CHECKOK(mp_copy(py, ry));
} else {
MP_CHECKOK(group->meth->field_div(NULL, pz, &z1, group->meth));
MP_CHECKOK(group->meth->field_sqr(&z1, &z2, group->meth));
MP_CHECKOK(group->meth->field_mul(&z1, &z2, &z3, group->meth));
MP_CHECKOK(group->meth->field_mul(px, &z2, rx, group->meth));
MP_CHECKOK(group->meth->field_mul(py, &z3, ry, group->meth));
}
CLEANUP:
mp_clear(&z1);
mp_clear(&z2);
mp_clear(&z3);
return res;
}
/* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
* Modified Jacobian coordinates.
*
* Assumes input is already field-encoded using field_enc, and returns
* output that is still field-encoded.
*
*/
mp_err
ec_GFp_pt_dbl_jm(const mp_int *px, const mp_int *py, const mp_int *pz,
const mp_int *paz4, mp_int *rx, mp_int *ry, mp_int *rz,
mp_int *raz4, mp_int scratch[], const ECGroup *group)
{
mp_err res = MP_OKAY;
mp_int *t0, *t1, *M, *S;
t0 = &scratch[0];
t1 = &scratch[1];
M = &scratch[2];
S = &scratch[3];
#if MAX_SCRATCH < 4
#error "Scratch array defined too small "
#endif
/* Check for point at infinity */
if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
/* Set r = pt at infinity by setting rz = 0 */
MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
goto CLEANUP;
}
/* M = 3 (px^2) + a*(pz^4) */
MP_CHECKOK(group->meth->field_sqr(px, t0, group->meth));
MP_CHECKOK(group->meth->field_add(t0, t0, M, group->meth));
MP_CHECKOK(group->meth->field_add(t0, M, t0, group->meth));
MP_CHECKOK(group->meth->field_add(t0, paz4, M, group->meth));
/* rz = 2 * py * pz */
MP_CHECKOK(group->meth->field_mul(py, pz, S, group->meth));
MP_CHECKOK(group->meth->field_add(S, S, rz, group->meth));
/* t0 = 2y^2 , t1 = 8y^4 */
MP_CHECKOK(group->meth->field_sqr(py, t0, group->meth));
MP_CHECKOK(group->meth->field_add(t0, t0, t0, group->meth));
MP_CHECKOK(group->meth->field_sqr(t0, t1, group->meth));
MP_CHECKOK(group->meth->field_add(t1, t1, t1, group->meth));
/* S = 4 * px * py^2 = 2 * px * t0 */
MP_CHECKOK(group->meth->field_mul(px, t0, S, group->meth));
MP_CHECKOK(group->meth->field_add(S, S, S, group->meth));
/* rx = M^2 - 2S */
MP_CHECKOK(group->meth->field_sqr(M, rx, group->meth));
MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));
MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));
/* ry = M * (S - rx) - t1 */
MP_CHECKOK(group->meth->field_sub(S, rx, S, group->meth));
MP_CHECKOK(group->meth->field_mul(S, M, ry, group->meth));
MP_CHECKOK(group->meth->field_sub(ry, t1, ry, group->meth));
/* ra*z^4 = 2*t1*(apz4) */
MP_CHECKOK(group->meth->field_mul(paz4, t1, raz4, group->meth));
MP_CHECKOK(group->meth->field_add(raz4, raz4, raz4, group->meth));
CLEANUP:
return res;
}
/* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
* (qx, qy, 1). Elliptic curve points P, Q, and R can all be identical.
* Uses mixed Modified_Jacobian-affine coordinates. Assumes input is
* already field-encoded using field_enc, and returns output that is still
* field-encoded. */
mp_err
ec_GFp_pt_add_jm_aff(const mp_int *px, const mp_int *py, const mp_int *pz,
const mp_int *paz4, const mp_int *qx,
const mp_int *qy, mp_int *rx, mp_int *ry, mp_int *rz,
mp_int *raz4, mp_int scratch[], const ECGroup *group)
{
mp_err res = MP_OKAY;
mp_int *A, *B, *C, *D, *C2, *C3;
A = &scratch[0];
B = &scratch[1];
C = &scratch[2];
D = &scratch[3];
C2 = &scratch[4];
C3 = &scratch[5];
#if MAX_SCRATCH < 6
#error "Scratch array defined too small "
#endif
/* If either P or Q is the point at infinity, then return the other
* point */
if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));
MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
MP_CHECKOK(group->meth->
field_mul(raz4, &group->curvea, raz4, group->meth));
goto CLEANUP;
}
if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) {
MP_CHECKOK(mp_copy(px, rx));
MP_CHECKOK(mp_copy(py, ry));
MP_CHECKOK(mp_copy(pz, rz));
MP_CHECKOK(mp_copy(paz4, raz4));
goto CLEANUP;
}
/* A = qx * pz^2, B = qy * pz^3 */
MP_CHECKOK(group->meth->field_sqr(pz, A, group->meth));
MP_CHECKOK(group->meth->field_mul(A, pz, B, group->meth));
MP_CHECKOK(group->meth->field_mul(A, qx, A, group->meth));
MP_CHECKOK(group->meth->field_mul(B, qy, B, group->meth));
/* C = A - px, D = B - py */
MP_CHECKOK(group->meth->field_sub(A, px, C, group->meth));
MP_CHECKOK(group->meth->field_sub(B, py, D, group->meth));
/* C2 = C^2, C3 = C^3 */
MP_CHECKOK(group->meth->field_sqr(C, C2, group->meth));
MP_CHECKOK(group->meth->field_mul(C, C2, C3, group->meth));
/* rz = pz * C */
MP_CHECKOK(group->meth->field_mul(pz, C, rz, group->meth));
/* C = px * C^2 */
MP_CHECKOK(group->meth->field_mul(px, C2, C, group->meth));
/* A = D^2 */
MP_CHECKOK(group->meth->field_sqr(D, A, group->meth));
/* rx = D^2 - (C^3 + 2 * (px * C^2)) */
MP_CHECKOK(group->meth->field_add(C, C, rx, group->meth));
MP_CHECKOK(group->meth->field_add(C3, rx, rx, group->meth));
MP_CHECKOK(group->meth->field_sub(A, rx, rx, group->meth));
/* C3 = py * C^3 */
MP_CHECKOK(group->meth->field_mul(py, C3, C3, group->meth));
/* ry = D * (px * C^2 - rx) - py * C^3 */
MP_CHECKOK(group->meth->field_sub(C, rx, ry, group->meth));
MP_CHECKOK(group->meth->field_mul(D, ry, ry, group->meth));
MP_CHECKOK(group->meth->field_sub(ry, C3, ry, group->meth));
/* raz4 = a * rz^4 */
MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
MP_CHECKOK(group->meth->
field_mul(raz4, &group->curvea, raz4, group->meth));
CLEANUP:
return res;
}
/* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
* Jacobian coordinates.
*
* Assumes input is already field-encoded using field_enc, and returns
* output that is still field-encoded.
*
* This routine implements Point Doubling in the Jacobian Projective
* space as described in the paper "Efficient elliptic curve exponentiation
* using mixed coordinates", by H. Cohen, A Miyaji, T. Ono.
*/
mp_err
ec_GFp_pt_dbl_jac(const mp_int *px, const mp_int *py, const mp_int *pz,
mp_int *rx, mp_int *ry, mp_int *rz, const ECGroup *group)
{
mp_err res = MP_OKAY;
mp_int t0, t1, M, S;
MP_DIGITS(&t0) = 0;
MP_DIGITS(&t1) = 0;
MP_DIGITS(&M) = 0;
MP_DIGITS(&S) = 0;
MP_CHECKOK(mp_init(&t0));
MP_CHECKOK(mp_init(&t1));
MP_CHECKOK(mp_init(&M));
MP_CHECKOK(mp_init(&S));
/* P == inf or P == -P */
if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES || mp_cmp_z(py) == 0) {
MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
goto CLEANUP;
}
if (mp_cmp_d(pz, 1) == 0) {
/* M = 3 * px^2 + a */
MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth));
MP_CHECKOK(group->meth->field_add(&t0, &t0, &M, group->meth));
MP_CHECKOK(group->meth->field_add(&t0, &M, &t0, group->meth));
MP_CHECKOK(group->meth->
field_add(&t0, &group->curvea, &M, group->meth));
} else if (MP_SIGN(&group->curvea) == MP_NEG &&
MP_USED(&group->curvea) == 1 &&
MP_DIGIT(&group->curvea, 0) == 3) {
/* M = 3 * (px + pz^2) * (px - pz^2) */
MP_CHECKOK(group->meth->field_sqr(pz, &M, group->meth));
MP_CHECKOK(group->meth->field_add(px, &M, &t0, group->meth));
MP_CHECKOK(group->meth->field_sub(px, &M, &t1, group->meth));
MP_CHECKOK(group->meth->field_mul(&t0, &t1, &M, group->meth));
MP_CHECKOK(group->meth->field_add(&M, &M, &t0, group->meth));
MP_CHECKOK(group->meth->field_add(&t0, &M, &M, group->meth));
} else {
/* M = 3 * (px^2) + a * (pz^4) */
MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth));
MP_CHECKOK(group->meth->field_add(&t0, &t0, &M, group->meth));
MP_CHECKOK(group->meth->field_add(&t0, &M, &t0, group->meth));
MP_CHECKOK(group->meth->field_sqr(pz, &M, group->meth));
MP_CHECKOK(group->meth->field_sqr(&M, &M, group->meth));
MP_CHECKOK(group->meth->
field_mul(&M, &group->curvea, &M, group->meth));
MP_CHECKOK(group->meth->field_add(&M, &t0, &M, group->meth));
}
/* rz = 2 * py * pz */
/* t0 = 4 * py^2 */
if (mp_cmp_d(pz, 1) == 0) {
MP_CHECKOK(group->meth->field_add(py, py, rz, group->meth));
MP_CHECKOK(group->meth->field_sqr(rz, &t0, group->meth));
} else {
MP_CHECKOK(group->meth->field_add(py, py, &t0, group->meth));
MP_CHECKOK(group->meth->field_mul(&t0, pz, rz, group->meth));
MP_CHECKOK(group->meth->field_sqr(&t0, &t0, group->meth));
}
/* S = 4 * px * py^2 = px * (2 * py)^2 */
MP_CHECKOK(group->meth->field_mul(px, &t0, &S, group->meth));
/* rx = M^2 - 2 * S */
MP_CHECKOK(group->meth->field_add(&S, &S, &t1, group->meth));
MP_CHECKOK(group->meth->field_sqr(&M, rx, group->meth));
MP_CHECKOK(group->meth->field_sub(rx, &t1, rx, group->meth));
/* ry = M * (S - rx) - 8 * py^4 */
MP_CHECKOK(group->meth->field_sqr(&t0, &t1, group->meth));
if (mp_isodd(&t1)) {
MP_CHECKOK(mp_add(&t1, &group->meth->irr, &t1));
}
MP_CHECKOK(mp_div_2(&t1, &t1));
MP_CHECKOK(group->meth->field_sub(&S, rx, &S, group->meth));
MP_CHECKOK(group->meth->field_mul(&M, &S, &M, group->meth));
MP_CHECKOK(group->meth->field_sub(&M, &t1, ry, group->meth));
CLEANUP:
mp_clear(&t0);
mp_clear(&t1);
mp_clear(&M);
mp_clear(&S);
return res;
}
/* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
* (qx, qy, 1). Elliptic curve points P, Q, and R can all be identical.
* Uses mixed Jacobian-affine coordinates. Assumes input is already
* field-encoded using field_enc, and returns output that is still
* field-encoded. Uses equation (2) from Brown, Hankerson, Lopez, and
* Menezes. Software Implementation of the NIST Elliptic Curves Over Prime
* Fields. */
mp_err
ec_GFp_pt_add_jac_aff(const mp_int *px, const mp_int *py, const mp_int *pz,
const mp_int *qx, const mp_int *qy, mp_int *rx,
mp_int *ry, mp_int *rz, const ECGroup *group)
{
mp_err res = MP_OKAY;
mp_int A, B, C, D, C2, C3;
MP_DIGITS(&A) = 0;
MP_DIGITS(&B) = 0;
MP_DIGITS(&C) = 0;
MP_DIGITS(&D) = 0;
MP_DIGITS(&C2) = 0;
MP_DIGITS(&C3) = 0;
MP_CHECKOK(mp_init(&A));
MP_CHECKOK(mp_init(&B));
MP_CHECKOK(mp_init(&C));
MP_CHECKOK(mp_init(&D));
MP_CHECKOK(mp_init(&C2));
MP_CHECKOK(mp_init(&C3));
/* If either P or Q is the point at infinity, then return the other
* point */
if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));
goto CLEANUP;
}
if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) {
MP_CHECKOK(mp_copy(px, rx));
MP_CHECKOK(mp_copy(py, ry));
MP_CHECKOK(mp_copy(pz, rz));
goto CLEANUP;
}
/* A = qx * pz^2, B = qy * pz^3 */
MP_CHECKOK(group->meth->field_sqr(pz, &A, group->meth));
MP_CHECKOK(group->meth->field_mul(&A, pz, &B, group->meth));
MP_CHECKOK(group->meth->field_mul(&A, qx, &A, group->meth));
MP_CHECKOK(group->meth->field_mul(&B, qy, &B, group->meth));
/* C = A - px, D = B - py */
MP_CHECKOK(group->meth->field_sub(&A, px, &C, group->meth));
MP_CHECKOK(group->meth->field_sub(&B, py, &D, group->meth));
if (mp_cmp_z(&C) == 0) {
/* P == Q or P == -Q */
if (mp_cmp_z(&D) == 0) {
/* P == Q */
/* It is cheaper to double (qx, qy, 1) than (px, py, pz). */
MP_DIGIT(&D, 0) = 1; /* Set D to 1. */
MP_CHECKOK(ec_GFp_pt_dbl_jac(qx, qy, &D, rx, ry, rz, group));
} else {
/* P == -Q */
MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
}
goto CLEANUP;
}
/* C2 = C^2, C3 = C^3 */
MP_CHECKOK(group->meth->field_sqr(&C, &C2, group->meth));
MP_CHECKOK(group->meth->field_mul(&C, &C2, &C3, group->meth));
/* rz = pz * C */
MP_CHECKOK(group->meth->field_mul(pz, &C, rz, group->meth));
/* C = px * C^2 */
MP_CHECKOK(group->meth->field_mul(px, &C2, &C, group->meth));
/* A = D^2 */
MP_CHECKOK(group->meth->field_sqr(&D, &A, group->meth));
/* rx = D^2 - (C^3 + 2 * (px * C^2)) */
MP_CHECKOK(group->meth->field_add(&C, &C, rx, group->meth));
MP_CHECKOK(group->meth->field_add(&C3, rx, rx, group->meth));
MP_CHECKOK(group->meth->field_sub(&A, rx, rx, group->meth));
/* C3 = py * C^3 */
MP_CHECKOK(group->meth->field_mul(py, &C3, &C3, group->meth));
/* ry = D * (px * C^2 - rx) - py * C^3 */
MP_CHECKOK(group->meth->field_sub(&C, rx, ry, group->meth));
MP_CHECKOK(group->meth->field_mul(&D, ry, ry, group->meth));
MP_CHECKOK(group->meth->field_sub(ry, &C3, ry, group->meth));
CLEANUP:
mp_clear(&A);
mp_clear(&B);
mp_clear(&C);
mp_clear(&D);
mp_clear(&C2);
mp_clear(&C3);
return res;
}
/* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
* Modified Jacobian coordinates.
*
* Assumes input is already field-encoded using field_enc, and returns
* output that is still field-encoded.
*
*/
mp_err
ec_GFp_pt_dbl_jm(const mp_int *px, const mp_int *py, const mp_int *pz,
const mp_int *paz4, mp_int *rx, mp_int *ry, mp_int *rz,
mp_int *raz4, const ECGroup *group)
{
mp_err res = MP_OKAY;
mp_int t0, t1, M, S;
MP_DIGITS(&t0) = 0;
MP_DIGITS(&t1) = 0;
MP_DIGITS(&M) = 0;
MP_DIGITS(&S) = 0;
MP_CHECKOK(mp_init(&t0));
MP_CHECKOK(mp_init(&t1));
MP_CHECKOK(mp_init(&M));
MP_CHECKOK(mp_init(&S));
/* Check for point at infinity */
if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
/* Set r = pt at infinity by setting rz = 0 */
MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
goto CLEANUP;
}
/* M = 3 (px^2) + a*(pz^4) */
MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth));
MP_CHECKOK(group->meth->field_add(&t0, &t0, &M, group->meth));
MP_CHECKOK(group->meth->field_add(&t0, &M, &t0, group->meth));
MP_CHECKOK(group->meth->field_add(&t0, paz4, &M, group->meth));
/* rz = 2 * py * pz */
MP_CHECKOK(group->meth->field_mul(py, pz, rz, group->meth));
MP_CHECKOK(group->meth->field_add(rz, rz, rz, group->meth));
/* t0 = 2y^2 , t1 = 8y^4 */
MP_CHECKOK(group->meth->field_sqr(py, &t0, group->meth));
MP_CHECKOK(group->meth->field_add(&t0, &t0, &t0, group->meth));
MP_CHECKOK(group->meth->field_sqr(&t0, &t1, group->meth));
MP_CHECKOK(group->meth->field_add(&t1, &t1, &t1, group->meth));
/* S = 4 * px * py^2 = 2 * px * t0 */
MP_CHECKOK(group->meth->field_mul(px, &t0, &S, group->meth));
MP_CHECKOK(group->meth->field_add(&S, &S, &S, group->meth));
/* rx = M^2 - 2S */
MP_CHECKOK(group->meth->field_sqr(&M, rx, group->meth));
MP_CHECKOK(group->meth->field_sub(rx, &S, rx, group->meth));
MP_CHECKOK(group->meth->field_sub(rx, &S, rx, group->meth));
/* ry = M * (S - rx) - t1 */
MP_CHECKOK(group->meth->field_sub(&S, rx, ry, group->meth));
MP_CHECKOK(group->meth->field_mul(ry, &M, ry, group->meth));
MP_CHECKOK(group->meth->field_sub(ry, &t1, ry, group->meth));
/* ra*z^4 = 2*t1*(apz4) */
MP_CHECKOK(group->meth->field_mul(paz4, &t1, raz4, group->meth));
MP_CHECKOK(group->meth->field_add(raz4, raz4, raz4, group->meth));
CLEANUP:
mp_clear(&t0);
mp_clear(&t1);
mp_clear(&M);
mp_clear(&S);
return res;
}
/* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
* (qx, qy, 1). Elliptic curve points P, Q, and R can all be identical.
* Uses mixed Modified_Jacobian-affine coordinates. Assumes input is
* already field-encoded using field_enc, and returns output that is still
* field-encoded. */
mp_err
ec_GFp_pt_add_jm_aff(const mp_int *px, const mp_int *py, const mp_int *pz,
const mp_int *paz4, const mp_int *qx,
const mp_int *qy, mp_int *rx, mp_int *ry, mp_int *rz,
mp_int *raz4, const ECGroup *group)
{
mp_err res = MP_OKAY;
mp_int A, B, C, D, C2, C3;
MP_DIGITS(&A) = 0;
MP_DIGITS(&B) = 0;
MP_DIGITS(&C) = 0;
MP_DIGITS(&D) = 0;
MP_DIGITS(&C2) = 0;
MP_DIGITS(&C3) = 0;
MP_CHECKOK(mp_init(&A));
MP_CHECKOK(mp_init(&B));
MP_CHECKOK(mp_init(&C));
MP_CHECKOK(mp_init(&D));
MP_CHECKOK(mp_init(&C2));
MP_CHECKOK(mp_init(&C3));
/* If either P or Q is the point at infinity, then return the other
* point */
if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));
MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
MP_CHECKOK(group->meth->
field_mul(raz4, &group->curvea, raz4, group->meth));
goto CLEANUP;
}
if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) {
MP_CHECKOK(mp_copy(px, rx));
MP_CHECKOK(mp_copy(py, ry));
MP_CHECKOK(mp_copy(pz, rz));
MP_CHECKOK(mp_copy(paz4, raz4));
goto CLEANUP;
}
/* A = qx * pz^2, B = qy * pz^3 */
MP_CHECKOK(group->meth->field_sqr(pz, &A, group->meth));
MP_CHECKOK(group->meth->field_mul(&A, pz, &B, group->meth));
MP_CHECKOK(group->meth->field_mul(&A, qx, &A, group->meth));
MP_CHECKOK(group->meth->field_mul(&B, qy, &B, group->meth));
/* C = A - px, D = B - py */
MP_CHECKOK(group->meth->field_sub(&A, px, &C, group->meth));
MP_CHECKOK(group->meth->field_sub(&B, py, &D, group->meth));
/* C2 = C^2, C3 = C^3 */
MP_CHECKOK(group->meth->field_sqr(&C, &C2, group->meth));
MP_CHECKOK(group->meth->field_mul(&C, &C2, &C3, group->meth));
/* rz = pz * C */
MP_CHECKOK(group->meth->field_mul(pz, &C, rz, group->meth));
/* C = px * C^2 */
MP_CHECKOK(group->meth->field_mul(px, &C2, &C, group->meth));
/* A = D^2 */
MP_CHECKOK(group->meth->field_sqr(&D, &A, group->meth));
/* rx = D^2 - (C^3 + 2 * (px * C^2)) */
MP_CHECKOK(group->meth->field_add(&C, &C, rx, group->meth));
MP_CHECKOK(group->meth->field_add(&C3, rx, rx, group->meth));
MP_CHECKOK(group->meth->field_sub(&A, rx, rx, group->meth));
/* C3 = py * C^3 */
MP_CHECKOK(group->meth->field_mul(py, &C3, &C3, group->meth));
/* ry = D * (px * C^2 - rx) - py * C^3 */
MP_CHECKOK(group->meth->field_sub(&C, rx, ry, group->meth));
MP_CHECKOK(group->meth->field_mul(&D, ry, ry, group->meth));
MP_CHECKOK(group->meth->field_sub(ry, &C3, ry, group->meth));
/* raz4 = a * rz^4 */
MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
MP_CHECKOK(group->meth->
field_mul(raz4, &group->curvea, raz4, group->meth));
CLEANUP:
mp_clear(&A);
mp_clear(&B);
mp_clear(&C);
mp_clear(&D);
mp_clear(&C2);
mp_clear(&C3);
return res;
}
