/**
* Compute the final lines for optimal ate pairings.
*
* @param[out] r - the result.
* @param[out] t - the resulting point.
* @param[in] q - the first point of the pairing, in G_2.
* @param[in] p - the second point of the pairing, in G_1.
* @param[in] a - the loop parameter.
*/
static void pp_fin_k12_oatep(fp12_t r, ep2_t t, ep2_t q, ep_t p) {
ep2_t q1, q2;
fp12_t tmp;
fp12_null(tmp);
ep2_null(q1);
ep2_null(q2);
TRY {
ep2_new(q1);
ep2_new(q2);
fp12_new(tmp);
fp12_zero(tmp);
fp2_set_dig(q1->z, 1);
fp2_set_dig(q2->z, 1);
ep2_frb(q1, q, 1);
ep2_frb(q2, q, 2);
ep2_neg(q2, q2);
pp_add_k12(tmp, t, q1, p);
fp12_mul_dxs(r, r, tmp);
pp_add_k12(tmp, t, q2, p);
fp12_mul_dxs(r, r, tmp);
} CATCH_ANY {
THROW(ERR_CAUGHT);
} FINALLY {
fp12_free(tmp);
ep2_free(q1);
ep2_free(q2);
}
}
/**
* Multiplies a point on a Barreto-Lynn-Soctt curve by the cofactor.
*
* @param[out] r - the result.
* @param[in] p - the point to multiply.
*/
void ep2_mul_cof_b12(ep2_t r, ep2_t p) {
bn_t x;
ep2_t t0, t1, t2, t3;
ep2_null(t0);
ep2_null(t1);
ep2_null(t2);
ep2_null(t3);
bn_null(x);
TRY {
ep2_new(t0);
ep2_new(t1);
ep2_new(t2);
ep2_new(t3);
bn_new(x);
fp_param_get_var(x);
/* Compute t0 = xP. */
ep2_mul(t0, p, x);
if (bn_sign(x) == BN_NEG) {
ep2_neg(t0, t0);
}
/* Compute t1 = [x^2]P. */
ep2_mul(t1, t0, x);
if (bn_sign(x) == BN_NEG) {
ep2_neg(t1, t1);
}
/* t2 = (x^2 - x - 1)P = x^2P - x*P - P. */
ep2_sub(t2, t1, t0);
ep2_sub(t2, t2, p);
/* t3 = \psi(x - 1)P. */
ep2_sub(t3, t0, p);
ep2_norm(t3, t3);
ep2_frb(t3, t3, 1);
ep2_add(t2, t2, t3);
/* t3 = \psi^2(2P). */
ep2_dbl(t3, p);
ep2_norm(t3, t3);
ep2_frb(t3, t3, 2);
ep2_add(t2, t2, t3);
ep2_norm(r, t2);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
ep2_free(t0);
ep2_free(t1);
ep2_free(t2);
ep2_free(t3);
bn_free(x);
}
}
/**
* Multiplies a point on a Barreto-Naehrig curve by the cofactor.
*
* @param[out] r - the result.
* @param[in] p - the point to multiply.
*/
void ep2_mul_cof_bn(ep2_t r, ep2_t p) {
bn_t x;
ep2_t t0, t1, t2;
ep2_null(t0);
ep2_null(t1);
ep2_null(t2);
bn_null(x);
TRY {
ep2_new(t0);
ep2_new(t1);
ep2_new(t2);
bn_new(x);
fp_param_get_var(x);
/* Compute t0 = xP. */
ep2_mul(t0, p, x);
if (bn_sign(x) == BN_NEG) {
ep2_neg(t0, t0);
}
/* Compute t1 = \psi(3xP). */
ep2_dbl(t1, t0);
ep2_add(t1, t1, t0);
ep2_norm(t1, t1);
ep2_frb(t1, t1, 1);
/* Compute t2 = \psi^3(P) + t0 + t1 + \psi^2(xP). */
ep2_frb(t2, p, 2);
ep2_frb(t2, t2, 1);
ep2_add(t2, t2, t0);
ep2_add(t2, t2, t1);
ep2_frb(t1, t0, 2);
ep2_add(t2, t2, t1);
ep2_norm(r, t2);
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
ep2_free(t0);
ep2_free(t1);
ep2_free(t2);
bn_free(x);
}
}
