int main(void)
{
field_t c;
field_t Z19;
element_t P, Q, R;
mpz_t q, z;
element_t a;
int i;
mpz_init(q);
mpz_init(z);
mpz_set_ui(q, 19);
field_init_fp(Z19, q);
element_init(a, Z19);
field_init_curve_singular_with_node(c, Z19);
element_init(P, c);
element_init(Q, c);
element_init(R, c);
//(3,+/-6) is a generator
//we have an isomorphism from E_ns to F_19^*
// (3,6) --> 3
//(generally (x,y) --> (y+x)/(y-x)
curve_set_si(R, 3, 6);
for (i=1; i<=18; i++) {
mpz_set_si(z, i);
element_mul_mpz(Q, R, z);
element_printf("%dR = %B\n", i, Q);
}
mpz_set_ui(z, 6);
element_mul_mpz(P, R, z);
//P has order 3
element_printf("P = %B\n", P);
for (i=1; i<=3; i++) {
mpz_set_si(z, i);
element_mul_mpz(Q, R, z);
tate_3(a, P, Q, R);
element_printf("e_3(P,%dP) = %B\n", i, a);
}
element_double(P, R);
//P has order 9
element_printf("P = %B\n", P);
for (i=1; i<=9; i++) {
mpz_set_si(z, i);
element_mul_mpz(Q, P, z);
tate_9(a, P, Q, R);
element_printf("e_9(P,%dP) = %B\n", i, a);
}
return 0;
}
void pairing_init_singular_with_node(pairing_t pairing, mpz_t q) {
sn_pairing_data_ptr p;
mpz_init(pairing->r);
mpz_sub_ui(pairing->r, q, 1);
field_init_fp(pairing->Zr, pairing->r);
pairing->map = sn_pairing;
p = pairing->data = pbc_malloc(sizeof(sn_pairing_data_t));
field_init_fp(p->Fq, q);
field_init_curve_singular_with_node(p->Eq, p->Fq);
//mpz_init(p->tateexp);
//mpz_sub_ui(p->tateexp, p->Fq->order, 1);
//mpz_divexact(p->tateexp, p->tateexp, pairing->r);
pairing->G2 = pairing->G1 = p->Eq;
pairing_GT_init(pairing, p->Fq);
}
