int main(void) {
field_t c;
field_t Z19;
element_t P, Q, R;
mpz_t q, z;
element_t a, b;
int i;
field_t Z19_2;
field_t c2;
element_t P2, Q2, R2;
element_t a2;
mpz_init(q);
mpz_init(z);
mpz_set_ui(q, 19);
field_init_fp(Z19, q);
element_init(a, Z19);
element_init(b, Z19);
element_set_si(a, 1);
element_set_si(b, 6);
mpz_set_ui(q, 18);
field_init_curve_ab(c, a, b, q, NULL);
element_init(P, c);
element_init(Q, c);
element_init(R, c);
printf("Y^2 = X^3 + X + 6 over F_19\n");
//(0,+/-5) is a generator
element_set0(a);
curve_from_x(R, a);
for (i=1; i<19; 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,%dR) = %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);
//we're supposed to use multiples of R
//but 2R works just as well and it allows us
//to use R as the offset every time
element_mul_mpz(Q, P, z);
tate_9(a, P, Q, R);
element_printf("e_9(P,%dP) = %B\n", i, a);
}
//to do the pairing on all of E(F_19) we need to move to F_19^2
//or compute the rational function explicitly
printf("moving to F_19^2\n");
field_init_fi(Z19_2, Z19);
//don't need to tell it the real order
field_init_curve_ab_map(c2, c, element_field_to_fi, Z19_2, q, NULL);
element_init(P2, c2);
element_init(Q2, c2);
element_init(R2, c2);
element_init(a2, Z19_2);
element_set0(a2);
curve_from_x(P2, a2);
element_random(R2);
element_printf("P = %B\n", P2);
for (i=1; i<=18; i++) {
mpz_set_si(z, i);
element_mul_mpz(Q2, P2, z);
tate_18(a2, P2, Q2, R2, P2);
element_printf("e_18(P,%dP) = %B\n", i, a2);
}
element_clear(P2);
element_clear(Q2);
element_clear(R2);
element_clear(a2);
field_clear(c2);
field_clear(Z19_2);
field_clear(c);
element_clear(a);
element_clear(b);
element_clear(P);
element_clear(Q);
element_clear(R);
field_clear(Z19);
mpz_clear(q);
mpz_clear(z);
return 0;
}
int main(void)
{
int i;
element_t g, h;
element_t w0, w1;
element_t a, b;
mpz_t prime, cofac;
mpz_init(prime);
mpz_init(order);
mpz_init(cofac);
mpz_set_ui(prime, 59);
field_init_fp(Fq, prime);
element_init(a, Fq);
element_init(b, Fq);
field_init_fi(Fq2, Fq);
element_set1(a);
element_set0(b);
mpz_set_ui(order, 5);
mpz_set_ui(cofac, 12);
field_init_curve_ab(E, a, b, order, cofac);
element_clear(a);
element_clear(b);
element_init(a, Fq2);
element_init(b, Fq2);
element_set1(a);
element_set0(b);
mpz_mul(cofac, cofac, cofac);
field_init_curve_ab(E2, a, b, order, NULL);
element_init(g, E2);
element_init(h, E2);
element_init(w0, Fq2);
element_init(w1, Fq2);
/*
do {
element_random(g);
} while (element_is1(g));
for (i=1; i<5; i++) {
element_mul(h, h, g);
element_printf("%d: %B\n", i, h);
element_printf("tangent = ");
do_tangent(h);
}
*/
element_set_str(g, "[[25,0],[30,0]", 0);
element_set_str(h, "[[34,0],[0,30]", 0);
weil(w0, g, h);
element_printf("weil: %B\n", w0);
element_set1(w1);
for (i=1; i<6; i++) {
element_mul(w1, w1, w0);
element_printf("%d: %B\n", i, w1);
}
fasterweil(w0, g, h);
element_printf("fasterweil: %B\n", w0);
element_set1(w1);
for (i=1; i<6; i++) {
element_mul(w1, w1, w0);
element_printf("%d: %B\n", i, w1);
}
fasterweil2(w0, g, h);
element_printf("fasterweil2: %B\n", w0);
tate(w0, g, h);
element_printf("tate: %B\n", w0);
element_set1(w1);
for (i=1; i<6; i++) {
element_mul(w1, w1, w0);
element_printf("%d: %B\n", i, w1);
}
shipseystange(w0, g, h);
element_printf("ss-tate: %B\n", w0);
element_set1(w1);
for (i=1; i<6; i++) {
element_mul(w1, w1, w0);
element_printf("%d: %B\n", i, w1);
}
return 0;
}
