/* Once we have found a D and q, this will find a curve and point.
* Returns: 0 (composite), 1 (didn't work), 2 (success)
* It's debatable what to do with a 1 return.
*/
static int find_curve(mpz_t a, mpz_t b, mpz_t x, mpz_t y,
long D, int poly_index, mpz_t m, mpz_t q, mpz_t N, int maxroots)
{
long nroots, npoints, i, rooti, unity, result;
mpz_t g, t, t2;
mpz_t* roots = 0;
/* TODO: A better way to do this, I believe, would be to have the root
* finder set up as an iterator. That way we'd get the first root,
* try to find a curve, and probably we'd be done. Only if we tried
* 10+ points on that root would we get another root. This would
* probably be set up as a stack (array) of polynomials plus one
* saved root (for when we solve a degree 2 poly).
*/
/* Step 1: Get the roots of the Hilbert class polynomial. */
nroots = find_roots(D, poly_index, N, &roots, maxroots);
if (nroots == 0)
return 1;
/* Step 2: Loop selecting curves and trying points.
* On average it takes about 3 points, but we'll try 100+. */
mpz_init(g); mpz_init(t); mpz_init(t2);
npoints = 0;
result = 1;
for (rooti = 0; result == 1 && rooti < 50*nroots; rooti++) {
/* Given this D and root, select curve a,b */
select_curve_params(a, b, g, D, roots, rooti % nroots, N, t);
if (mpz_sgn(g) == 0) { result = 0; break; }
/* See Cohen 5.3.1, page 231 */
unity = (D == -3) ? 6 : (D == -4) ? 4 : 2;
for (i = 0; result == 1 && i < unity; i++) {
if (i > 0)
update_ab(a, b, D, g, N);
npoints++;
select_point(x, y, a, b, N, t, t2);
result = ecpp_check_point(x, y, m, q, a, N, t, t2);
}
}
if (npoints > 10 && get_verbose_level() > 0)
printf(" # point finding took %ld points\n", npoints);
if (roots != 0) {
for (rooti = 0; rooti < nroots; rooti++)
mpz_clear(roots[rooti]);
Safefree(roots);
}
mpz_clear(g); mpz_clear(t); mpz_clear(t2);
return result;
}
/* Once we have found a D and q, this will find a curve and point.
* Returns: 0 (composite), 1 (didn't work), 2 (success)
* It's debatable what to do with a 1 return.
*/
static int find_curve(mpz_t a, mpz_t b, mpz_t x, mpz_t y,
long D, mpz_t m, mpz_t q, mpz_t N)
{
long nroots, npoints, i, rooti, unity, result;
mpz_t g, t, t2;
mpz_t* roots = 0;
int verbose = get_verbose_level();
/* Step 1: Get the roots of the Hilbert class polynomial. */
nroots = find_roots(D, N, &roots);
if (nroots == 0)
return 1;
/* Step 2: Loop selecting curves and trying points.
* On average it takes about 3 points, but we'll try 100+. */
mpz_init(g); mpz_init(t); mpz_init(t2);
npoints = 0;
result = 1;
for (rooti = 0; result == 1 && rooti < 50*nroots; rooti++) {
/* Given this D and root, select curve a,b */
select_curve_params(a, b, g, D, roots, rooti % nroots, N, t);
if (mpz_sgn(g) == 0) { result = 0; break; }
/* See Cohen 5.3.1, page 231 */
unity = (D == -3) ? 6 : (D == -4) ? 4 : 2;
for (i = 0; result == 1 && i < unity; i++) {
if (i > 0)
update_ab(a, b, D, g, N);
npoints++;
select_point(x, y, a, b, N, t, t2);
result = ecpp_check_point(x, y, m, q, a, N, t, t2);
}
}
if (verbose && npoints > 10)
printf(" # point finding took %ld points\n", npoints);
if (roots != 0) {
for (rooti = 0; rooti < nroots; rooti++)
mpz_clear(roots[rooti]);
Safefree(roots);
}
mpz_clear(g); mpz_clear(t); mpz_clear(t2);
return result;
}
