//--------------------------------------------------------------
void testApp::mousePressed(int x, int y, int button){
for ( int i = 0; i < 4; i++ )
{
if ( select_point(ofVec2f(x, y), quadmesh.getPos(i), 10) ){ id = i; return; }
}
}
void mouse(int button, int state, int x, int y)
{
frame_x = (float) x / (VPw/2) - 1.0; //formula derived from example on pg. 100 of
frame_y = (float) (VPh - y) / (VPh/2) - 1.0; // Interactive Computer Graphics textbook
//----------------------------------------------------------------------------------------------
//control point selection
if (button == GLUT_LEFT_BUTTON && state == GLUT_DOWN)
{
move_index = select_point(frame_x, frame_y); //Returns index number of a control point.
//Returns -1 if no point is present at cursor's coordinates
if (move_index > -1)
{
if (grab > -1)
{
colors[grab] = color4(1.0, 0.0, 0.0, 1.0); // make previously selected control point red (deselected)
}
grab = move_index;
colors[grab] = color4(0.0, 1.0, 0.0, 1.0); // make selected control point green
}
if (grab > -1)
{
control_points[grab] = point4(frame_x, frame_y, 0.0, 1.0);
colors[grab] = color4(0.0, 1.0, 0.0, 1.0); // make selected control point green
}
glutPostRedisplay();
}
//----------------------------------------------------------------------------------------------
//deselect points (disable editing of point)
if (button == GLUT_MIDDLE_BUTTON && state == GLUT_DOWN)
{
if (grab > -1)
{
colors[grab] = color4(1.0, 0.0, 0.0, 1.0); // make selected control point red
glutPostRedisplay();
grab = -1;
}
}
//----------------------------------------------------------------------------------------------
//Create new control points
if (button == GLUT_RIGHT_BUTTON && state == GLUT_DOWN)
{
control_points[control_index] = point4(frame_x, frame_y, 0.0, 1.0);
colors[control_index] = color4(1.0, 0.0, 0.0, 1.0); // make new control point red
++control_index;
++num_controls;
glutPostRedisplay();
}
}
/* 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;
}
// Interleaved point multiplication using precomputed point multiples: The
// small point multiples 0*P, 1*P, ..., 17*P are in p_pre_comp, the scalar
// in p_scalar, if non-NULL. If g_scalar is non-NULL, we also add this multiple
// of the generator, using certain (large) precomputed multiples in g_pre_comp.
// Output point (X, Y, Z) is stored in x_out, y_out, z_out.
static void batch_mul(fe x_out, fe y_out, fe z_out,
const uint8_t *p_scalar, const uint8_t *g_scalar,
const fe p_pre_comp[17][3]) {
// set nq to the point at infinity
fe nq[3] = {{0},{0},{0}}, ftmp, tmp[3];
uint64_t bits;
uint8_t sign, digit;
// Loop over both scalars msb-to-lsb, interleaving additions of multiples
// of the generator (two in each of the last 32 rounds) and additions of p
// (every 5th round).
int skip = 1; // save two point operations in the first round
size_t i = p_scalar != NULL ? 255 : 31;
for (;;) {
// double
if (!skip) {
point_double(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2]);
}
// add multiples of the generator
if (g_scalar != NULL && i <= 31) {
// first, look 32 bits upwards
bits = get_bit(g_scalar, i + 224) << 3;
bits |= get_bit(g_scalar, i + 160) << 2;
bits |= get_bit(g_scalar, i + 96) << 1;
bits |= get_bit(g_scalar, i + 32);
// select the point to add, in constant time
select_point(bits, 16, g_pre_comp[1], tmp);
if (!skip) {
point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 1 /* mixed */,
tmp[0], tmp[1], tmp[2]);
} else {
fe_copy(nq[0], tmp[0]);
fe_copy(nq[1], tmp[1]);
fe_copy(nq[2], tmp[2]);
skip = 0;
}
// second, look at the current position
bits = get_bit(g_scalar, i + 192) << 3;
bits |= get_bit(g_scalar, i + 128) << 2;
bits |= get_bit(g_scalar, i + 64) << 1;
bits |= get_bit(g_scalar, i);
// select the point to add, in constant time
select_point(bits, 16, g_pre_comp[0], tmp);
point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 1 /* mixed */, tmp[0],
tmp[1], tmp[2]);
}
// do other additions every 5 doublings
if (p_scalar != NULL && i % 5 == 0) {
bits = get_bit(p_scalar, i + 4) << 5;
bits |= get_bit(p_scalar, i + 3) << 4;
bits |= get_bit(p_scalar, i + 2) << 3;
bits |= get_bit(p_scalar, i + 1) << 2;
bits |= get_bit(p_scalar, i) << 1;
bits |= get_bit(p_scalar, i - 1);
ec_GFp_nistp_recode_scalar_bits(&sign, &digit, bits);
// select the point to add or subtract, in constant time.
select_point(digit, 17, p_pre_comp, tmp);
fe_opp(ftmp, tmp[1]); // (X, -Y, Z) is the negative point.
fe_cmovznz(tmp[1], sign, tmp[1], ftmp);
if (!skip) {
point_add(nq[0], nq[1], nq[2], nq[0], nq[1], nq[2], 0 /* mixed */,
tmp[0], tmp[1], tmp[2]);
} else {
fe_copy(nq[0], tmp[0]);
fe_copy(nq[1], tmp[1]);
fe_copy(nq[2], tmp[2]);
skip = 0;
}
}
if (i == 0) {
break;
}
--i;
}
fe_copy(x_out, nq[0]);
fe_copy(y_out, nq[1]);
fe_copy(z_out, nq[2]);
}
