virtual BOOL on_mouse(HELEMENT he, HELEMENT target, UINT event_type, POINT pt, UINT mouseButtons, UINT keyboardStates )
{
if( mouseButtons != MAIN_MOUSE_BUTTON )
return false;
if( event_type == MOUSE_UP)
{
dom::element el = he;
el.release_capture();
return true;
}
if( event_type != MOUSE_MOVE && event_type != MOUSE_DOWN)
return false;
// mouse moved and pressed
// el is our splitter element;
dom::element splitter_el = he;
dom::element parent_element = splitter_el.parent();
// what kind of splitter do we have?
bool horizontal = equal(parent_element.get_style_attribute("flow"),L"horizontal");
dom::element first = splitter_el.prev_sibling();
dom::element second = splitter_el.next_sibling();
if(!first.is_valid() || !second.is_valid())
return false; // nothing to do
bool need_update = horizontal?
do_horizontal(event_type, pt, splitter_el,first,second, parent_element):
do_vertical(event_type, pt,splitter_el,first,second, parent_element);
if(need_update && event_type == MOUSE_MOVE)
parent_element.update(true); //done! update changes on the view
return true; // it is ours - stop event bubbling
}
static void miller(element_t res, element_t P, element_ptr QR, element_ptr R, int n) {
// Collate divisions.
mp_bitcnt_t m;
element_t v, vd;
element_t Z;
element_t a, b, c;
const element_ptr cca = curve_a_coeff(P);
const element_ptr Px = curve_x_coord(P);
const element_ptr Py = curve_y_coord(P);
element_t e0, e1;
mpz_t q;
element_ptr Zx, Zy;
const element_ptr numx = curve_x_coord(QR);
const element_ptr numy = curve_y_coord(QR);
const element_ptr denomx = curve_x_coord(R);
const element_ptr denomy = curve_y_coord(R);
#define do_vertical(e, edenom) { \
element_sub(e0, numx, Zx); \
element_mul((e), (e), e0); \
\
element_sub(e0, denomx, Zx); \
element_mul((edenom), (edenom), e0); \
}
#define do_tangent(e, edenom) { \
/*a = -slope_tangent(A.x, A.y); \
b = 1; \
c = -(A.y + a * A.x); \
but we multiply by 2*A.y to avoid division*/ \
\
/*a = -Ax * (Ax + Ax + Ax + twicea_2) - a_4; \
Common curves: a2 = 0 (and cc->a is a_4), so \
a = -(3 Ax^2 + cc->a) \
b = 2 * Ay \
c = -(2 Ay^2 + a Ax); */ \
\
if (element_is0(Zy)) { \
do_vertical((e), (edenom)); \
} else { \
element_square(a, Zx); \
element_mul_si(a, a, 3); \
element_add(a, a, cca); \
element_neg(a, a); \
\
element_add(b, Zy, Zy); \
\
element_mul(e0, b, Zy); \
element_mul(c, a, Zx); \
element_add(c, c, e0); \
element_neg(c, c); \
\
element_mul(e0, a, numx); \
element_mul(e1, b, numy); \
element_add(e0, e0, e1); \
element_add(e0, e0, c); \
element_mul((e), (e), e0); \
\
element_mul(e0, a, denomx); \
element_mul(e1, b, denomy); \
element_add(e0, e0, e1); \
element_add(e0, e0, c); \
element_mul((edenom), (edenom), e0); \
} \
}
#define do_line(e, edenom) { \
if (!element_cmp(Zx, Px)) { \
if (!element_cmp(Zy, Py)) { \
do_tangent(e, edenom); \
} else { \
do_vertical(e, edenom); \
} \
} else { \
element_sub(b, Px, Zx); \
element_sub(a, Zy, Py); \
element_mul(c, Zx, Py); \
element_mul(e0, Zy, Px); \
element_sub(c, c, e0); \
\
element_mul(e0, a, numx); \
element_mul(e1, b, numy); \
element_add(e0, e0, e1); \
element_add(e0, e0, c); \
element_mul(e, e, e0); \
\
element_mul(e0, a, denomx); \
element_mul(e1, b, denomy); \
element_add(e0, e0, e1); \
element_add(e0, e0, c); \
element_mul(edenom, edenom, e0); \
} \
}
element_init(a, res->field);
element_init(b, res->field);
element_init(c, res->field);
element_init(e0, res->field);
element_init(e1, res->field);
element_init(v, res->field);
element_init(vd, res->field);
element_init(Z, P->field);
element_set(Z, P);
Zx = curve_x_coord(Z);
Zy = curve_y_coord(Z);
element_set1(v);
element_set1(vd);
mpz_init(q);
mpz_set_ui(q, n);
m = (mp_bitcnt_t)mpz_sizeinbase(q, 2);
m = (m > 2 ? m - 2 : 0);
for (;;) {
element_square(v, v);
element_square(vd, vd);
do_tangent(v, vd);
element_double(Z, Z);
do_vertical(vd, v);
if (mpz_tstbit(q, m)) {
do_line(v, vd);
element_add(Z, Z, P);
if (m) {
do_vertical(vd, v);
}
}
if (!m) break;
m--;
}
mpz_clear(q);
element_invert(vd, vd);
element_mul(res, v, vd);
element_clear(v);
element_clear(vd);
element_clear(Z);
element_clear(a);
element_clear(b);
element_clear(c);
element_clear(e0);
element_clear(e1);
#undef do_vertical
#undef do_tangent
#undef do_line
}
static void e_miller_proj(element_t res, element_t P,
element_ptr QR, element_ptr R,
e_pairing_data_ptr p) {
//collate divisions
int n;
element_t v, vd;
element_t v1, vd1;
element_t Z, Z1;
element_t a, b, c;
const element_ptr cca = curve_a_coeff(P);
element_t e0, e1;
const element_ptr e2 = a, e3 = b;
element_t z, z2;
int i;
element_ptr Zx, Zy;
const element_ptr Px = curve_x_coord(P);
const element_ptr numx = curve_x_coord(QR);
const element_ptr numy = curve_y_coord(QR);
const element_ptr denomx = curve_x_coord(R);
const element_ptr denomy = curve_y_coord(R);
//convert Z from weighted projective (Jacobian) to affine
//i.e. (X, Y, Z) --> (X/Z^2, Y/Z^3)
//also sets z to 1
#define to_affine() { \
element_invert(z, z); \
element_square(e0, z); \
element_mul(Zx, Zx, e0); \
element_mul(e0, e0, z); \
element_mul(Zy, Zy, e0); \
element_set1(z); \
element_set1(z2); \
}
#define proj_double() { \
const element_ptr x = Zx; \
const element_ptr y = Zy; \
/* e0 = 3x^2 + (cc->a) z^4 */ \
element_square(e0, x); \
/* element_mul_si(e0, e0, 3); */ \
element_double(e1, e0); \
element_add(e0, e0, e1); \
element_square(e1, z2); \
element_mul(e1, e1, cca); \
element_add(e0, e0, e1); \
\
/* z_out = 2 y z */ \
element_mul(z, y, z); \
/* element_mul_si(z, z, 2); */ \
element_double(z, z); \
element_square(z2, z); \
\
/* e1 = 4 x y^2 */ \
element_square(e2, y); \
element_mul(e1, x, e2); \
/* element_mul_si(e1, e1, 4); */ \
element_double(e1, e1); \
element_double(e1, e1); \
\
/* x_out = e0^2 - 2 e1 */ \
/* element_mul_si(e3, e1, 2); */ \
element_double(e3, e1); \
element_square(x, e0); \
element_sub(x, x, e3); \
\
/* e2 = 8y^4 */ \
element_square(e2, e2); \
/* element_mul_si(e2, e2, 8); */ \
element_double(e2, e2); \
element_double(e2, e2); \
element_double(e2, e2); \
\
/* y_out = e0(e1 - x_out) - e2 */ \
element_sub(e1, e1, x); \
element_mul(e0, e0, e1); \
element_sub(y, e0, e2); \
}
#define do_tangent(e, edenom) { \
/* a = -(3x^2 + cca z^4) */ \
/* b = 2 y z^3 */ \
/* c = -(2 y^2 + x a) */ \
/* a = z^2 a */ \
element_square(a, z2); \
element_mul(a, a, cca); \
element_square(b, Zx); \
/* element_mul_si(b, b, 3); */ \
element_double(e0, b); \
element_add(b, b, e0); \
element_add(a, a, b); \
element_neg(a, a); \
\
/* element_mul_si(e0, Zy, 2); */ \
element_double(e0, Zy); \
element_mul(b, e0, z2); \
element_mul(b, b, z); \
\
element_mul(c, Zx, a); \
element_mul(a, a, z2); \
element_mul(e0, e0, Zy); \
element_add(c, c, e0); \
element_neg(c, c); \
\
element_mul(e0, a, numx); \
element_mul(e1, b, numy); \
element_add(e0, e0, e1); \
element_add(e0, e0, c); \
element_mul(e, e, e0); \
\
element_mul(e0, a, denomx); \
element_mul(e1, b, denomy); \
element_add(e0, e0, e1); \
element_add(e0, e0, c); \
element_mul(edenom, edenom, e0); \
}
#define do_vertical(e, edenom, Ax) { \
element_mul(e0, numx, z2); \
element_sub(e0, e0, Ax); \
element_mul(e, e, e0); \
\
element_mul(e0, denomx, z2); \
element_sub(e0, e0, Ax); \
element_mul(edenom, edenom, e0); \
}
#define do_line(e, edenom, A, B) { \
element_ptr Ax = curve_x_coord(A); \
element_ptr Ay = curve_y_coord(A); \
element_ptr Bx = curve_x_coord(B); \
element_ptr By = curve_y_coord(B); \
\
element_sub(b, Bx, Ax); \
element_sub(a, Ay, By); \
element_mul(c, Ax, By); \
element_mul(e0, Ay, Bx); \
element_sub(c, c, e0); \
\
element_mul(e0, a, numx); \
element_mul(e1, b, numy); \
element_add(e0, e0, e1); \
element_add(e0, e0, c); \
element_mul(e, e, e0); \
\
element_mul(e0, a, denomx); \
element_mul(e1, b, denomy); \
element_add(e0, e0, e1); \
element_add(e0, e0, c); \
element_mul(edenom, edenom, e0); \
}
element_init(a, res->field);
element_init(b, res->field);
element_init(c, res->field);
element_init(e0, res->field);
element_init(e1, res->field);
element_init(z, res->field);
element_init(z2, res->field);
element_set1(z);
element_set1(z2);
element_init(v, res->field);
element_init(vd, res->field);
element_init(v1, res->field);
element_init(vd1, res->field);
element_init(Z, P->field);
element_init(Z1, P->field);
element_set(Z, P);
Zx = curve_x_coord(Z);
Zy = curve_y_coord(Z);
element_set1(v);
element_set1(vd);
element_set1(v1);
element_set1(vd1);
n = p->exp1;
for (i=0; i<n; i++) {
element_square(v, v);
element_square(vd, vd);
do_tangent(v, vd);
proj_double();
do_vertical(vd, v, Zx);
}
to_affine();
if (p->sign1 < 0) {
element_set(v1, vd);
element_set(vd1, v);
do_vertical(vd1, v1, Zx);
element_neg(Z1, Z);
} else {
element_set(v1, v);
element_set(vd1, vd);
element_set(Z1, Z);
}
n = p->exp2;
for (; i<n; i++) {
element_square(v, v);
element_square(vd, vd);
do_tangent(v, vd);
proj_double();
do_vertical(vd, v, Zx);
}
to_affine();
element_mul(v, v, v1);
element_mul(vd, vd, vd1);
do_line(v, vd, Z, Z1);
element_add(Z, Z, Z1);
do_vertical(vd, v, Zx);
if (p->sign0 > 0) {
do_vertical(v, vd, Px);
}
element_invert(vd, vd);
element_mul(res, v, vd);
element_clear(v);
element_clear(vd);
element_clear(v1);
element_clear(vd1);
element_clear(z);
element_clear(z2);
element_clear(Z);
element_clear(Z1);
element_clear(a);
element_clear(b);
element_clear(c);
element_clear(e0);
element_clear(e1);
#undef to_affine
#undef proj_double
#undef do_tangent
#undef do_vertical
#undef do_line
}
//TODO: the following code is useless as the Tate pairing is degenerate on singular curves
static void sn_miller(element_t res, mpz_t q, element_t P,
element_ptr Qx, element_ptr Qy) {
//collate divisions
int m;
element_t v, vd;
element_t Z;
element_t a, b, c;
element_t e0, e1;
element_ptr Zx;
element_ptr Zy;
const element_ptr Px = curve_x_coord(P);
const element_ptr Py = curve_y_coord(P);
#define do_vertical(e) \
element_sub(e0, Qx, Zx); \
element_mul(e, e, e0);
//a = -slope_tangent(Z.x, Z.y);
//b = 1;
//c = -(Z.y + a * Z.x);
//but we multiply by 2*Z.y to avoid division
//a = -Zx * (Zx + Zx + Zx + 2)
//b = 2 * Zy
//c = -(2 Zy^2 + a Zx);
#define do_tangent(e) \
element_double(e0, Zx); \
element_add(a, Zx, e0); \
element_set_si(e0, 2); \
element_add(a, a, e0); \
element_mul(a, a, Zx); \
element_neg(a, a); \
element_add(b, Zy, Zy); \
element_mul(e0, b, Zy); \
element_mul(c, a, Zx); \
element_add(c, c, e0); \
element_neg(c, c); \
element_mul(e0, a, Qx); \
element_mul(e1, b, Qy); \
element_add(e0, e0, e1); \
element_add(e0, e0, c); \
element_mul(e, e, e0);
//a = -(B.y - A.y) / (B.x - A.x);
//b = 1;
//c = -(A.y + a * A.x);
//but we'll multiply by B.x - A.x to avoid division
#define do_line(e) \
element_sub(b, Px, Zx); \
element_sub(a, Zy, Py); \
element_mul(e0, b, Zy); \
element_mul(c, a, Zx); \
element_add(c, c, e0); \
element_neg(c, c); \
element_mul(e0, a, Qx); \
element_mul(e1, b, Qy); \
element_add(e0, e0, e1); \
element_add(e0, e0, c); \
element_mul(e, e, e0);
element_init(a, Px->field);
element_init(b, Px->field);
element_init(c, Px->field);
element_init(e0, res->field);
element_init(e1, res->field);
element_init(v, res->field);
element_init(vd, res->field);
element_init(Z, P->field);
element_set(Z, P);
Zx = curve_x_coord(Z);
Zy = curve_y_coord(Z);
element_set1(v);
element_set1(vd);
m = mpz_sizeinbase(q, 2) - 2;
while(m >= 0) {
element_mul(v, v, v);
element_mul(vd, vd, vd);
do_tangent(v);
element_double(Z, Z);
do_vertical(vd);
if (mpz_tstbit(q, m)) {
do_line(v);
element_add(Z, Z, P);
do_vertical(vd);
}
m--;
}
#undef do_tangent
#undef do_vertical
#undef do_line
element_invert(vd, vd);
element_mul(res, v, vd);
element_clear(v);
element_clear(vd);
element_clear(Z);
element_clear(a);
element_clear(b);
element_clear(c);
element_clear(e0);
element_clear(e1);
}
static void e_miller_affine(element_t res, element_t P,
element_ptr QR, element_ptr R,
e_pairing_data_ptr p) {
//collate divisions
int n;
element_t v, vd;
element_t v1, vd1;
element_t Z, Z1;
element_t a, b, c;
element_t e0, e1;
const element_ptr Px = curve_x_coord(P);
const element_ptr cca = curve_a_coeff(P);
element_ptr Zx, Zy;
int i;
const element_ptr numx = curve_x_coord(QR);
const element_ptr numy = curve_y_coord(QR);
const element_ptr denomx = curve_x_coord(R);
const element_ptr denomy = curve_y_coord(R);
#define do_vertical(e, edenom, Ax) { \
element_sub(e0, numx, Ax); \
element_mul(e, e, e0); \
\
element_sub(e0, denomx, Ax); \
element_mul(edenom, edenom, e0); \
}
#define do_tangent(e, edenom) { \
/* a = -slope_tangent(A.x, A.y); */ \
/* b = 1; */ \
/* c = -(A.y + a * A.x); */ \
/* but we multiply by 2*A.y to avoid division */ \
\
/* a = -Ax * (Ax + Ax + Ax + twicea_2) - a_4; */ \
/* Common curves: a2 = 0 (and cc->a is a_4), so */ \
/* a = -(3 Ax^2 + cc->a) */ \
/* b = 2 * Ay */ \
/* c = -(2 Ay^2 + a Ax); */ \
\
element_square(a, Zx); \
element_mul_si(a, a, 3); \
element_add(a, a, cca); \
element_neg(a, a); \
\
element_add(b, Zy, Zy); \
\
element_mul(e0, b, Zy); \
element_mul(c, a, Zx); \
element_add(c, c, e0); \
element_neg(c, c); \
\
element_mul(e0, a, numx); \
element_mul(e1, b, numy); \
element_add(e0, e0, e1); \
element_add(e0, e0, c); \
element_mul(e, e, e0); \
\
element_mul(e0, a, denomx); \
element_mul(e1, b, denomy); \
element_add(e0, e0, e1); \
element_add(e0, e0, c); \
element_mul(edenom, edenom, e0); \
}
#define do_line(e, edenom, A, B) { \
element_ptr Ax = curve_x_coord(A); \
element_ptr Ay = curve_y_coord(A); \
element_ptr Bx = curve_x_coord(B); \
element_ptr By = curve_y_coord(B); \
\
element_sub(b, Bx, Ax); \
element_sub(a, Ay, By); \
element_mul(c, Ax, By); \
element_mul(e0, Ay, Bx); \
element_sub(c, c, e0); \
\
element_mul(e0, a, numx); \
element_mul(e1, b, numy); \
element_add(e0, e0, e1); \
element_add(e0, e0, c); \
element_mul(e, e, e0); \
\
element_mul(e0, a, denomx); \
element_mul(e1, b, denomy); \
element_add(e0, e0, e1); \
element_add(e0, e0, c); \
element_mul(edenom, edenom, e0); \
}
element_init(a, res->field);
element_init(b, res->field);
element_init(c, res->field);
element_init(e0, res->field);
element_init(e1, res->field);
element_init(v, res->field);
element_init(vd, res->field);
element_init(v1, res->field);
element_init(vd1, res->field);
element_init(Z, P->field);
element_init(Z1, P->field);
element_set(Z, P);
Zx = curve_x_coord(Z);
Zy = curve_y_coord(Z);
element_set1(v);
element_set1(vd);
element_set1(v1);
element_set1(vd1);
n = p->exp1;
for (i=0; i<n; i++) {
element_square(v, v);
element_square(vd, vd);
do_tangent(v, vd);
element_double(Z, Z);
do_vertical(vd, v, Zx);
}
if (p->sign1 < 0) {
element_set(v1, vd);
element_set(vd1, v);
do_vertical(vd1, v1, Zx);
element_neg(Z1, Z);
} else {
element_set(v1, v);
element_set(vd1, vd);
element_set(Z1, Z);
}
n = p->exp2;
for (; i<n; i++) {
element_square(v, v);
element_square(vd, vd);
do_tangent(v, vd);
element_double(Z, Z);
do_vertical(vd, v, Zx);
}
element_mul(v, v, v1);
element_mul(vd, vd, vd1);
do_line(v, vd, Z, Z1);
element_add(Z, Z, Z1);
do_vertical(vd, v, Zx);
if (p->sign0 > 0) {
do_vertical(v, vd, Px);
}
element_invert(vd, vd);
element_mul(res, v, vd);
element_clear(v);
element_clear(vd);
element_clear(v1);
element_clear(vd1);
element_clear(Z);
element_clear(Z1);
element_clear(a);
element_clear(b);
element_clear(c);
element_clear(e0);
element_clear(e1);
#undef do_vertical
#undef do_tangent
#undef do_line
}
