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-rw-r--r--moon-abe/pbc-0.5.14/guru/sing.c263
1 files changed, 0 insertions, 263 deletions
diff --git a/moon-abe/pbc-0.5.14/guru/sing.c b/moon-abe/pbc-0.5.14/guru/sing.c
deleted file mode 100644
index d29e3ff5..00000000
--- a/moon-abe/pbc-0.5.14/guru/sing.c
+++ /dev/null
@@ -1,263 +0,0 @@
-/*
- * Example of a singular curve, similar to 19.c
- * but the Tate pairing degenerates
- *
- * Consider the curve E: y^2 = x^3 + x^2 over F_19:
- * E_ns(F_19) is a cyclic group of order 18.
- */
-
-#include "pbc.h"
-#include "pbc_singular.h"
-#include "pbc_fp.h"
-
-static void miller(element_t res, element_t P, element_t Q, element_t R, int n)
-{
- //collate divisions
- int m;
- element_t v, vd;
- element_t Z;
- element_t a, b, c;
- element_t e0, e1;
- mpz_t q;
- element_ptr Zx, Zy;
- const element_ptr Px = curve_x_coord(P);
- const element_ptr Py = curve_y_coord(P);
- const element_ptr numx = curve_x_coord(Q);
- const element_ptr numy = curve_y_coord(Q);
- const element_ptr denomx = curve_x_coord(R);
- const element_ptr denomy = curve_y_coord(R);
-
- void do_vertical(element_t e, element_t edenom)
- {
- element_sub(e0, numx, Zx);
- element_mul(e, e, e0);
-
- element_sub(e0, denomx, Zx);
- element_mul(edenom, edenom, e0);
- }
-
- void do_tangent(element_t e, element_t 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;
- //This curve is special:
- //a = -(3 Ax^2 + 2Ax)
- //b = 2 * Ay
- //c = -(2 Ay^2 + a Ax);
-
- if (element_is0(Zy)) {
- do_vertical(e, edenom);
- return;
- }
- element_square(a, Zx);
- element_mul_si(a, a, 3);
- element_add(a, a, Zx);
- element_add(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, 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);
- }
-
- void do_line(element_ptr e, element_ptr edenom)
- {
- if (!element_cmp(Zx, Px)) {
- if (!element_cmp(Zy, Py)) {
- do_tangent(e, edenom);
- } else {
- do_vertical(e, edenom);
- }
- return;
- }
-
- 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 = mpz_sizeinbase(q, 2) - 2;
-
- while(m >= 0) {
- 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);
- }
- }
- 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);
-}
-
-static void tate_3(element_ptr out, element_ptr P, element_ptr Q, element_ptr R)
-{
- mpz_t six;
-
- mpz_init(six);
- mpz_set_ui(six, 6);
- element_t QR;
- element_t e0;
-
- element_init(QR, P->field);
- element_init(e0, out->field);
-
- element_add(QR, Q, R);
-
- //for subgroup size 3, -2P = P, hence
- //the tangent line at P has divisor 3(P) - 3(O)
-
- miller(out, P, QR, R, 3);
-
- element_pow_mpz(out, out, six);
- element_clear(QR);
- element_clear(e0);
- mpz_clear(six);
-}
-
-static void tate_9(element_ptr out, element_ptr P, element_ptr Q, element_ptr R)
-{
- element_t QR;
- element_init(QR, P->field);
-
- element_add(QR, Q, R);
-
- miller(out, P, QR, R, 9);
-
- element_square(out, out);
-
- element_clear(QR);
-}
-
-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;
-}