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Diffstat (limited to 'moon-abe/pbc-0.5.14/guru/sing.c')
| -rw-r--r-- | moon-abe/pbc-0.5.14/guru/sing.c | 263 |
1 files changed, 263 insertions, 0 deletions
diff --git a/moon-abe/pbc-0.5.14/guru/sing.c b/moon-abe/pbc-0.5.14/guru/sing.c new file mode 100644 index 00000000..d29e3ff5 --- /dev/null +++ b/moon-abe/pbc-0.5.14/guru/sing.c @@ -0,0 +1,263 @@ +/* + * 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; +} |