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Diffstat (limited to 'moon-abe/pbc-0.5.14/guru/59.c')
| -rw-r--r-- | moon-abe/pbc-0.5.14/guru/59.c | 783 |
1 files changed, 783 insertions, 0 deletions
diff --git a/moon-abe/pbc-0.5.14/guru/59.c b/moon-abe/pbc-0.5.14/guru/59.c new file mode 100644 index 00000000..d543a757 --- /dev/null +++ b/moon-abe/pbc-0.5.14/guru/59.c @@ -0,0 +1,783 @@ +// Step-by-step Weil and Tate pairings. +// For my thesis. +#include <string.h> +#include "pbc.h" +#include "pbc_fp.h" +#include "pbc_fieldquadratic.h" + +static field_t Fq, Fq2, E, E2; +static mpz_t order; + +static void do_vert(element_ptr z, element_ptr V, element_ptr Q) +{ + element_ptr Vx = curve_x_coord(V); + element_ptr Qx = curve_x_coord(Q); + element_ptr Qy = curve_y_coord(Q); + + element_t a, b, c; + element_init_same_as(a, Vx); + element_init_same_as(b, Vx); + element_init_same_as(c, Vx); + + //a = 1 + //b = 0; + //c = -Vx + element_set1(a); + element_set0(b); + element_neg(c, Vx); + + element_printf("vert at %B: %B %B %B\n", Vx, a, b, c); + element_mul(a, a, Qx); + element_mul(b, b, Qy); + element_add(c, c, a); + element_add(z, c, b); + element_printf("vert eval = %B\n", z); + element_clear(a); + element_clear(b); + element_clear(c); +} + +static void do_tangent(element_ptr z, element_ptr V, element_ptr Q) +{ + element_ptr Vx = curve_x_coord(V); + element_ptr Vy = curve_y_coord(V); + element_ptr Qx = curve_x_coord(Q); + element_ptr Qy = curve_y_coord(Q); + + element_t a, b, c; + element_init_same_as(a, Vx); + element_init_same_as(b, Vx); + element_init_same_as(c, Vx); + + //a = -slope_tangent(V.x, V.y); + //b = 1; + //c = -(V.y + aV.x); + /* + //we could multiply by -2*V.y to avoid division so: + //a = -(3 Vx^2 + cc->a) + //b = 2 * Vy + //c = -(2 Vy^2 + a Vx); + // + //actually no, since fasterweil won't work if we do this + */ + element_square(a, Vx); + //element_mul_si(a, a, 3); + element_add(b, a, a); + element_add(a, b, a); + element_set1(b); + element_add(a, a, b); + element_neg(a, a); + element_double(b, Vy); + element_div(a, a, b); + element_set1(b); + element_mul(c, a, Vx); + element_add(c, c, Vy); + element_neg(c, c); + + element_printf("tan at %B: %B %B %B\n", V, a, b, c); + + element_mul(a, a, Qx); + element_mul(b, b, Qy); + element_add(c, c, a); + element_add(z, c, b); + element_printf("tan eval = %B\n", z); + element_clear(a); + element_clear(b); + element_clear(c); +} + +static void do_line(element_ptr z, element_ptr V, element_ptr P, element_ptr Q) +{ + element_ptr Vx = curve_x_coord(V); + element_ptr Vy = curve_y_coord(V); + element_ptr Px = curve_x_coord(P); + element_ptr Py = curve_y_coord(P); + element_ptr Qx = curve_x_coord(Q); + element_ptr Qy = curve_y_coord(Q); + + element_t a, b, c, e0; + element_init_same_as(a, Vx); + element_init_same_as(b, Vx); + element_init_same_as(c, Vx); + element_init_same_as(e0, Vx); + + //a = -(B.y - A.y) / (B.x - A.x); + //b = 1; + //c = -(A.y + a * A.x); + + element_sub(a, Py, Vy); + element_sub(b, Vx, Px); + element_div(a, a, b); + element_set1(b); + element_mul(c, a, Vx); + element_add(c, c, Vy); + element_neg(c, c); + + /* + //but we could multiply by B.x - A.x to avoid division, so + //a = -(By - Ay) + //b = Bx - Ax + //c = -(Ay b + a Ax); + element_sub(a, Vy, Py); + element_sub(b, Px, Vx); + element_mul(c, Vx, Py); + element_mul(e0, Vy, Px); + element_sub(c, c, e0); + // + //actually no, since fasterweil won't work if we do this + */ + + element_printf("line at %B: %B %B %B\n", V, a, b, c); + element_mul(a, a, Qx); + element_mul(b, b, Qy); + element_add(c, c, a); + element_add(z, c, b); + element_printf(" = %B\n", z); + + element_clear(a); + element_clear(b); + element_clear(c); + element_clear(e0); +} + +void millertate(element_t z, element_t P, element_t Q) +{ + element_t Z; + element_t z0; + + element_init_same_as(Z, P); + element_init_same_as(z0, z); + + element_set(Z, P); + + do_tangent(z, Z, Q); + + element_double(Z, Z); + + do_vert(z0, Z, Q); + element_div(z, z, z0); + + element_printf("presquare: z = %B\n", z); + + element_square(z, z); + + element_printf("square: z = %B\n", z); + + do_tangent(z0, Z, Q); + element_mul(z, z, z0); + + element_clear(z0); + element_clear(Z); +} + +void tate(element_t z, element_t P, element_t Q) +{ + mpz_t q1r; + + mpz_init(q1r); + mpz_set_ui(q1r, 696); + + /* + millertate(z, P, Q); + element_printf("prepow: z = %B\n", z); + element_pow_mpz(z, z, q1r); + */ + { + element_t R, QR; + element_t z0; + + element_init_same_as(R, P); + element_init_same_as(QR, P); + element_init_same_as(z0, z); + + element_random(R); + element_add(QR, Q, R); + + millertate(z, P, QR); + millertate(z0, P, R); + element_div(z, z, z0); + element_pow_mpz(z, z, q1r); + element_clear(R); + element_clear(QR); + } + + mpz_clear(q1r); +} + +void shipseystange(element_t z, element_t P, element_t Q) +{ + mpz_t q1r; + + mpz_init(q1r); + mpz_set_ui(q1r, 696); + + element_ptr x = curve_x_coord(P); + element_ptr y = curve_y_coord(P); + + element_ptr x2 = curve_x_coord(Q); + element_ptr y2 = curve_y_coord(Q); + + element_t v0m1, v0m2, v0m3; + element_t v00, v01, v02, v03, v04; + element_t v1m1, v10, v11; + element_t t0, t1, t2; + element_t W20inv; + element_t Wm11inv; + element_t W2m1inv; + element_t sm2, sm1, s0, s1, s2, s3; + element_t pm2, pm1, p0, p1, p2, p3; + + element_init_same_as(sm2, z); + element_init_same_as(sm1, z); + element_init_same_as(s0, z); + element_init_same_as(s1, z); + element_init_same_as(s2, z); + element_init_same_as(s3, z); + + element_init_same_as(pm2, z); + element_init_same_as(pm1, z); + element_init_same_as(p0, z); + element_init_same_as(p1, z); + element_init_same_as(p2, z); + element_init_same_as(p3, z); + + element_init_same_as(v0m3, z); + element_init_same_as(v0m2, z); + element_init_same_as(v0m1, z); + element_init_same_as(v00, z); + element_init_same_as(v01, z); + element_init_same_as(v02, z); + element_init_same_as(v03, z); + element_init_same_as(v04, z); + + element_init_same_as(v1m1, z); + element_init_same_as(v10, z); + element_init_same_as(v11, z); + + element_init_same_as(W20inv, z); + element_init_same_as(Wm11inv, z); + element_init_same_as(W2m1inv, z); + + element_init_same_as(t0, z); + element_init_same_as(t1, z); + element_init_same_as(t2, z); + + element_set0(v0m1); + element_set1(v00); + element_neg(v0m2, v00); + element_double(v01, y); + + element_neg(v0m3, v01); + + element_invert(W20inv, v01); + + element_sub(Wm11inv, x, x2); + element_square(t1, Wm11inv); + element_invert(Wm11inv, Wm11inv); + element_double(t0, x); + element_add(t0, t0, x2); + element_mul(t1, t0, t1); + element_add(t0, y, y2); + element_square(t0, t0); + element_sub(t0, t0, t1); + element_invert(W2m1inv, t0); + + /* Let P=(x,y) since A=1, B=0 we have: + * W(3,0) = 3x^4 + 6x^2 - 1 + * W(4,0) = 4y(x^6 + 5x^4 - 5x^2 - 1) + */ + + //t0 = x^2 + element_square(t0, x); + + //t1 = x^4 + element_square(t1, t0); + + //t2 = x^4 + 2 x^2 + element_double(t2, t0); + element_add(t2, t2, t1); + + //v02 = W(3,0) + element_double(v02, t2); + element_add(v02, v02, t2); + element_add(v02, v02, v0m2); + + //t2 = x^4 - x^2 + element_sub(t2, t1, t0); + + //v03 = 5(x^4 - x^2) + element_double(v03, t2); + element_double(v03, v03); + element_add(v03, v03, t2); + + //t2 = x^6 + element_mul(t2, t0, t1); + + //v03 = W(4,0) + element_add(v03, v03, t2); + element_add(v03, v03, v0m2); + element_double(v03, v03); + element_double(v03, v03); + element_mul(v03, v03, y); + + //v04 = W(5,0) = W(2,0)^3 W(4,0) - W(3,0)^3 + element_square(t0, v01); + element_mul(t0, t0, v01); + element_mul(v04, t0, v03); + element_square(t0, v02); + element_mul(t0, t0, v02); + element_sub(v04, v04, t0); + + element_set1(v1m1); + element_set1(v10); + + element_printf("x y: %B %B\n", x, y); + element_printf("x2 y2: %B %B\n", x2, y2); + element_sub(t0, x2, x); + element_sub(t1, y2, y); + element_div(t0, t1, t0); + element_square(t0, t0); + element_double(v11, x); + element_add(v11, v11, x2); + element_sub(v11, v11, t0); + + element_printf("VEC1: %B %B %B\n", v1m1, v10, v11); + element_printf("VEC0: %B %B %B %B %B %B %B %B\n", + v0m3, v0m2, v0m1, v00, v01, v02, v03, v04); + + //Double + element_square(sm2, v0m2); + element_square(sm1, v0m1); + element_square(s0, v00); + element_square(s1, v01); + element_square(s2, v02); + element_square(s3, v03); + + element_mul(pm2, v0m3, v0m1); + element_mul(pm1, v0m2, v00); + element_mul(p0, v0m1, v01); + element_mul(p1, v00, v02); + element_mul(p2, v01, v03); + element_mul(p3, v02, v04); + + element_mul(t0, pm1, sm2); + element_mul(t1, pm2, sm1); + element_sub(v0m3, t0, t1); + + element_mul(t1, pm2, s0); + element_mul(t0, p0, sm2); + element_sub(v0m2, t0, t1); + element_mul(v0m2, v0m2, W20inv); + + element_mul(t0, p0, sm1); + element_mul(t1, pm1, s0); + element_sub(v0m1, t0, t1); + + element_mul(t1, pm1, s1); + element_mul(t0, p1, sm1); + element_sub(v00, t0, t1); + element_mul(v00, v00, W20inv); + + element_mul(t0, p1, s0); + element_mul(t1, p0, s1); + element_sub(v01, t0, t1); + + element_mul(t1, p0, s2); + element_mul(t0, p2, s0); + element_sub(v02, t0, t1); + element_mul(v02, v02, W20inv); + + element_mul(t0, p2, s1); + element_mul(t1, p1, s2); + element_sub(v03, t0, t1); + + element_mul(t1, p1, s3); + element_mul(t0, p3, s1); + element_sub(v04, t0, t1); + element_mul(v04, v04, W20inv); + + element_square(t0, v10); + element_mul(t1, v1m1, v11); + + element_mul(t2, pm1, t0); + element_mul(v1m1, t1, sm1); + element_sub(v1m1, v1m1, t2); + + element_mul(t2, p0, t0); + element_mul(v10, t1, s0); + element_sub(v10, v10, t2); + + element_mul(t2, p1, t0); + element_mul(v11, t1, s1); + element_sub(v11, v11, t2); + element_mul(v11, v11, Wm11inv); + + element_printf("VEC1: %B %B %B\n", v1m1, v10, v11); + element_printf("VEC0: %B %B %B %B %B %B %B %B\n", + v0m3, v0m2, v0m1, v00, v01, v02, v03, v04); + + //DoubleAdd + element_square(sm2, v0m2); + element_square(sm1, v0m1); + element_square(s0, v00); + element_square(s1, v01); + element_square(s2, v02); + element_square(s3, v03); + + element_mul(pm2, v0m3, v0m1); + element_mul(pm1, v0m2, v00); + element_mul(p0, v0m1, v01); + element_mul(p1, v00, v02); + element_mul(p2, v01, v03); + element_mul(p3, v02, v04); + + element_mul(t1, pm2, s0); + element_mul(t0, p0, sm2); + element_sub(v0m3, t0, t1); + element_mul(v0m3, v0m3, W20inv); + + element_mul(t0, p0, sm1); + element_mul(t1, pm1, s0); + element_sub(v0m2, t0, t1); + + element_mul(t1, pm1, s1); + element_mul(t0, p1, sm1); + element_sub(v0m1, t0, t1); + element_mul(v0m1, v0m1, W20inv); + + element_mul(t0, p1, s0); + element_mul(t1, p0, s1); + element_sub(v00, t0, t1); + + element_mul(t1, p0, s2); + element_mul(t0, p2, s0); + element_sub(v01, t0, t1); + element_mul(v01, v01, W20inv); + + element_mul(t0, p2, s1); + element_mul(t1, p1, s2); + element_sub(v02, t0, t1); + + element_mul(t1, p1, s3); + element_mul(t0, p3, s1); + element_sub(v03, t0, t1); + element_mul(v03, v03, W20inv); + + element_mul(t0, p3, s2); + element_mul(t1, p2, s3); + element_sub(v04, t0, t1); + + element_square(t0, v10); + element_mul(t1, v1m1, v11); + + element_mul(t2, p0, t0); + element_mul(v1m1, t1, s0); + element_sub(v1m1, v1m1, t2); + + element_mul(t2, p1, t0); + element_mul(v10, t1, s1); + element_sub(v10, v10, t2); + element_mul(v10, v10, Wm11inv); + + element_mul(t2, t1, s2); + element_mul(v11, p2, t0); + element_sub(v11, v11, t2); + element_mul(v11, v11, W2m1inv); + + element_printf("VEC1: %B %B %B\n", v1m1, v10, v11); + element_printf("VEC0: %B %B %B %B %B %B %B %B\n", + v0m3, v0m2, v0m1, v00, v01, v02, v03, v04); + element_div(z, v11, v01); + element_printf("prepow: %B\n", z); + + element_pow_mpz(z, z, q1r); + + mpz_clear(q1r); +} + +void miller(element_t z, element_t PR, element_t R, element_t P, element_t Q) +{ + int m = mpz_sizeinbase(order, 2) - 2; + + element_t Z; + element_t z1; + element_t x1; + element_init_same_as(Z, PR); + + element_set(Z, P); + element_set1(z); + element_init_same_as(z1, z); + element_init_same_as(x1, z); + + do_vert(x1, PR, Q); + element_printf("vert(P+R) %B\n", x1); + do_line(z1, P, R, Q); + element_printf("line(P,R) %B\n", z1); + element_div(x1, x1, z1); + element_printf("x1 %B\n", x1); + element_set(z, x1); + + for (;;) { + printf("iteration %d: %d\n", m, mpz_tstbit(order,m)); + element_square(z, z); + element_printf("squared: %B\n", z); + do_tangent(z1, Z, Q); + element_mul(z, z, z1); + + element_double(Z, Z); + do_vert(z1, Z, Q); + element_div(z, z, z1); + element_printf("pre-if: %B\n", z); + + if (mpz_tstbit(order, m)) { + element_mul(z, z, x1); + do_vert(z1, P, Q); + element_mul(z, z, z1); + element_printf("done %B\n", z); + /* + do_line(z1, Z, P, Q); + element_mul(z, z, z1); + element_add(Z, Z, P); + do_vert(z1, Z, Q); + element_div(z, z, z1); + */ + } + if (!m) break; + m--; + } + + element_clear(x1); + element_clear(z1); +} +/* +*/ + +void weil(element_t w, element_t g, element_t h) +{ + element_t gr; + element_t hs; + element_t r; + element_t s; + element_t z, z0, z1; + + element_init(z, Fq2); + element_init(z0, Fq2); + element_init(z1, Fq2); + + element_init_same_as(gr, g); + element_init_same_as(hs, h); + element_init_same_as(r, g); + element_init_same_as(s, h); + + element_random(r); + element_random(s); + //point_random always takes the same square root + //why not take the other one for once? + element_neg(r, r); + element_set_str(r, "[[40,0],[54,0]]", 0); + element_set_str(s, "[[48,55],[28,51]]", 0); + + element_printf("chose R = %B\n", r); + element_printf("chose S = %B\n", s); + element_add(gr, g, r); + element_add(hs, h, s); + + element_printf("P+R = %B\n", gr); + element_printf("Q+S = %B\n", hs); + miller(z, gr, r, g, hs); + miller(z0, gr, r, g, s); + element_div(z1, z, z0); + element_printf("num: %B\n", z1); + + miller(z, hs, s, h, gr); + miller(z0, hs, s, h, r); + element_div(w, z, z0); + element_printf("denom: %B\n", w); + + element_div(w, z1, w); + + element_clear(gr); + element_clear(r); + element_clear(hs); + element_clear(s); + element_clear(z); + element_clear(z0); + element_clear(z1); +} + +void fasterweil(element_t w, element_t g, element_t h) +{ + element_t hs; + element_t s; + element_t z, z0, z1; + + element_init(z, Fq2); + element_init(z0, Fq2); + element_init(z1, Fq2); + + element_init_same_as(hs, h); + element_init_same_as(s, h); + + element_random(s); + //point_random always takes the same square root + //why not take the other one for once? + element_set_str(s, "[[48,55],[28,51]]", 0); + + element_printf("chose S = %B\n", s); + element_add(hs, h, s); + + element_printf("Q+S = %B\n", hs); + + millertate(z, g, hs); + millertate(z0, g, s); + element_div(z1, z, z0); + element_printf("num: %B\n", z1); + + miller(w, hs, s, h, g); + element_printf("denom: %B\n", w); + + element_div(w, z1, w); + + element_clear(z); + element_clear(z0); + element_clear(z1); + element_clear(hs); + element_clear(s); +} + +void fasterweil2(element_t w, element_t g, element_t h) +{ + element_t gr; + element_t r; + element_t z, z0, z1; + + element_init(z, Fq2); + element_init(z0, Fq2); + element_init(z1, Fq2); + + element_init_same_as(gr, g); + element_init_same_as(r, g); + + element_random(r); + //point_random always takes the same square root + //why not take the other one for once? + element_set_str(r, "[[48,55],[28,51]]", 0); + + element_printf("chose R = %B\n", r); + element_add(gr, g, r); + + element_printf("P+R = %B\n", gr); + + miller(w, gr, r, g, h); + element_printf("num: %B\n", w); + + millertate(z, h, gr); + millertate(z0, h, r); + element_div(z1, z, z0); + element_printf("denom: %B\n", z1); + + element_div(w, w, z1); + + element_clear(z); + element_clear(z0); + element_clear(z1); + element_clear(gr); + element_clear(r); +} + +int main(void) +{ + int i; + element_t g, h; + element_t w0, w1; + element_t a, b; + mpz_t prime, cofac; + + mpz_init(prime); + mpz_init(order); + mpz_init(cofac); + mpz_set_ui(prime, 59); + + field_init_fp(Fq, prime); + + element_init(a, Fq); + element_init(b, Fq); + + field_init_fi(Fq2, Fq); + + element_set1(a); + element_set0(b); + mpz_set_ui(order, 5); + mpz_set_ui(cofac, 12); + + field_init_curve_ab(E, a, b, order, cofac); + + element_clear(a); + element_clear(b); + element_init(a, Fq2); + element_init(b, Fq2); + element_set1(a); + element_set0(b); + + mpz_mul(cofac, cofac, cofac); + field_init_curve_ab(E2, a, b, order, NULL); + + element_init(g, E2); + element_init(h, E2); + + element_init(w0, Fq2); + element_init(w1, Fq2); + + /* + do { + element_random(g); + } while (element_is1(g)); + for (i=1; i<5; i++) { + element_mul(h, h, g); + element_printf("%d: %B\n", i, h); + element_printf("tangent = "); + do_tangent(h); + } + */ + element_set_str(g, "[[25,0],[30,0]", 0); + element_set_str(h, "[[34,0],[0,30]", 0); + weil(w0, g, h); + element_printf("weil: %B\n", w0); + + element_set1(w1); + for (i=1; i<6; i++) { + element_mul(w1, w1, w0); + element_printf("%d: %B\n", i, w1); + } + + fasterweil(w0, g, h); + element_printf("fasterweil: %B\n", w0); + + element_set1(w1); + for (i=1; i<6; i++) { + element_mul(w1, w1, w0); + element_printf("%d: %B\n", i, w1); + } + + fasterweil2(w0, g, h); + element_printf("fasterweil2: %B\n", w0); + + tate(w0, g, h); + element_printf("tate: %B\n", w0); + + element_set1(w1); + for (i=1; i<6; i++) { + element_mul(w1, w1, w0); + element_printf("%d: %B\n", i, w1); + } + + shipseystange(w0, g, h); + element_printf("ss-tate: %B\n", w0); + + element_set1(w1); + for (i=1; i<6; i++) { + element_mul(w1, w1, w0); + element_printf("%d: %B\n", i, w1); + } + return 0; +} |