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Diffstat (limited to 'moon-abe/pbc-0.5.14/ecc/eta_T_3.c')
-rw-r--r-- | moon-abe/pbc-0.5.14/ecc/eta_T_3.c | 835 |
1 files changed, 0 insertions, 835 deletions
diff --git a/moon-abe/pbc-0.5.14/ecc/eta_T_3.c b/moon-abe/pbc-0.5.14/ecc/eta_T_3.c deleted file mode 100644 index 44396b76..00000000 --- a/moon-abe/pbc-0.5.14/ecc/eta_T_3.c +++ /dev/null @@ -1,835 +0,0 @@ -#include <stdarg.h> -#include <stdio.h> -#include <stdint.h> -#include <gmp.h> -#include "pbc_utils.h" -#include "pbc_field.h" -#include "pbc_fp.h" -#include "pbc_memory.h" -#include "pbc_param.h" -#include "pbc_pairing.h" -#include "pbc_ternary_extension_field.h" -#include "param.h" - -typedef struct { /* private data of $GF(3^m)$ */ - unsigned int len; /* the number of native machine integers required to represent one GF(3^m) element */ - int m; /* the irreducible polynomial is $x^m + x^t + 2$ */ - int t; /* the irreducible polynomial is $x^m + x^t + 2$ */ - element_ptr p; /* $p$ is the irreducible polynomial. */ - mpz_t n; /* group order of $G_1$, $G_2$, $G_T$ */ - mpz_t n2; /* order(elliptic curve points) / order(G_1) */ -} params; - -struct pairing_data { - field_t gf3m, gf32m, gf36m; - mpz_t n2; // cofactor -}; -typedef struct pairing_data *pairing_data_ptr; - -#define PARAM(e) ((params *)e->field->data) -#define ITEM(e,x,y) (element_item(element_item(e,x),y)) -#define print(e) {printf(#e": "); element_out_str(stdout, 10, e); printf("\n");} - -struct point_s { // points on the elliptic curve $y^2=x^3-x+1$ - int isinf; - element_t x, y; -}; -typedef struct point_s *point_ptr; -typedef struct point_s point_t[1]; - -#define FIELD(e) ((field_ptr) e->field) -#define BASE(e) ((field_ptr) FIELD(e)->data) -#define DATA(e) ((point_ptr) e->data) - -static void point_set(element_t e, element_t a) { - point_ptr r = DATA(e), p = DATA(a); - r->isinf = p->isinf; - if (!p->isinf) { - element_set(r->x, p->x); - element_set(r->y, p->y); - } -} - -static void point_init(element_t e) { - field_ptr f = BASE(e); - e->data = pbc_malloc(sizeof(struct point_s)); - point_ptr p = DATA(e); - element_init(p->x, f); - element_init(p->y, f); - p->isinf = 1; -} - -static void point_clear(element_t e) { - point_ptr p = DATA(e); - element_clear(p->x); - element_clear(p->y); - pbc_free(p); -} - -/* return 1 if $a!=b$, 0 otherwise. */ -static int point_cmp(element_t a, element_t b) { - point_ptr pa = DATA(a), pb = DATA(b); - if (pa->isinf == pb->isinf) { - if (pa->isinf) - return 0; - else - return element_cmp(pa->x, pb->x) || element_cmp(pa->y, pb->y); - } else - return 1; -} - -static void point_set0(element_ptr e) { - DATA(e)->isinf = 1; -} - -static int point_is0(element_ptr e) { - return DATA(e)->isinf; -} - -static void point_random(element_t a) { - point_ptr p = DATA(a); - element_ptr x = p->x, y = p->y; - field_ptr f = x->field; - p->isinf = 0; - element_t t, t2, e1; - element_init(t, f); - element_init(e1, f); - element_set1(e1); - element_init(t2, f); - do { - element_random(x); - if (element_is0(x)) - continue; - element_cubic(t, x); // t == x^3 - element_sub(t, t, x); // t == x^3 - x - element_add(t, t, e1); // t == x^3 - x + 1 - element_sqrt(y, t); // y == sqrt(x^3 - x + 1) - element_mul(t2, y, y); // t2 == x^3 - x + 1 - } while (element_cmp(t2, t)); // t2 != t - - // make sure order of $a$ is order of $G_1$ - pairing_ptr pairing = FIELD(a)->pairing; - pairing_data_ptr dp = pairing->data; - element_pow_mpz(a, a, dp->n2); - - element_clear(t); - element_clear(t2); - element_clear(e1); -} - -static void point_add(element_t c, element_t a, element_t b) { - point_ptr p1 = DATA(a), p2 = DATA(b), p3 = DATA(c); - int inf1 = p1->isinf, inf2 = p2->isinf; - element_ptr x1 = p1->x, y1 = p1->y, x2 = p2->x, y2 = p2->y; - field_ptr f = FIELD(x1); - if (inf1) { - point_set(c, b); - return; - } - if (inf2) { - point_set(c, a); - return; - } - element_t v0, v1, v2, v3, v4, ny2; - element_init(v0, f); - element_init(v1, f); - element_init(v2, f); - element_init(v3, f); - element_init(v4, f); - element_init(ny2, f); - if (!element_cmp(x1, x2)) { // x1 == x2 - element_neg(ny2, y2); // ny2 == -y2 - if (!element_cmp(y1, ny2)) { - p3->isinf = 1; - goto end; - } - if (!element_cmp(y1, y2)) { // y1 == y2 - element_invert(v0, y1); // v0 == y1^{-1} - element_mul(v1, v0, v0); // v1 == [y1^{-1}]^2 - element_add(p3->x, v1, x1); // v1 == [y1^{-1}]^2 + x1 - element_cubic(v2, v0); // v2 == [y1^{-1}]^3 - element_add(v2, v2, y1); // v2 == [y1^{-1}]^3 + y1 - element_neg(p3->y, v2); // p3 == -([y1^{-1}]^3 + y1) - p3->isinf = 0; - goto end; - } - } - // $P1 \ne \pm P2$ - element_sub(v0, x2, x1); // v0 == x2-x1 - element_invert(v1, v0); // v1 == (x2-x1)^{-1} - element_sub(v0, y2, y1); // v0 == y2-y1 - element_mul(v2, v0, v1); // v2 == (y2-y1)/(x2-x1) - element_mul(v3, v2, v2); // v3 == [(y2-y1)/(x2-x1)]^2 - element_cubic(v4, v2); // v4 == [(y2-y1)/(x2-x1)]^3 - element_add(v0, x1, x2); // v0 == x1+x2 - element_sub(v3, v3, v0); // v3 == [(y2-y1)/(x2-x1)]^2 - (x1+x2) - element_add(v0, y1, y2); // v0 == y1+y2 - element_sub(v4, v0, v4); // v4 == (y1+y2) - [(y2-y1)/(x2-x1)]^3 - p3->isinf = 0; - element_set(p3->x, v3); - element_set(p3->y, v4); - end: element_clear(v0); - element_clear(v1); - element_clear(v2); - element_clear(v3); - element_clear(v4); - element_clear(ny2); -} - -static void point_invert(element_ptr e, element_ptr a) { - point_ptr r = DATA(e), p = DATA(a); - r->isinf = p->isinf; - if (!p->isinf) { - element_set(r->x, p->x); - element_neg(r->y, p->y); - } -} - -static size_t point_out_str(FILE *stream, int base, element_ptr a) { - point_ptr p = DATA(a); - size_t size = 0; - if (p->isinf) - return fprintf(stream, "O"); - else { - size += element_out_str(stream, base, p->x); - size += element_out_str(stream, base, p->y); - return size; - } -} - -static void point_field_clear(field_ptr f) { - UNUSED_VAR(f); -} - -void field_init_eta_T_3(field_t f, field_t base) { - field_init(f); - f->data = (void *) base; - f->init = point_init; - f->clear = point_clear; - f->random = point_random; - f->set = point_set; - f->cmp = point_cmp; - f->invert = f->neg = point_invert; - f->mul = f->add = point_add; - f->set1 = f->set0 = point_set0; - f->is1 = f->is0 = point_is0; - f->mul_mpz = f->pow_mpz; - f->out_str = point_out_str; - f->field_clear = point_field_clear; - f->name = "eta_T_3 point group"; -} - -/* computing of $(-t^2 +u*s -t*p -p^2)^3$ - * The algorithm is by J.Beuchat et.al, in the paper of "Algorithms and Arithmetic Operators for Computing - * the $eta_T$ Pairing in Characteristic Three", algorithm 4 in the appendix */ -static void algorithm4a(element_t S, element_t t, element_t u) { - field_ptr f = FIELD(t); - element_t e1, c0, c1, m0, v0, v2; - element_init(e1, f); - element_init(c0, f); - element_init(c1, f); - element_init(m0, f); - element_init(v0, f); - element_init(v2, f); - element_set1(e1); - element_cubic(c0, t); // c0 == t^3 - element_cubic(c1, u); - element_neg(c1, c1); // c1 == -u^3 - element_mul(m0, c0, c0); // m0 == c0^2 - element_neg(v0, m0); // v0 == -c0^2 - element_sub(v0, v0, c0); // v0 == -c0^2 -c0 - element_sub(v0, v0, e1); // v0 == -c0^2 -c0 -1 - element_set1(v2); - element_sub(v2, v2, c0); // v2 == 1 -c0 - // v1 == c1 - // S == [[v0, v1], [v2, f3m.zero()], [f3m.two(), f3m.zero()]] - element_set(ITEM(S,0,0), v0); - element_set(ITEM(S,0,1), c1); - element_set(ITEM(S,1,0), v2); - element_set0(ITEM(S,1,1)); - element_neg(ITEM(S,2,0), e1); - element_set0(ITEM(S,2,1)); - element_clear(e1); - element_clear(c0); - element_clear(c1); - element_clear(m0); - element_clear(v0); - element_clear(v2); -} - -static void algorithm5(element_t c, element_ptr xp, element_ptr yp, - element_ptr xq, element_ptr yq) { - params *p = PARAM(xp); - unsigned int re = p->m % 12; - field_ptr f = FIELD(xp) /*GF(3^m)*/, f6 = FIELD(c) /*GF(3^{6*m})*/; - element_t e1, xpp, ypp, xqq, yqq, t, nt, nt2, v1, v2, a1, a2, R, u, nu, S, S2; - element_init(e1, f); - element_init(xpp, f); - element_init(ypp, f); - element_init(xqq, f); - element_init(yqq, f); - element_init(t, f); - element_init(nt, f); - element_init(nt2, f); - element_init(v1, f); - element_init(v2, f); - element_init(a1, f6); - element_init(a2, f6); - element_init(R, f6); - element_init(u, f); - element_init(nu, f); - element_init(S, f6); - element_init(S2, f6); - element_set1(e1); - element_set(xpp, xp); - xp = xpp; // clone - element_add(xp, xp, e1); // xp == xp + b - element_set(ypp, yp); - yp = ypp; // clone - if (re == 1 || re == 11) - element_neg(yp, yp); // yp == -\mu*b*yp, \mu == 1 when re==1, or 11 - element_set(xqq, xq); - xq = xqq; // clone - element_cubic(xq, xq); // xq == xq^3 - element_set(yqq, yq); - yq = yqq; // clone - element_cubic(yq, yq); // yq == yq^3 - element_add(t, xp, xq); // t == xp+xq - element_neg(nt, t); // nt == -t - element_mul(nt2, t, nt); // nt2 == -t^2 - element_mul(v2, yp, yq); // v2 == yp*yq - element_mul(v1, yp, t); // v1 == yp*t - if (re == 7 || re == 11) { // \lambda == 1 - element_t nyp, nyq; - element_init(nyp, f); - element_init(nyq, f); - element_neg(nyp, yp); // nyp == -yp - element_neg(nyq, yq); // nyq == -yq - element_set(ITEM(a1,0,0), v1); - element_set(ITEM(a1,0,1), nyq); - element_set(ITEM(a1,1,0), nyp); - element_clear(nyp); - element_clear(nyq); - } else { // \lambda == -1 - element_neg(v1, v1); // v1 == -yp*t - element_set(ITEM(a1,0,0), v1); - element_set(ITEM(a1,0,1), yq); - element_set(ITEM(a1,1,0), yp); - } - // a2 == -t^2 +yp*yq*s -t*p -p^2 - element_set(ITEM(a2,0,0), nt2); - element_set(ITEM(a2,0,1), v2); - element_set(ITEM(a2,1,0), nt); - element_neg(ITEM(a2,2,0), e1); - element_mul(R, a1, a2); - int i; - for (i = 0; i < (p->m - 1) / 4; i++) { - element_cubic(R, R); - element_cubic(R, R); // R <= R^9 - element_cubic(xq, xq); - element_cubic(xq, xq); - element_sub(xq, xq, e1); // xq <= xq^9-b - element_cubic(yq, yq); - element_cubic(yq, yq); // yq <= yq^9 - element_add(t, xp, xq); // t == xp+xq - element_mul(u, yp, yq); // u == yp*yq - element_neg(nu, u); // nu == -yp*yq - algorithm4a(S, t, nu); // S == (-t^2 -u*s -t*p -p^2)^3 - element_cubic(xq, xq); - element_cubic(xq, xq); - element_sub(xq, xq, e1); // xq <= xq^9-b - element_cubic(yq, yq); - element_cubic(yq, yq); // yq <= yq^9 - element_add(t, xp, xq); // t == xp+xq - element_mul(u, yp, yq); // u == yp*yq - element_neg(nt, t); // nt == -t - element_mul(nt2, t, nt); // nt2 == -t^2 - // S2 = [[nt2, u], [nt, f3m.zero()], [f3m.two(), f3m.zero()]] - // S2 == -t^2 +u*s -t*p -p^2 - element_set(ITEM(S2,0,0), nt2); - element_set(ITEM(S2,0,1), u); - element_set(ITEM(S2,1,0), nt); - element_set0(ITEM(S2,1,1)); - element_neg(ITEM(S2,2,0), e1); - element_set0(ITEM(S2,2,1)); - element_mul(S, S, S2); - element_mul(R, R, S); - } - element_set(c, R); - element_clear(e1); - element_clear(xpp); - element_clear(ypp); - element_clear(xqq); - element_clear(yqq); - element_clear(t); - element_clear(nt); - element_clear(nt2); - element_clear(v1); - element_clear(v2); - element_clear(a1); - element_clear(a2); - element_clear(R); - element_clear(u); - element_clear(nu); - element_clear(S); - element_clear(S2); -} - -/* this is the algorithm 4 in the paper of J.Beuchat et.al, "Algorithms and Arithmetic Operators for Computing - * the $eta_T$ Pairing in Characteristic Three" */ -static void algorithm4(element_t c, element_ptr xp, element_ptr yp, - element_ptr xq, element_ptr yq) { - params *p = PARAM(xp); - unsigned int re = p->m % 12; - field_ptr f = FIELD(xp) /*GF(3^m)*/, f6 = FIELD(c) /*GF(3^{6*m})*/; - element_t e1, xpp, ypp, xqq, yqq, t, nt, nt2, v1, v2, a1, a2, R, u, S; - element_init(e1, f); - element_init(xpp, f); - element_init(ypp, f); - element_init(xqq, f); - element_init(yqq, f); - element_init(t, f); - element_init(nt, f); - element_init(nt2, f); - element_init(v1, f); - element_init(v2, f); - element_init(a1, f6); - element_init(a2, f6); - element_init(R, f6); - element_init(u, f); - element_init(S, f6); - element_set1(e1); - element_set(xpp, xp); - xp = xpp; // clone - element_add(xp, xp, e1); // xp == xp + b - element_set(ypp, yp); - yp = ypp; // clone - if (re == 1 || re == 11) - element_neg(yp, yp); // yp == -\mu*b*yp, \mu == 1 when re==1, or 11 - element_set(xqq, xq); - xq = xqq; // clone - element_cubic(xq, xq); // xq == xq^3 - element_set(yqq, yq); - yq = yqq; // clone - element_cubic(yq, yq); // yq == yq^3 - element_add(t, xp, xq); // t == xp+xq - element_neg(nt, t); // nt == -t - element_mul(nt2, t, nt); // nt2 == -t^2 - element_mul(v2, yp, yq); // v2 == yp*yq - element_mul(v1, yp, t); // v1 == yp*t - if (re == 7 || re == 11) { // \lambda == 1 - element_t nyp, nyq; - element_init(nyp, f); - element_init(nyq, f); - element_neg(nyp, yp); // nyp == -yp - element_neg(nyq, yq); // nyq == -yq - element_set(ITEM(a1,0,0), v1); - element_set(ITEM(a1,0,1), nyq); - element_set(ITEM(a1,1,0), nyp); - element_clear(nyp); - element_clear(nyq); - } else { // \lambda == -1 - element_neg(v1, v1); // v1 == -yp*t - element_set(ITEM(a1,0,0), v1); - element_set(ITEM(a1,0,1), yq); - element_set(ITEM(a1,1,0), yp); - } - // a2 == -t^2 +yp*yq*s -t*p -p^2 - element_set(ITEM(a2,0,0), nt2); - element_set(ITEM(a2,0,1), v2); - element_set(ITEM(a2,1,0), nt); - element_neg(ITEM(a2,2,0), e1); - element_mul(R, a1, a2); - int i; - for (i = 0; i < (p->m - 1) / 2; i++) { - element_cubic(R, R); - element_cubic(xq, xq); - element_cubic(xq, xq); - element_sub(xq, xq, e1); // xq <= xq^9-b - element_cubic(yq, yq); - element_cubic(yq, yq); - element_neg(yq, yq); // yq <= -yq^9 - element_add(t, xp, xq); // t == xp+xq - element_neg(nt, t); // nt == -t - element_mul(nt2, t, nt); // nt2 == -t^2 - element_mul(u, yp, yq); // u == yp*yq - element_set0(S); - element_set(ITEM(S,0,0), nt2); - element_set(ITEM(S,0,1), u); - element_set(ITEM(S,1,0), nt); - element_neg(ITEM(S,2,0), e1); - element_mul(R, R, S); - } - element_set(c, R); - element_clear(e1); - element_clear(xpp); - element_clear(ypp); - element_clear(xqq); - element_clear(yqq); - element_clear(t); - element_clear(nt); - element_clear(nt2); - element_clear(v1); - element_clear(v2); - element_clear(a1); - element_clear(a2); - element_clear(R); - element_clear(u); - element_clear(S); -} - -/* computation of $c <- U ^ {3^{3m} - 1}$ - * This is the algorithm 6 in the paper above. */ -static void algorithm6(element_t c, element_t u) { - element_ptr u0 = ITEM(u,0,0), u1 = ITEM(u,0,1), u2 = ITEM(u,1,0), u3 = - ITEM(u,1,1), u4 = ITEM(u,2,0), u5 = ITEM(u,2,1); - field_ptr f = FIELD(u0); /*GF(3^m)*/ - field_t f3; /*GF(3^{3*m})*/ - field_init_gf33m(f3, f); - element_t v0, v1, m0, m1, m2, a0, a1, i; - element_init(v0, f3); - element_init(v1, f3); - element_init(m0, f3); - element_init(m1, f3); - element_init(m2, f3); - element_init(a0, f3); - element_init(a1, f3); - element_init(i, f3); - element_set(element_item(v0, 0), u0); - element_set(element_item(v0, 1), u2); - element_set(element_item(v0, 2), u4); - element_set(element_item(v1, 0), u1); - element_set(element_item(v1, 1), u3); - element_set(element_item(v1, 2), u5); - element_mul(m0, v0, v0); - element_mul(m1, v1, v1); - element_mul(m2, v0, v1); - element_sub(a0, m0, m1); - element_add(a1, m0, m1); - element_invert(i, a1); - element_mul(v0, a0, i); - element_mul(v1, m2, i); - element_set(ITEM(c,0,0), element_item(v0, 0)); - element_set(ITEM(c,1,0), element_item(v0, 1)); - element_set(ITEM(c,2,0), element_item(v0, 2)); - element_set(ITEM(c,0,1), element_item(v1, 0)); - element_set(ITEM(c,1,1), element_item(v1, 1)); - element_set(ITEM(c,2,1), element_item(v1, 2)); - element_clear(v0); - element_clear(v1); - element_clear(m0); - element_clear(m1); - element_clear(m2); - element_clear(a0); - element_clear(a1); - element_clear(i); - field_clear(f3); -} - -/* computation of $c <- U ^ {3^m+1}$, $U \in T_2(F_{3^3M})$ - * This is the algorithm 7 in the paper above. */ -static void algorithm7(element_t c, element_t u) { - element_ptr u0 = ITEM(u,0,0), u1 = ITEM(u,0,1), u2 = ITEM(u,1,0), u3 = - ITEM(u,1,1), u4 = ITEM(u,2,0), u5 = ITEM(u,2,1); - field_ptr f = FIELD(u0); /*GF(3^m)*/ - params *p = PARAM(u0); - element_t a0, a1, a2, a3, a4, a5, a6, m0, m1, m2, m3, m4, m5, m6, m7, m8, - v0, v1, v2, v3, v4, v5, e1; - element_init(a0, f); - element_init(a1, f); - element_init(a2, f); - element_init(a3, f); - element_init(a4, f); - element_init(a5, f); - element_init(a6, f); - element_init(m0, f); - element_init(m1, f); - element_init(m2, f); - element_init(m3, f); - element_init(m4, f); - element_init(m5, f); - element_init(m6, f); - element_init(m7, f); - element_init(m8, f); - element_init(v0, f); - element_init(v1, f); - element_init(v2, f); - element_init(v3, f); - element_init(v4, f); - element_init(v5, f); - element_init(e1, f); - element_set1(e1); - element_add(a0, u0, u1); - element_add(a1, u2, u3); - element_sub(a2, u4, u5); - element_mul(m0, u0, u4); - element_mul(m1, u1, u5); - element_mul(m2, u2, u4); - element_mul(m3, u3, u5); - element_mul(m4, a0, a2); - element_mul(m5, u1, u2); - element_mul(m6, u0, u3); - element_mul(m7, a0, a1); - element_mul(m8, a1, a2); - element_add(a3, m5, m6); - element_sub(a3, a3, m7); - element_neg(a4, m2); - element_sub(a4, a4, m3); - element_sub(a5, m3, m2); - element_sub(a6, m1, m0); - element_add(a6, a6, m4); - if (p->m % 6 == 1) { - element_add(v0, m0, m1); - element_add(v0, v0, a4); - element_add(v0, e1, v0); - element_sub(v1, m5, m6); - element_add(v1, v1, a6); - element_sub(v2, a4, a3); - element_add(v3, m8, a5); - element_sub(v3, v3, a6); - element_add(v4, a3, a4); - element_neg(v4, v4); - element_add(v5, m8, a5); - } else { // p->m % 6 == 5 - element_add(v0, m0, m1); - element_sub(v0, v0, a4); - element_add(v0, e1, v0); - element_sub(v1, m6, m5); - element_add(v1, v1, a6); - element_set(v2, a3); - element_add(v3, m8, a5); - element_add(v3, v3, a6); - element_add(v4, a3, a4); - element_neg(v4, v4); - element_add(v5, m8, a5); - element_neg(v5, v5); - } - element_set(ITEM(c,0,0), v0); - element_set(ITEM(c,0,1), v1); - element_set(ITEM(c,1,0), v2); - element_set(ITEM(c,1,1), v3); - element_set(ITEM(c,2,0), v4); - element_set(ITEM(c,2,1), v5); - element_clear(a0); - element_clear(a1); - element_clear(a2); - element_clear(a3); - element_clear(a4); - element_clear(a5); - element_clear(a6); - element_clear(m0); - element_clear(m1); - element_clear(m2); - element_clear(m3); - element_clear(m4); - element_clear(m5); - element_clear(m6); - element_clear(m7); - element_clear(m8); - element_clear(v0); - element_clear(v1); - element_clear(v2); - element_clear(v3); - element_clear(v4); - element_clear(v5); - element_clear(e1); -} - -/* computing $c <- U^M, M=(3^{3m}-1)*(3^m+1)*(3^m+1-\mu*b*3^{(m+1)//2})$ - * This is the algorithm 8 in the paper above. */ -static void algorithm8(element_t c, element_t u) { - field_ptr f6 = FIELD(u), f = FIELD(ITEM(u,0,0)); - params *p = (params *) f->data; - element_t v, w; - element_init(v, f6); - element_init(w, f6); - algorithm6(v, u); - algorithm7(v, v); - element_set(w, v); - int i; - for (i = 0; i < (p->m + 1) / 2; i++) - element_cubic(w, w); - algorithm7(v, v); - if (p->m % 12 == 1 || p->m % 12 == 11) { // w <= w^{-\mu*b} - element_ptr e; - e = ITEM(w,0,1); - element_neg(e, e); - e = ITEM(w,1,1); - element_neg(e, e); - e = ITEM(w,2,1); - element_neg(e, e); - } - element_mul(c, v, w); - element_clear(v); - element_clear(w); -} - -/* computing the Eta_T bilinear pairing $c <- Eta_T pairing(P,R)$ */ -static void eta_T_pairing(element_ptr c, element_ptr P, element_ptr R, struct pairing_s *p) { - UNUSED_VAR(p); - if (DATA(P)->isinf || DATA(R)->isinf) - element_set1(c); - else { - element_ptr x1 = DATA(P)->x, y1 = DATA(P)->y, x2 = DATA(R)->x, y2 = - DATA(R)->y; - if((PARAM(x1)->m - 1) / 2 % 2 == 0) - algorithm5(c, x1, y1, x2, y2); - else - algorithm4(c, x1, y1, x2, y2); - algorithm8(c, c); - } -} - -static void eta_T_3_clear(params *p) { - mpz_clear(p->n); - mpz_clear(p->n2); - pbc_free(p); -} - -static void GT_random(element_ptr e) { - element_t a, b; - element_init(a, e->field->pairing->G1); - element_init(b, e->field->pairing->G1); - element_random(a); - element_random(b); - element_pairing(e, a, b); - element_clear(a); - element_clear(b); -} - -static void eta_T_3_pairing_clear(pairing_t pairing) { - mpz_clear(pairing->r); - field_clear(pairing->Zr); - field_clear(pairing->GT); - field_clear(pairing->G1); - pbc_free(pairing->G1); - pairing_data_ptr dp = pairing->data; - field_clear(dp->gf3m); - field_clear(dp->gf32m); - field_clear(dp->gf36m); - mpz_clear(dp->n2); - pbc_free(dp); -} - -static void eta_T_3_init_pairing(pairing_t pairing, params *p) { - mpz_init(pairing->r); - mpz_set(pairing->r, p->n); - field_init_fp(pairing->Zr, pairing->r); - - pairing_data_ptr dp = pbc_malloc(sizeof(*dp)); - mpz_init(dp->n2); - mpz_set(dp->n2, p->n2); - field_init_gf3m(dp->gf3m, p->m, p->t); - field_init_gf32m(dp->gf32m, dp->gf3m); - field_init_gf33m(dp->gf36m, dp->gf32m); - pairing_GT_init(pairing, dp->gf36m); - pairing->GT->name = "eta_T_3 group of roots of 1"; - pairing->GT->random = GT_random; - pairing->G2 = pairing->G1 = pbc_malloc(sizeof(field_t)); - field_init_eta_T_3(pairing->G1, dp->gf3m); - pairing->G1->pairing = pairing; - mpz_set(pairing->G1->order, p->n); - mpz_set(pairing->GT->order, p->n); - pairing->map = eta_T_pairing; - pairing->data = dp; - pairing->clear_func = eta_T_3_pairing_clear; -} - -static void eta_T_3_out_str(FILE *stream, params *p) { - param_out_type(stream, "i"); - param_out_int(stream, "m", p->m); - param_out_int(stream, "t", p->t); - param_out_mpz(stream, "n", p->n); - param_out_mpz(stream, "n2", p->n2); -} - -static void param_init(pbc_param_ptr p) { - static pbc_param_interface_t interface = {{ - (void (*)(void *))eta_T_3_clear, - (void (*)(pairing_t, void *))eta_T_3_init_pairing, - (void (*)(FILE *, void *))eta_T_3_out_str, - }}; - p->api = interface; - params *param = p->data = pbc_malloc(sizeof(*param)); - mpz_init(param->n); - mpz_init(param->n2); -} - -int pbc_param_init_i(pbc_param_ptr p, struct symtab_s *tab) { - param_init(p); - params *param = p->data; - int err = 0; - err += lookup_int(¶m->m, tab, "m"); - err += lookup_int(¶m->t, tab, "t"); - err += lookup_mpz(param->n, tab, "n"); - err += lookup_mpz(param->n2, tab, "n2"); - return err; -} - -void pbc_param_init_i_gen(pbc_param_ptr par, int group_size) { - param_init(par); - params *p = par->data; - if (group_size <= 150) { - p->m = 97; - p->t = 12; - mpz_set_str(p->n, "2726865189058261010774960798134976187171462721", 10); - mpz_set_str(p->n2, "7", 10); - } else if (group_size <= 206) { - p->m = 199; - p->t = 164; - mpz_set_str(p->n, "167725321489096000055336949742738378351010268990525380470313869", 10); - mpz_set_str(p->n2, "527874953560391326545598291952743", 10); - } else if (group_size <= 259) { - p->m = 235; - p->t = 26; - mpz_set_str(p->n, "1124316700897695330265827797088699345032488681307846555184025129863722718180241", 10); - mpz_set_str(p->n2, "11819693021332914275777073321995059", 10); - } else if (group_size <= 316) { - p->m = 385; - p->t = 22; - mpz_set_str(p->n, "140884762419712839999909157778648717913595360839856026704744558309545986970238264714753014287541", 10); - mpz_set_str(p->n2, "34899486997246711147841377458771182755186809219564106252058066150110543296498189654810187", 10); - } else if (group_size <= 376) { - p->m = 337; - p->t = 30; - mpz_set_str(p->n, "250796519030408069744426774377542635685621984993105288007781750196791322190409525696108840742205849171229571431053", 10); - mpz_set_str(p->n2, "245777055088325363697128811262733732423405120899", 10); - } else if (group_size <= 430) { - p->m = 373; - p->t = 198; - mpz_set_str(p->n, "2840685307599487500956683789051368080919805957805957356540760731597378326586402072132959867084691357708217739285576524329854284197", 10); - mpz_set_str(p->n2, "3256903458766749542151641063558247849550904613763", 10); - } else if (group_size <= 484) { - p->m = 395; - p->t = 338; - mpz_set_str(p->n, "80172097064154181257340545445945701478615643539554910656655431171167598268341527430200810544156625333601812351266052856520678455274751591367269291", 10); - mpz_set_str(p->n2, "3621365590261279902324876775553649595261567", 10); - } else if (group_size <= 552) { - p->m = 433; - p->t = 120; - mpz_set_str(p->n, "15699907553631673835088720676147779193076555382157913339177784853763686462870506492752576492212322736133645158157557950634628006965882177348385366381692092784577773463", 10); - mpz_set_str(p->n2, "24980791723059119877470531054938874784049", 10); - } else if (group_size <= 644) { - p->m = 467; - p->t = 48; - mpz_set_str(p->n, "108220469499363631995525712756135494735252733492048868417164002000654321383482753640072319529019505742300964525569770933946381504691909098938045089999753901375631613294579329433690943459352138231", 10); - mpz_set_str(p->n2, "60438898450096967424971813347", 10); - } else if (group_size <= 696) { - p->m = 503; - p->t = 104; - mpz_set_str(p->n, "545523657676112447260904563578912738373307867219686215849632469801471112426878939776725222290437653718473962733760874627315930933126581248465899651120481066111839081575164964589811985885719017214938514563804313", 10); - mpz_set_str(p->n2, "1799606423432800810122901025413", 10); - } else if (group_size <= 803) { - p->m = 509; - p->t = 358; - mpz_set_str(p->n, "102239946202586852409809887418093021457150612495255706614733003327526279081563687830782748305746187060264985869283524441819589592750998086186315250781067131293823177124077445718802216415539934838376431091001197641295264650596195201747790167311", 10); - mpz_set_str(p->n2, "7", 10); - } else if (group_size <= 892) { - p->m = 617; - p->t = 88; - mpz_set_str(p->n, "57591959284219511220590893724691916802833742568034971006633345422620650391172287893878655658086794200963521584019889327992536532560877385225451713282279597074750857647455565899702728629166541223955196002755787520206774906606158388947359746178875040401304783332742806641", 10); - mpz_set_str(p->n2, "42019638181715250622338241", 10); - } else - pbc_die("unsupported group size"); -} - |