aboutsummaryrefslogtreecommitdiffstats
path: root/moon-abe/pbc-0.5.14/ecc/eta_T_3.c
diff options
context:
space:
mode:
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.c835
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(&param->m, tab, "m");
- err += lookup_int(&param->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");
-}
-