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Diffstat (limited to 'moon-abe/pbc-0.5.14/ecc/f_param.c')
-rw-r--r--moon-abe/pbc-0.5.14/ecc/f_param.c599
1 files changed, 0 insertions, 599 deletions
diff --git a/moon-abe/pbc-0.5.14/ecc/f_param.c b/moon-abe/pbc-0.5.14/ecc/f_param.c
deleted file mode 100644
index 2477ace1..00000000
--- a/moon-abe/pbc-0.5.14/ecc/f_param.c
+++ /dev/null
@@ -1,599 +0,0 @@
-#include <stdarg.h>
-#include <stdio.h>
-#include <stdint.h> // for intptr_t
-#include <stdlib.h>
-#include <gmp.h>
-#include "pbc_utils.h"
-#include "pbc_field.h"
-#include "pbc_fp.h"
-#include "pbc_fieldquadratic.h"
-#include "pbc_param.h"
-#include "pbc_pairing.h"
-#include "pbc_poly.h"
-#include "pbc_curve.h"
-#include "pbc_memory.h"
-#include "pbc_f_param.h"
-#include "ecc/param.h"
-
-struct f_param_s {
- mpz_t q; // Curve defined over F_q.
- mpz_t r; // The order of the curve.
- mpz_t b; // E: y^2 = x^3 + b
- mpz_t beta; //beta is a quadratic nonresidue in Fq
- //we use F_q^2 = F_q[sqrt(beta)]
- mpz_t alpha0, alpha1;
- //the polynomial x^6 + alpha0 + alpha1 sqrt(beta)
- //is irreducible over F_q^2[x], so
- //we can extend F_q^2 to F_q^12 using the
- //sixth root of -(alpha0 + alpha1 sqrt(beta))
-};
-typedef struct f_param_s f_param_t[1];
-typedef struct f_param_s *f_param_ptr;
-
-// TODO: we never use phikonr so don't bother computing it,
-// but one day other routines might need it
-struct f_pairing_data_s {
- field_t Fq, Fq2, Fq2x, Fq12;
- field_t Eq, Etwist;
- element_t negalpha;
- element_t negalphainv;
- mpz_t tateexp;
-
- //for tate exponentiation speedup:
- //x^{q^k} for various k
- element_t xpowq2, xpowq6, xpowq8;
-};
-typedef struct f_pairing_data_s f_pairing_data_t[1];
-typedef struct f_pairing_data_s *f_pairing_data_ptr;
-
-static void f_clear(void *data) {
- f_param_ptr fp = data;
- mpz_clear(fp->q);
- mpz_clear(fp->r);
- mpz_clear(fp->b);
- mpz_clear(fp->beta);
- mpz_clear(fp->alpha0);
- mpz_clear(fp->alpha1);
- pbc_free(data);
-}
-
-static void f_out_str(FILE *stream, void *data) {
- f_param_ptr p = data;
- param_out_type(stream, "f");
- param_out_mpz(stream, "q", p->q);
- param_out_mpz(stream, "r", p->r);
- param_out_mpz(stream, "b", p->b);
- param_out_mpz(stream, "beta", p->beta);
- param_out_mpz(stream, "alpha0", p->alpha0);
- param_out_mpz(stream, "alpha1", p->alpha1);
-}
-
-static void tryminusx(mpz_ptr q, mpz_ptr x) {
- //36x4 - 36x3 + 24x2 - 6x + 1
- //= ((36(x - 1)x + 24)x - 6)x + 1
- mpz_sub_ui(q, x, 1);
- mpz_mul(q, q, x);
- mpz_mul_ui(q, q, 36);
- mpz_add_ui(q, q, 24);
- mpz_mul(q, q, x);
- mpz_sub_ui(q, q, 6);
- mpz_mul(q, q, x);
- mpz_add_ui(q, q, 1);
-}
-
-static void tryplusx(mpz_ptr q, mpz_ptr x) {
- //36x4 + 36x3 + 24x2 + 6x + 1
- //= ((36(x + 1)x + 24)x + 6)x + 1
- mpz_add_ui(q, x, 1);
- mpz_mul(q, q, x);
- mpz_mul_ui(q, q, 36);
- mpz_add_ui(q, q, 24);
- mpz_mul(q, q, x);
- mpz_add_ui(q, q, 6);
- mpz_mul(q, q, x);
- mpz_add_ui(q, q, 1);
-}
-
-static void cc_miller_no_denom(element_t res, mpz_t q, element_t P,
- element_ptr Qx, element_ptr Qy, element_t negalpha) {
- int m;
- element_t v;
- element_t Z;
- element_t a, b, c;
- element_t t0;
- element_t e0, e1;
- element_ptr Zx, Zy;
- const element_ptr Px = curve_x_coord(P);
- const element_ptr Py = curve_y_coord(P);
-
- #define do_term(i, j, k, flag) { \
- element_ptr e2; \
- e2 = element_item(e0, i); \
- element_mul(e1, element_item(v, j), Qx); \
- if (flag == 1) element_mul(e1, e1, negalpha); \
- element_mul(element_x(e1), element_x(e1), a); \
- element_mul(element_y(e1), element_y(e1), a); \
- element_mul(e2, element_item(v, k), Qy); \
- element_mul(element_x(e2), element_x(e2), b); \
- element_mul(element_y(e2), element_y(e2), b); \
- element_add(e2, e2, e1); \
- if (flag == 2) element_mul(e2, e2, negalpha); \
- element_mul(element_x(e1), element_x(element_item(v, i)), c); \
- element_mul(element_y(e1), element_y(element_item(v, i)), c); \
- element_add(e2, e2, e1); \
- }
-
- // a, b, c lie in Fq
- // Qx, Qy lie in Fq^2
- // Qx is coefficient of x^4
- // Qy is coefficient of x^3
- //
- // computes v *= (a Qx x^4 + b Qy x^3 + c)
- //
- // recall x^6 = -alpha thus
- // x^4 (u0 + u1 x^1 + ... + u5 x^5) =
- // u0 x^4 + u1 x^5
- // - alpha u2 - alpha u3 x - alpha u4 x^2 - alpha u5 x^3
- // and
- // x^4 (u0 + u1 x^1 + ... + u5 x^5) =
- // u0 x^3 + u1 x^4 + u2 x^5
- // - alpha u3 - alpha u4 x - alpha u5 x^2
- #define f_miller_evalfn() { \
- do_term(0, 2, 3, 2); \
- do_term(1, 3, 4, 2); \
- do_term(2, 4, 5, 2); \
- do_term(3, 5, 0, 1); \
- do_term(4, 0, 1, 0); \
- do_term(5, 1, 2, 0); \
- element_set(v, e0); \
- }
- /*
- element_ptr e1;
-
- e1 = element_item(e0, 4);
-
- element_mul(element_x(e1), element_x(Qx), a);
- element_mul(element_y(e1), element_y(Qx), a);
-
- e1 = element_item(e0, 3);
-
- element_mul(element_x(e1), element_x(Qy), b);
- element_mul(element_y(e1), element_y(Qy), b);
-
- element_set(element_x(element_item(e0, 0)), c);
-
- element_mul(v, v, e0);
- */
-
- //a = -3 Zx^2 since cc->a is 0 for D = 3
- //b = 2 * Zy
- //c = -(2 Zy^2 + a Zx);
- #define do_tangent() { \
- element_square(a, Zx); \
- element_mul_si(a, a, 3); \
- element_neg(a, a); \
- \
- element_add(b, Zy, Zy); \
- \
- element_mul(t0, b, Zy); \
- element_mul(c, a, Zx); \
- element_add(c, c, t0); \
- element_neg(c, c); \
- \
- f_miller_evalfn(); \
- }
-
- //a = -(B.y - A.y) / (B.x - A.x);
- //b = 1;
- //c = -(A.y + a * A.x);
- //but we'll multiply by B.x - A.x to avoid division
- #define do_line() { \
- element_sub(b, Px, Zx); \
- element_sub(a, Zy, Py); \
- element_mul(t0, b, Zy); \
- element_mul(c, a, Zx); \
- element_add(c, c, t0); \
- element_neg(c, c); \
- \
- f_miller_evalfn(); \
- }
-
- element_init(a, Px->field);
- element_init(b, a->field);
- element_init(c, a->field);
- element_init(t0, a->field);
- element_init(e0, res->field);
- element_init(e1, Qx->field);
-
- element_init(v, res->field);
- element_init(Z, P->field);
-
- element_set(Z, P);
- Zx = curve_x_coord(Z);
- Zy = curve_y_coord(Z);
-
- element_set1(v);
- m = mpz_sizeinbase(q, 2) - 2;
-
- //TODO: sliding NAF
- for(;;) {
- do_tangent();
-
- if (!m) break;
-
- element_double(Z, Z);
- if (mpz_tstbit(q, m)) {
- do_line();
- element_add(Z, Z, P);
- }
- m--;
- element_square(v, v);
- }
-
- element_set(res, v);
-
- element_clear(v);
- element_clear(Z);
- element_clear(a);
- element_clear(b);
- element_clear(c);
- element_clear(t0);
- element_clear(e0);
- element_clear(e1);
- #undef do_term
- #undef f_miller_evalfn
- #undef do_tangent
- #undef do_line
-}
-
-static void f_tateexp(element_t out) {
- element_t x, y, epow;
- f_pairing_data_ptr p = out->field->pairing->data;
- element_init(x, p->Fq12);
- element_init(y, p->Fq12);
- element_init(epow, p->Fq2);
-
- #define qpower(e1, e) { \
- element_set(element_item(e1, 0), element_item(out, 0)); \
- element_mul(element_item(e1, 1), element_item(out, 1), e); \
- element_square(epow, e); \
- element_mul(element_item(e1, 2), element_item(out, 2), epow); \
- element_mul(epow, epow, e); \
- element_mul(element_item(e1, 3), element_item(out, 3), epow); \
- element_mul(epow, epow, e); \
- element_mul(element_item(e1, 4), element_item(out, 4), epow); \
- element_mul(epow, epow, e); \
- element_mul(element_item(e1, 5), element_item(out, 5), epow); \
- }
-
- qpower(y, p->xpowq8);
- qpower(x, p->xpowq6);
- element_mul(y, y, x);
- qpower(x, p->xpowq2);
- element_mul(x, x, out);
- element_invert(x, x);
- element_mul(out, y, x);
-
- element_clear(epow);
- element_clear(x);
- element_clear(y);
- element_pow_mpz(out, out, p->tateexp);
- #undef qpower
-}
-
-static void f_finalpow(element_t out) {
- f_tateexp(out->data);
-}
-
-static void f_pairing(element_ptr out, element_ptr in1, element_ptr in2,
- pairing_t pairing) {
- element_ptr Qbase = in2;
- element_t x, y;
- f_pairing_data_ptr p = pairing->data;
-
- element_init(x, p->Fq2);
- element_init(y, p->Fq2);
- //map from twist: (x, y) --> (v^-2 x, v^-3 y)
- //where v is the sixth root used to construct the twist
- //i.e. v^6 = -alpha
- //thus v^-2 = -alpha^-1 v^4
- //and v^-3 = -alpha^-1 v^3
- element_mul(x, curve_x_coord(Qbase), p->negalphainv);
- element_mul(y, curve_y_coord(Qbase), p->negalphainv);
-
- cc_miller_no_denom(out, pairing->r, in1, x, y, p->negalpha);
-
- element_clear(x);
- element_clear(y);
-
- f_tateexp(out);
-}
-
-static void f_pairing_clear(pairing_t pairing) {
- field_clear(pairing->GT);
- f_pairing_data_ptr p = pairing->data;
- element_clear(p->negalpha);
- element_clear(p->negalphainv);
- mpz_clear(p->tateexp);
- element_clear(p->xpowq2);
- element_clear(p->xpowq6);
- element_clear(p->xpowq8);
- field_clear(p->Etwist);
- field_clear(p->Eq);
-
- field_clear(p->Fq12);
- field_clear(p->Fq2x);
- field_clear(p->Fq2);
- field_clear(p->Fq);
- pbc_free(p);
-
- mpz_clear(pairing->r);
- field_clear(pairing->Zr);
-}
-
-static void f_init_pairing(pairing_t pairing, void *data) {
- f_param_ptr param = data;
- f_pairing_data_ptr p;
- element_t irred;
- element_t e0, e1, e2;
- p = pairing->data = pbc_malloc(sizeof(f_pairing_data_t));
- mpz_init(pairing->r);
- mpz_set(pairing->r, param->r);
- field_init_fp(pairing->Zr, pairing->r);
- field_init_fp(p->Fq, param->q);
- p->Fq->nqr = pbc_malloc(sizeof(element_t));
- element_init(p->Fq->nqr, p->Fq);
- element_set_mpz(p->Fq->nqr, param->beta);
- field_init_quadratic(p->Fq2, p->Fq);
- field_init_poly(p->Fq2x, p->Fq2);
- element_init(irred, p->Fq2x);
- // Call poly_set_coeff1() first so we can use element_item() for the other
- // coefficients.
- poly_set_coeff1(irred, 6);
-
- element_init(p->negalpha, p->Fq2);
- element_init(p->negalphainv, p->Fq2);
- element_set_mpz(element_x(p->negalpha), param->alpha0);
- element_set_mpz(element_y(p->negalpha), param->alpha1);
-
- element_set(element_item(irred, 0), p->negalpha);
- field_init_polymod(p->Fq12, irred);
- element_neg(p->negalpha, p->negalpha);
- element_invert(p->negalphainv, p->negalpha);
- element_clear(irred);
-
- element_init(e0, p->Fq);
- element_init(e1, p->Fq);
- element_init(e2, p->Fq2);
-
- // Initialize the curve Y^2 = X^3 + b.
- element_set_mpz(e1, param->b);
- field_init_curve_ab(p->Eq, e0, e1, pairing->r, NULL);
-
- // Initialize the curve Y^2 = X^3 - alpha0 b - alpha1 sqrt(beta) b.
- element_set_mpz(e0, param->alpha0);
- element_neg(e0, e0);
- element_mul(element_x(e2), e0, e1);
- element_set_mpz(e0, param->alpha1);
- element_neg(e0, e0);
- element_mul(element_y(e2), e0, e1);
- element_clear(e0);
- element_init(e0, p->Fq2);
- field_init_curve_ab(p->Etwist, e0, e2, pairing->r, NULL);
- element_clear(e0);
- element_clear(e1);
- element_clear(e2);
-
- mpz_t ndonr;
- mpz_init(ndonr);
- // ndonr temporarily holds the trace.
- mpz_sub(ndonr, param->q, param->r);
- mpz_add_ui(ndonr, ndonr, 1);
- // TODO: We can use a smaller quotient_cmp, but I have to figure out
- // BN curves again.
- pbc_mpz_curve_order_extn(ndonr, param->q, ndonr, 12);
- mpz_divexact(ndonr, ndonr, param->r);
- mpz_divexact(ndonr, ndonr, param->r);
- field_curve_set_quotient_cmp(p->Etwist, ndonr);
- mpz_clear(ndonr);
-
- pairing->G1 = p->Eq;
- pairing->G2 = p->Etwist;
- pairing_GT_init(pairing, p->Fq12);
- pairing->finalpow = f_finalpow;
- pairing->map = f_pairing;
- pairing->clear_func = f_pairing_clear;
-
- mpz_init(p->tateexp);
- /* unoptimized tate exponent
- mpz_pow_ui(p->tateexp, param->q, 12);
- mpz_sub_ui(p->tateexp, p->tateexp, 1);
- mpz_divexact(p->tateexp, p->tateexp, param->r);
- */
- mpz_ptr z = p->tateexp;
- mpz_mul(z, param->q, param->q);
- mpz_sub_ui(z, z, 1);
- mpz_mul(z, z, param->q);
- mpz_mul(z, z, param->q);
- mpz_add_ui(z, z, 1);
- mpz_divexact(z, z, param->r);
-
- element_init(p->xpowq2, p->Fq2);
- element_init(p->xpowq6, p->Fq2);
- element_init(p->xpowq8, p->Fq2);
- element_t xpowq;
- element_init(xpowq, p->Fq12);
-
- //there are smarter ways since we know q = 1 mod 6
- //and that x^6 = -alpha
- //but this is fast enough
- element_set1(element_item(xpowq, 1));
- element_pow_mpz(xpowq, xpowq, param->q);
- element_pow_mpz(xpowq, xpowq, param->q);
- element_set(p->xpowq2, element_item(xpowq, 1));
-
- element_pow_mpz(xpowq, xpowq, param->q);
- element_pow_mpz(xpowq, xpowq, param->q);
- element_pow_mpz(xpowq, xpowq, param->q);
- element_pow_mpz(xpowq, xpowq, param->q);
- element_set(p->xpowq6, element_item(xpowq, 1));
-
- element_pow_mpz(xpowq, xpowq, param->q);
- element_pow_mpz(xpowq, xpowq, param->q);
- element_set(p->xpowq8, element_item(xpowq, 1));
-
- element_clear(xpowq);
-}
-
-static void f_init(pbc_param_ptr p) {
- static pbc_param_interface_t interface = {{
- f_clear,
- f_init_pairing,
- f_out_str,
- }};
- p->api = interface;
- f_param_ptr fp = p->data = pbc_malloc(sizeof(*fp));
- mpz_init(fp->q);
- mpz_init(fp->r);
- mpz_init(fp->b);
- mpz_init(fp->beta);
- mpz_init(fp->alpha0);
- mpz_init(fp->alpha1);
-}
-
-// Public interface:
-
-int pbc_param_init_f(pbc_param_ptr par, struct symtab_s *tab) {
- f_init(par);
- f_param_ptr p = par->data;
-
- int err = 0;
- err += lookup_mpz(p->q, tab, "q");
- err += lookup_mpz(p->r, tab, "r");
- err += lookup_mpz(p->b, tab, "b");
- err += lookup_mpz(p->beta, tab, "beta");
- err += lookup_mpz(p->alpha0, tab, "alpha0");
- err += lookup_mpz(p->alpha1, tab, "alpha1");
- return err;
-}
-
-void pbc_param_init_f_gen(pbc_param_t p, int bits) {
- f_init(p);
- f_param_ptr fp = p->data;
- //36 is a 6-bit number
- int xbit = (bits - 6) / 4;
- //TODO: use binary search to find smallest appropriate x
- mpz_t x, t;
- mpz_ptr q = fp->q;
- mpz_ptr r = fp->r;
- mpz_ptr b = fp->b;
- field_t Fq, Fq2, Fq2x;
- element_t e1;
- element_t f;
- field_t c;
- element_t P;
-
- mpz_init(x);
- mpz_init(t);
- mpz_setbit(x, xbit);
- for (;;) {
- mpz_mul(t, x, x);
- mpz_mul_ui(t, t, 6);
- mpz_add_ui(t, t, 1);
- tryminusx(q, x);
- mpz_sub(r, q, t);
- mpz_add_ui(r, r, 1);
- if (mpz_probab_prime_p(q, 10) && mpz_probab_prime_p(r, 10)) break;
-
- tryplusx(q, x);
- mpz_sub(r, q, t);
- mpz_add_ui(r, r, 1);
- if (mpz_probab_prime_p(q, 10) && mpz_probab_prime_p(r, 10)) break;
-
- mpz_add_ui(x, x, 1);
- }
-
- field_init_fp(Fq, q);
- element_init(e1, Fq);
-
- for (;;) {
- element_random(e1);
- field_init_curve_b(c, e1, r, NULL);
- element_init(P, c);
-
- element_random(P);
-
- element_mul_mpz(P, P, r);
- if (element_is0(P)) break;
- element_clear(P);
- field_clear(c);
- }
- element_to_mpz(b, e1);
- element_clear(e1);
- field_init_quadratic(Fq2, Fq);
- element_to_mpz(fp->beta, field_get_nqr(Fq));
- field_init_poly(Fq2x, Fq2);
- element_init(f, Fq2x);
-
- // Find an irreducible polynomial of the form f = x^6 + alpha.
- // Call poly_set_coeff1() first so we can use element_item() for the other
- // coefficients.
- poly_set_coeff1(f, 6);
- for (;;) {
- element_random(element_item(f, 0));
- if (poly_is_irred(f)) break;
- }
-
- //extend F_q^2 using f = x^6 + alpha
- //see if sextic twist contains a subgroup of order r
- //if not, it's the wrong twist: replace alpha with alpha^5
- {
- field_t ctest;
- element_t Ptest;
- mpz_t z0, z1;
- mpz_init(z0);
- mpz_init(z1);
- element_init(e1, Fq2);
- element_set_mpz(e1, fp->b);
- element_mul(e1, e1, element_item(f, 0));
- element_neg(e1, e1);
-
- field_init_curve_b(ctest, e1, r, NULL);
- element_init(Ptest, ctest);
- element_random(Ptest);
-
- //I'm not sure what the #E'(F_q^2) is, but
- //it definitely divides n_12 = #E(F_q^12). It contains a
- //subgroup of order r if and only if
- //(n_12 / r^2)P != O for some (in fact most) P in E'(F_q^6)
- mpz_pow_ui(z0, q, 12);
- mpz_add_ui(z0, z0, 1);
- pbc_mpz_trace_n(z1, q, t, 12);
- mpz_sub(z1, z0, z1);
- mpz_mul(z0, r, r);
- mpz_divexact(z1, z1, z0);
-
- element_mul_mpz(Ptest, Ptest, z1);
- if (element_is0(Ptest)) {
- mpz_set_ui(z0, 5);
- element_pow_mpz(element_item(f, 0), element_item(f, 0), z0);
- }
- element_clear(e1);
- element_clear(Ptest);
- field_clear(ctest);
- mpz_clear(z0);
- mpz_clear(z1);
- }
-
- element_to_mpz(fp->alpha0, element_x(element_item(f, 0)));
- element_to_mpz(fp->alpha1, element_y(element_item(f, 0)));
-
- element_clear(f);
-
- field_clear(Fq2x);
- field_clear(Fq2);
- field_clear(Fq);
-
- mpz_clear(t);
- mpz_clear(x);
-}