// The final powering, where we standardize the coset representative.
static void cc_tatepower(element_ptr out, element_ptr in, pairing_t pairing) {
  pptr p = pairing->data;
  #define qpower(sign) {                         \
    polymod_const_mul(e2, inre[1], p->xpowq);    \
    element_set(e0re, e2);                       \
    polymod_const_mul(e2, inre[2], p->xpowq2);   \
    element_add(e0re, e0re, e2);                 \
    element_add(e0re0, e0re0, inre[0]);          \
                                                 \
    if (sign > 0) {                              \
      polymod_const_mul(e2, inim[1], p->xpowq);  \
      element_set(e0im, e2);                     \
      polymod_const_mul(e2, inim[2], p->xpowq2); \
      element_add(e0im, e0im, e2);               \
      element_add(e0im0, e0im0, inim[0]);        \
    } else {                                     \
      polymod_const_mul(e2, inim[1], p->xpowq);  \
      element_neg(e0im, e2);                     \
      polymod_const_mul(e2, inim[2], p->xpowq2); \
      element_sub(e0im, e0im, e2);               \
      element_sub(e0im0, e0im0, inim[0]);        \
    }                                            \
  }
  if (p->k == 6) {
    // See thesis, section 6.9, "The Final Powering", which gives a formula
    // for the first step of the final powering when Fq6 has been implemented
    // as a quadratic extension on top of a cubic extension.
    element_t e0, e2, e3;
    element_init(e0, p->Fqk);
    element_init(e2, p->Fqd);
    element_init(e3, p->Fqk);
    element_ptr e0re = element_x(e0);
    element_ptr e0im = element_y(e0);
    element_ptr e0re0 = ((element_t *) e0re->data)[0];
    element_ptr e0im0 = ((element_t *) e0im->data)[0];
    element_t *inre = element_x(in)->data;
    element_t *inim = element_y(in)->data;
    // Expressions in the formula are similar, hence the following function.
    qpower(1);
    element_set(e3, e0);
    element_set(e0re, element_x(in));
    element_neg(e0im, element_y(in));
    element_mul(e3, e3, e0);
    qpower(-1);
    element_mul(e0, e0, in);
    element_invert(e0, e0);
    element_mul(in, e3, e0);

    element_set(e0, in);
    // We use Lucas sequences to complete the final powering.
    lucas_even(out, e0, pairing->phikonr);

    element_clear(e0);
    element_clear(e2);
    element_clear(e3);
  } else {
    element_pow_mpz(out, in, p->tateexp);
  }
  #undef qpower
}

//c_iとk_iをペアリングする関数
//¬記号で別々の処理する
//(v_i - x_t)も必要→とりあえず置いておこう……→一応できた？
Element *pairing_c_k(EC_PAIRING p, rho_i *rho, EC_POINT *c, EC_POINT *k, mpz_t *alpha_i) {
	int i;
	Element *result;
	result = (Element*)malloc(sizeof(Element));
	Element egg, tempegg1, tempegg2;
	element_init(egg, p->g3);
	element_init(tempegg1, p->g3);
	element_init(tempegg2, p->g3);
	element_init(*result, p->g3);
	mpz_t temp1;
	mpz_init(temp1);
	mpz_t temp2;
	mpz_init(temp2);
	mpz_t order;
	mpz_init(order);
	mpz_set(order, *pairing_get_order(p));
	element_set_one(*result);

	if (alpha_i == NULL && rho == NULL) { //e(c_0, k_0)
			for (i = 0; i < 5; i++) {
				pairing_map(tempegg1, c[i], k[i], p);
				element_mul(tempegg2, tempegg1, *result);
				element_set(*result, tempegg2);
			}
	}
    else if (mpz_cmp_ui(*alpha_i, 0) == 0) {//return 1
    }
	else if (rho->is_negated == FALSE) {
			for (i = 0; i < 7; i++) {
				pairing_map(tempegg1, c[i], k[i], p);
				element_mul(tempegg2, tempegg1, *result);
				element_set(*result, tempegg2);
			}
			element_pow(tempegg1, *result, *alpha_i);
			element_set(*result, tempegg1);
	}
	else { //is_negated == TRUE
			for (i = 0; i < 7; i++) {
				pairing_map(tempegg1, c[i], k[i], p);
				element_mul(tempegg2, tempegg1, *result);
				element_set(*result, tempegg2);
			}
		mpz_set_ui(temp1, rho->v_t[0]); //v_i - x_t
		mpz_invert(temp2, temp1, order);
		mpz_mul(temp1, temp2, *alpha_i); // alpha_i / (v_i - x_t)
		mpz_mod(*alpha_i, temp1, order);
		element_pow(tempegg1, *result, *alpha_i);
		element_set(*result, tempegg1);
	}

    mpz_clear(order);
    mpz_clear(temp2);
    mpz_clear(temp1);
	element_clear(egg);
	element_clear(tempegg1);
	element_clear(tempegg2);

	return result;
}

void bb_free_pk(bb_public_key_t pk)
{
	element_clear(pk->g1);
	element_clear(pk->g2);
	element_clear(pk->u);
	element_clear(pk->v);
	element_clear(pk->z);
}

void bbs_free_gsk(bbs_group_private_key_t *gsk, int n)
{
  int i = 0;
  for(i = 0; i < n; i++) {
    element_clear(gsk[i]->A);
    element_clear(gsk[i]->x);
    element_clear(gsk[i]->pr_A_g2);
  }
}

static void sn_add(element_t c, element_t a, element_t b) {
  point_ptr r = c->data;
  point_ptr p = a->data;
  point_ptr q = b->data;
  if (p->inf_flag) {
    sn_set(c, b);
    return;
  }
  if (q->inf_flag) {
    sn_set(c, a);
    return;
  }
  if (!element_cmp(p->x, q->x)) {
    if (!element_cmp(p->y, q->y)) {
      if (element_is0(p->y)) {
        r->inf_flag = 1;
        return;
      } else {
        sn_double_no_check(r, p);
        return;
      }
    }
    //points are inverses of each other
    r->inf_flag = 1;
    return;
  } else {
    element_t lambda, e0, e1;

    element_init(lambda, p->x->field);
    element_init(e0, p->x->field);
    element_init(e1, p->x->field);

    //lambda = (y2-y1)/(x2-x1)
    element_sub(e0, q->x, p->x);
    element_invert(e0, e0);
    element_sub(lambda, q->y, p->y);
    element_mul(lambda, lambda, e0);
    //x3 = lambda^2 - x1 - x2 - 1
    element_square(e0, lambda);
    element_sub(e0, e0, p->x);
    element_sub(e0, e0, q->x);
    element_set1(e1);
    element_sub(e0, e0, e1);
    //y3 = (x1-x3)lambda - y1
    element_sub(e1, p->x, e0);
    element_mul(e1, e1, lambda);
    element_sub(e1, e1, p->y);

    element_set(r->x, e0);
    element_set(r->y, e1);
    r->inf_flag = 0;

    element_clear(lambda);
    element_clear(e0);
    element_clear(e1);
  }
}

void
pbgp_ibe_signature_clear(ibe_signature_t *s)
{
  if (s) {
    element_clear(s->u);
    element_clear(s->v);
    element_clear(s->w);
    xfree(s);
  }
}

void FreeCT(ct_t myct)
{
  if(!myct) {
    printf("error: null pointer passed to freeCT\n");
    return;
  }
  element_clear(myct->C0);
  element_clear(myct->C1);
  return;
}

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 curve_mul(element_ptr c, element_ptr a, element_ptr b) {
	curve_data_ptr cdp = (curve_data_ptr)a->field->data;
  point_ptr r = (point_ptr)c->data, p = (point_ptr)a->data, q = (point_ptr)b->data;

  if (p->inf_flag) {
    curve_set(c, b);
    return;
  }
  if (q->inf_flag) {
    curve_set(c, a);
    return;
  }
  if (!element_cmp(p->x, q->x)) {
    if (!element_cmp(p->y, q->y)) {
      if (element_is0(p->y)) {
        r->inf_flag = 1;
        return;
      } else {
        double_no_check(r, p, cdp->a);
        return;
      }
    }
    //points are inverses of each other
    r->inf_flag = 1;
    return;
  } else {
    element_t lambda, e0, e1;

    element_init(lambda, cdp->field);
    element_init(e0, cdp->field);
    element_init(e1, cdp->field);

    //lambda = (y2-y1)/(x2-x1)
    element_sub(e0, q->x, p->x);
    element_invert(e0, e0);
    element_sub(lambda, q->y, p->y);
    element_mul(lambda, lambda, e0);
    //x3 = lambda^2 - x1 - x2
    element_square(e0, lambda);
    element_sub(e0, e0, p->x);
    element_sub(e0, e0, q->x);
    //y3 = (x1-x3)lambda - y1
    element_sub(e1, p->x, e0);
    element_mul(e1, e1, lambda);
    element_sub(e1, e1, p->y);

    element_set(r->x, e0);
    element_set(r->y, e1);
    r->inf_flag = 0;

    element_clear(lambda);
    element_clear(e0);
    element_clear(e1);
  }
}

int main(int argc, char ** argv) {
  pbc_param_t ec_params;
  pairing_t pairing;
  unsigned int rbits = 40, qbits = 128;
  element_t *g1, *g2, *gt;
  
  for (int s = 10; s <= 1000; s += 10) {
  while (qbits <= 4096) {
    fprintf(stderr, "%d", qbits);
    pbc_param_init_a_gen(ec_params, rbits, qbits);

    pairing_init_pbc_param(pairing, ec_params);


    element_init_G1(g1, pairing);
    element_init_G2(g2, pairing);
    element_init_GT(gt, pairing);

    struct timeval tv1, tv2;
    int bc = element_length_in_bytes(g1);

    for (int i = 0; i < 100; i++) {
      if (0 == i % 10)
	fprintf(stderr, ".");

      element_random(g1);
      element_random(g2);

      gettimeofday(&tv1, NULL);
      pairing_apply(gt, g1, g2, pairing);
      gettimeofday(&tv2, NULL);

      double time = tv2.tv_sec - tv1.tv_sec;
      time *= (1000 * 1000);
      time += tv2.tv_usec - tv1.tv_usec;

      fprintf(stdout, "%d %d %d %d %d\n", bc, rbits, qbits, i, ((int) time));
    }

    for (int j = 0; j < s; j++) {
      element_clear(g1[j]);
      element_clear(g2[j]);
      element_clear(gt[j]);
    }

    rbits *= 2;
    qbits *= 2;

    fprintf(stderr, "\n");
  }
  free(g1);
  free(g2);
  free(g3);
  }
}

void FreeBCS(broadcast_system_t bcs)
{
  if(!bcs) {
    printf("error: null pointer passed to freeBCS\n");
    return;
  }
  element_clear(bcs->encr_prod);
  element_clear(bcs->pub_key);  
  element_clear(bcs->priv_key);
  return;
}

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 bn254_fp2_clear(Element x)
{
    if (x->data != NULL)
    {
        element_clear(rep0(x));
        element_clear(rep1(x));

        free(x->data);
        x->data = NULL;
    }
}

void FreePK(priv_key_t key)
{
  if(!key) {
    printf("error: null pointer passed to freePK\n");
    return;
  }
  element_clear(key->g_i_gamma);
  element_clear(key->g_i);  
  element_clear(key->decr_prod);
  return;
}

void
pbgp_ibe_keypair_clear(ibe_keypair_t *keys)
{
  if (keys) {
    element_clear(keys->pub0);
    element_clear(keys->priv0);
    element_clear(keys->pub1);
    element_clear(keys->priv1);
    xfree(keys);
  }
}

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);
}

/* $e <- a^{-1}$ */
static void gf33m_invert(element_t e, element_t a) {
    element_ptr a0 = GF33M(a)->_0, a1 = GF33M(a)->_1, a2 = GF33M(a)->_2, e0 =
            GF33M(e)->_0, e1 = GF33M(e)->_1, e2 = GF33M(e)->_2;
    field_ptr base = BASE(e);
    element_t a02, a12, a22;
    element_init(a02, base);
    element_init(a12, base);
    element_init(a22, base);
    element_mul(a02, a0, a0);
    element_mul(a12, a1, a1);
    element_mul(a22, a2, a2);
    element_t v0;
    element_init(v0, base);
    element_sub(v0, a0, a2); // v0 == a0-a2
    element_t delta;
    element_init(delta, base);
    element_mul(delta, v0, a02); // delta = (a0-a2)*(a0^2), free
    element_sub(v0, a1, a0); // v0 == a1-a0
    element_t c0;
    element_init(c0, base);
    element_mul(c0, v0, a12); // c0 == (a1-a0)*(a1^2)
    element_add(delta, delta, c0); // delta = (a0-a2)*(a0^2) + (a1-a0)*(a1^2)
    element_sub(v0, a2, v0); // v0 == a2-(a1-a0) = a0-a1+a2
    element_t c1;
    element_init(c1, base);
    element_mul(c1, v0, a22); // c1 == (a0-a1+a2)*(a2^2)
    element_add(delta, delta, c1); // delta = (a0-a2)*(a0^2) + (a1-a0)*(a1^2) + (a0-a1+a2)*(a2^2)
    element_invert(delta, delta); // delta = [(a0-a2)*(a0^2) + (a1-a0)*(a1^2) + (a0-a1+a2)*(a2^2)] ^ {-1}
    element_add(v0, a02, a22); // v0 == a0^2+a2^2
    element_t c2;
    element_init(c2, base);
    element_mul(c2, a0, a2); // c2 == a0*a2
    element_sub(c0, v0, c2); // c0 == a0^2+a2^2-a0*a2
    element_add(v0, a1, a2); // v0 == a1+a2
    element_t c3;
    element_init(c3, base);
    element_mul(c3, a1, v0); // c3 == a1*(a1+a2)
    element_sub(c0, c0, c3); // c0 == a0^2+a2^2-a0*a2-a1*(a1+a2)
    element_mul(c0, c0, delta); // c0 *= delta
    element_mul(c1, a0, a1); // c1 == a0*a1
    element_sub(c1, a22, c1); // c1 == a2^2-a0*a1
    element_mul(c1, c1, delta); // c1 *= delta
    element_sub(c2, a12, c2); // c2 == a1^2-a0*a2
    element_sub(c2, c2, a22); // c2 == a1^2-a0*a2-a2^2
    element_mul(c2, c2, delta); // c2 *= delta
    element_set(e0, c0);
    element_set(e1, c1);
    element_set(e2, c2);
    element_clear(a02);
    element_clear(a12);
    element_clear(a22);
    element_clear(v0);
    element_clear(delta);
    element_clear(c0);
    element_clear(c1);
    element_clear(c2);
    element_clear(c3);
}

/* $c <- a*b$ */
static void gf33m_mult(element_t e, element_t a, element_t b) {
    element_ptr a0 = GF33M(a)->_0, a1 = GF33M(a)->_1, a2 = GF33M(a)->_2, b0 =
            GF33M(b)->_0, b1 = GF33M(b)->_1, b2 = GF33M(b)->_2, e0 =
            GF33M(e)->_0, e1 = GF33M(e)->_1, e2 = GF33M(e)->_2;
    field_ptr base = BASE(e);
    element_t t0, t1, c1, a0b0, a1b1, a2b2;
    element_init(t0, base);
    element_init(t1, base);
    element_init(c1, base);
    element_init(a0b0, base);
    element_init(a1b1, base);
    element_init(a2b2, base);
    element_mul(a0b0, a0, b0);
    element_mul(a1b1, a1, b1);
    element_mul(a2b2, a2, b2);
    element_ptr d0 = a0b0;
    element_add(t0, a1, a0);
    element_add(t1, b1, b0);
    element_t d1;
    element_init(d1, base);
    element_mul(d1, t0, t1);
    element_sub(d1, d1, a1b1);
    element_sub(d1, d1, a0b0);
    element_add(t0, a2, a0);
    element_add(t1, b2, b0);
    element_t d2;
    element_init(d2, base);
    element_mul(d2, t0, t1);
    element_add(d2, d2, a1b1);
    element_sub(d2, d2, a2b2);
    element_sub(d2, d2, a0b0);
    element_add(t0, a2, a1);
    element_add(t1, b2, b1);
    element_t d3;
    element_init(d3, base);
    element_mul(d3, t0, t1);
    element_sub(d3, d3, a2b2);
    element_sub(d3, d3, a1b1);
    element_ptr d4 = a2b2;
    element_add(t0, d0, d3);
    element_ptr c0 = t0;
    element_add(c1, d1, d3);
    element_add(c1, c1, d4);
    element_add(t1, d2, d4);
    element_ptr c2 = t1;
    element_set(e0, c0);
    element_set(e1, c1);
    element_set(e2, c2);
    element_clear(t0);
    element_clear(t1);
    element_clear(c1);
    element_clear(a0b0);
    element_clear(a1b1);
    element_clear(a2b2);
    element_clear(d1);
    element_clear(d2);
    element_clear(d3);
}

void FreeCT(ct CT)
{
  if(!CT) {
    printf("error: null pointer passed to freeCT\n");
    return;
  }
  element_clear(CT->OC0);
  element_clear(CT->OC1);
  element_clear(CT->C0);
  element_clear(CT->C1);
  pbc_free(CT);
  return;
}

void bbs_free_gpk(bbs_group_public_key_ptr gpk)
{
  element_clear(gpk->g1);
  element_clear(gpk->g2);

  element_clear(gpk->h);
  element_clear(gpk->u);
  element_clear(gpk->v);
  element_clear(gpk->w);

  element_clear(gpk->pr_g1_g2);
  element_clear(gpk->pr_h_g2);
  element_clear(gpk->pr_h_w);
  element_clear(gpk->pr_g1_g2_inv);
}