void CipherText::langrange(element_t* ys, int index, int k, int num){
element_t delta;
element_t numerator;
element_t denominator;
element_t temp;
element_init_Zr(delta, *(this->p));
element_init_Zr(numerator, *(this->p));
element_init_Zr(denominator, *(this->p));
element_init_Zr(temp, *(this->p));
element_init_Zr(ys[index], *(this->p));
element_set0(ys[index]);
int i, j;
for(i = 0; i < k; i++){
//compute the langrange coefficent l
element_set1(delta);
for(j = 0; j < k; j++){
if( j != i){
element_set_si(numerator, index - j);
element_set_si(denominator, i - j);
element_div(numerator, numerator, denominator);
element_mul(delta, delta, numerator);
}
}
element_mul(temp, ys[i], delta);
element_add(ys[index], ys[index], temp);
}
}
void cc_pairings_affine(element_ptr out, element_t in1[], element_t in2[],
int n_prod, pairing_t pairing) {
element_ptr Qbase;
element_t* Qx = pbc_malloc(sizeof(element_t)*n_prod);
element_t* Qy = pbc_malloc(sizeof(element_t)*n_prod);
pptr p = pairing->data;
int i;
for(i=0; i<n_prod; i++){
element_init(Qx[i], p->Fqd);
element_init(Qy[i], p->Fqd);
Qbase = in2[i];
// Twist: (x, y) --> (v^-1 x, v^-(3/2) y)
// where v is the quadratic nonresidue used to construct the twist.
element_mul(Qx[i], curve_x_coord(Qbase), p->nqrinv);
// v^-3/2 = v^-2 * v^1/2
element_mul(Qy[i], curve_y_coord(Qbase), p->nqrinv2);
}
cc_millers_no_denom_affine(out, pairing->r, in1, Qx, Qy, n_prod);
cc_tatepower(out, out, pairing);
for(i=0; i<n_prod; i++){
element_clear(Qx[i]);
element_clear(Qy[i]);
}
pbc_free(Qx);
pbc_free(Qy);
}
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 test_gf3m_cubic(void) {
element_random(a);
element_mul(b, a, a);
element_mul(b, a, b);
element_cubic(a, a);
EXPECT(!element_cmp(a, b));
}
void miller(element_t res, mpz_t q, element_t P, element_ptr Qx, element_ptr Qy) {
int m;
element_t v;
element_t Z;
element_t a, b, c;
element_t t0;
element_t e0;
const element_ptr cca = curve_a_coeff(P);
const element_ptr Px = curve_x_coord(P);
const element_ptr Py = curve_y_coord(P);
element_ptr Zx, Zy;
void do_tangent(void) {
// a = -(3 Zx^2 + cc->a)
// b = 2 * Zy
// c = -(2 Zy^2 + a Zx);
element_square(a, Zx); mult1++;
element_mul_si(a, a, 3); add1++; add1++; add1++;
element_add(a, a, cca); add1++;
element_neg(a, a);
element_add(b, Zy, Zy); add1++;
element_mul(t0, b, Zy); mult1++;
element_mul(c, a, Zx); mult1++;
element_add(c, c, t0); add1++;
element_neg(c, c);
d_miller_evalfn(e0, a, b, c, Qx, Qy);
element_mul(v, v, e0); multk++;
}
static void test_gf32m_cubic(void) {
element_random(a2);
element_mul(b2, a2, a2);
element_mul(b2, b2, a2);
element_cubic(a2, a2);
EXPECT(!element_cmp(a2, b2));
}
static void test_gf33m_cubic(void) {
element_random(a3);
element_mul(b3, a3, a3);
element_mul(b3, b3, a3);
element_cubic(a3, a3);
EXPECT(!element_cmp(a3, b3));
}
// 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
}
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 fi_mul(element_ptr n, element_ptr a, element_ptr b) {
eptr p = a->data;
eptr q = b->data;
eptr r = n->data;
element_t e0, e1, e2;
element_init(e0, p->x->field);
element_init(e1, e0->field);
element_init(e2, e0->field);
/* Naive method:
element_mul(e0, p->x, q->x);
element_mul(e1, p->y, q->y);
element_sub(e0, e0, e1);
element_mul(e1, p->x, q->y);
element_mul(e2, p->y, q->x);
element_add(e1, e1, e2);
element_set(r->x, e0);
element_set(r->y, e1);
*/
// Karatsuba multiplicaiton:
element_add(e0, p->x, p->y);
element_add(e1, q->x, q->y);
element_mul(e2, e0, e1);
element_mul(e0, p->x, q->x);
element_sub(e2, e2, e0);
element_mul(e1, p->y, q->y);
element_sub(r->x, e0, e1);
element_sub(r->y, e2, e1);
element_clear(e0);
element_clear(e1);
element_clear(e2);
}
/* $e<- a*b$ */
static void gf32m_mult(element_t e, element_t a, element_t b) {
element_ptr a0 = GF32M(a)->_0, a1 = GF32M(a)->_1, b0 = GF32M(b)->_0, b1 =
GF32M(b)->_1, e0 = GF32M(e)->_0, e1 = GF32M(e)->_1;
field_ptr base = BASE(a);
element_t a0b0, a1b1, t0, t1, c1;
element_init(a0b0, base);
element_init(a1b1, base);
element_init(t0, base);
element_init(t1, base);
element_init(c1, base);
element_mul(a0b0, a0, b0);
element_mul(a1b1, a1, b1);
element_add(t0, a1, a0);
element_add(t1, b1, b0);
element_mul(c1, t0, t1); // c1 == (a1+a0)*(b1+b0)
element_sub(c1, c1, a1b1);
element_sub(c1, c1, a0b0);
element_ptr c0 = a0b0;
element_sub(c0, c0, a1b1); // c0 == a0*b0 - a1*b1
element_set(e0, c0);
element_set(e1, c1);
element_clear(a0b0);
element_clear(a1b1);
element_clear(t0);
element_clear(t1);
element_clear(c1);
}
static void e_miller_proj(element_t res, element_t P,
element_ptr QR, element_ptr R,
e_pairing_data_ptr p) {
//collate divisions
int n;
element_t v, vd;
element_t v1, vd1;
element_t Z, Z1;
element_t a, b, c;
const element_ptr cca = curve_a_coeff(P);
element_t e0, e1;
const element_ptr e2 = a, e3 = b;
element_t z, z2;
int i;
element_ptr Zx, Zy;
const element_ptr Px = curve_x_coord(P);
const element_ptr numx = curve_x_coord(QR);
const element_ptr numy = curve_y_coord(QR);
const element_ptr denomx = curve_x_coord(R);
const element_ptr denomy = curve_y_coord(R);
//convert Z from weighted projective (Jacobian) to affine
//i.e. (X, Y, Z) --> (X/Z^2, Y/Z^3)
//also sets z to 1
void to_affine(void)
{
element_invert(z, z);
element_square(e0, z);
element_mul(Zx, Zx, e0);
element_mul(e0, e0, z);
element_mul(Zy, Zy, e0);
element_set1(z);
element_set1(z2);
}
static void test_gf36m_cubic(void) {
element_random(a6);
element_mul(b6, a6, a6);
element_mul(b6, b6, a6);
element_cubic(a6, a6);
EXPECT(!element_cmp(a6, b6));
}
static void fi_sqrt(element_ptr n, element_ptr e) {
eptr p = e->data;
eptr r = n->data;
element_t e0, e1, e2;
// If (a+bi)^2 = x+yi then 2a^2 = x +- sqrt(x^2 + y^2)
// where we choose the sign so that a exists, and 2ab = y.
// Thus 2b^2 = - (x -+ sqrt(x^2 + y^2)).
element_init(e0, p->x->field);
element_init(e1, e0->field);
element_init(e2, e0->field);
element_square(e0, p->x);
element_square(e1, p->y);
element_add(e0, e0, e1);
element_sqrt(e0, e0);
// e0 = sqrt(x^2 + y^2)
element_add(e1, p->x, e0);
element_set_si(e2, 2);
element_invert(e2, e2);
element_mul(e1, e1, e2);
// e1 = (x + sqrt(x^2 + y^2))/2
if (!element_is_sqr(e1)) {
element_sub(e1, e1, e0);
// e1 should be a square.
}
element_sqrt(e0, e1);
element_add(e1, e0, e0);
element_invert(e1, e1);
element_mul(r->y, p->y, e1);
element_set(r->x, e0);
element_clear(e0);
element_clear(e1);
element_clear(e2);
}
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);
}
//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;
}
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);
}
}
//--------------------------------------------------
// square root in extended Fp
//--------------------------------------------------
int bn254_fp2_sqrt(Element z, const Element x)
{
mpz_t _v;
int m, r, i;
field_precomp_sqrt_p ps;
Element *t = field(z)->tmp;
if (!element_is_sqr(x)) {
return FALSE;
}
ps = ((field_precomp_p)(field(x)->precomp))->ps;
element_set(t[0], ps->n_v); // t0 = n^v
r = ps->e; // r = e
mpz_init_set(_v, ps->v);
mpz_sub_ui(_v, _v, 1);
mpz_tdiv_q_2exp(_v, _v, 1);
element_pow(t[1], x, _v); // t1 = x^{(v-1)/2}
element_sqr(t[2], t[1]);
element_mul(t[2], t[2], x); // t2 = x*t1^2
element_mul(t[1], x, t[1]); // t1 = x*t1
mpz_clear(_v);
while (!element_is_one(t[2]))
{
m = 0;
element_set(t[3], t[2]);
do {
element_sqr(t[3], t[3]);
m++;
}
while (!element_is_one(t[3]) && m < r);
r = r - m - 1;
element_set(t[3], t[0]);
for (i = 1; i <= r; i++) {
element_sqr(t[3], t[3]);
} // t3 = t2^{r-m-1}
element_sqr(t[0], t[3]); // t0 = t3^2
r = m;
element_mul(t[1], t[1], t[3]);// t1 = t1*t3
element_mul(t[2], t[2], t[0]);// t2 = t2*t0
}
element_set(z, t[1]);
return TRUE;
}
void do_vertical(element_t e, element_t edenom, element_ptr Ax)
{
element_mul(e0, numx, z2);
element_sub(e0, e0, Ax);
element_mul(e, e, e0);
element_mul(e0, denomx, z2);
element_sub(e0, e0, Ax);
element_mul(edenom, edenom, e0);
}
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);
}
}
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 Change_decr_prod_indicies(global_broadcast_params_t gbp, int receiver,
int *adds, int N_adds, int *rems, int N_rems,
priv_key_t mykey)
{
// REMOVES THE OLD ONES, THEN ADDS THE NEW ONES
int i;
element_t temp_inv;
int incl_num;
if(!gbp) {
printf("ACK! You gave me no broadcast params! I die.\n");
return;
}
if(!mykey) {
printf("ACK! You gave me no broadcast system! I die.\n");
return;
}
int n = gbp->num_users;
element_init(temp_inv, gbp->pairing->G1);
if(rems) {
for(i = 0; i < N_rems; i++) {
//removing elements from the set after
//checking if it's in the bit-vector
incl_num = rems[i];
if(incl_num < 1 || incl_num > gbp->num_users) {
printf("element %d was outside the range of valid users\n",i);
printf("only give me valid values. i die.\n");
return;
}
if(incl_num == receiver) {
if(DEBUG) printf("incl_num == receiver, continuing\n");
continue;
}
element_invert(temp_inv, gbp->gs[(n-incl_num)+receiver]);
element_mul(mykey->decr_prod, mykey->decr_prod, temp_inv);
}
}
if(adds) {
for(i = 0; i < N_adds; i++) {
//adding elements to the set after checking if they're already there
incl_num = adds[i];
if(incl_num < 1 || incl_num > gbp->num_users) {
printf("element %d was outside the range of valid users\n",i);
printf("only give me valid values. i die.\n");
return;
}
if(incl_num == receiver) {
if(DEBUG) printf("incl_num == receiver, continuing\n");
continue;
}
element_mul(mykey->decr_prod, mykey->decr_prod,
gbp->gs[(n-incl_num)+receiver]);
}
}
}
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);
}
// Define l = aX + bY + c where a, b, c are in Fq.
// Compute e0 = l(Q) specialized for the case when Q has the form
// (Qx, Qy * sqrt(v)) where Qx, Qy are in Fqd and v is the quadratic nonresidue
// used to construct the quadratic field extension Fqk of Fqd.
static inline void d_miller_evalfn(element_t e0,
element_t a, element_t b, element_t c, element_t Qx, element_t Qy) {
element_ptr re_out = element_x(e0);
element_ptr im_out = element_y(e0);
int i;
int d = polymod_field_degree(re_out->field);
for (i = 0; i < d; i++) {
element_mul(element_item(re_out, i), element_item(Qx, i), a);
element_mul(element_item(im_out, i), element_item(Qy, i), b);
}
element_add(element_item(re_out, 0), element_item(re_out, 0), c);
}
void DecryptKEM_using_product(global_broadcast_params_t gbp,
priv_key_t mykey, element_t key,
ct_t myct)
{
if(!gbp) {
printf("ACK! You gave me no broadcast params! I die.\n");
return;
}
if(!mykey) {
printf("ACK! You gave me no private key info I die.\n");
return;
}
if(!myct) {
printf("ACK! No struct cipher text to decode I die.\n");
return;
}
if(!key) {
printf("ACK! No place to put my key! I die.\n");
return;
}
if(!mykey->decr_prod) {
printf("ACK! Calculate decryption prodcut before ");
printf("calling this function! I die.\n");
return;
}
element_t temp;
element_t temp2;
element_t di_de;
element_t temp3;
element_init(temp, gbp->pairing->GT);
element_init(temp2, gbp->pairing->GT);
element_init(di_de, gbp->pairing->G1);
element_init(temp3, gbp->pairing->GT);
//Generate the numerator
element_pairing(temp, myct->C1, mykey->g_i);
//G1 element in denom
element_mul(di_de, mykey->g_i_gamma, mykey->decr_prod);
//Generate the denominator
element_pairing(temp2, di_de, myct->C0);
//Invert the denominator
element_invert(temp3, temp2);
element_init(key, gbp->pairing->GT);
//multiply the numerator by the inverted denominator
element_mul(key, temp, temp3);
}
void do_line(element_ptr e, element_ptr edenom, element_ptr A, element_ptr B)
{
element_ptr Ax = curve_x_coord(A);
element_ptr Ay = curve_y_coord(A);
element_ptr Bx = curve_x_coord(B);
element_ptr By = curve_y_coord(B);
element_sub(b, Bx, Ax);
element_sub(a, Ay, By);
element_mul(c, Ax, By);
element_mul(e0, Ay, Bx);
element_sub(c, c, e0);
element_mul(e0, a, numx);
element_mul(e1, b, numy);
element_add(e0, e0, e1);
element_add(e0, e0, c);
element_mul(e, e, e0);
element_mul(e0, a, denomx);
element_mul(e1, b, denomy);
element_add(e0, e0, e1);
element_add(e0, e0, c);
element_mul(edenom, edenom, e0);
}
static void test_gf3m_mult(void) {
element_random(a);
element_mul(a, a, e0);
EXPECT(!element_cmp(a, e0));
element_random(a);
element_mul(b, a, e1);
EXPECT(!element_cmp(a, b));
element_random(a);
element_mul(b, a, e2);
element_add(a, a, b);
EXPECT(!element_cmp(a, e0));
}
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);
}
/**
* @param witness gets modified
*/
void
pbgp_witness_update(setup_params_t *setup,
store_t *added, store_t *revoked,
uint32_t id, element_t witness)
{
element_t num, den, witt;
element_init_G1(num, setup->pairing);
element_init_G1(den, setup->pairing);
element_init_G1(witt, setup->pairing);
_witness_set_product(setup, added, id, num);
_witness_set_product(setup, revoked, id, den);
// Multiply
//
// g[np1 - j + i] added
// w *= ---------------------
// g[np1 - j + i] revoked
//
// asnum(s) during last epoch
element_div(witt, num, den);
element_mul(witness, witness, witt);
element_clear(num);
element_clear(den);
element_clear(witt);
}
static void test_gf33m_inverse(void) {
element_random(a3);
element_invert(b3, a3);
element_mul(a3, a3, b3);
element_ptr a0 = element_item(a3, 0);
EXPECT(!element_cmp(a0, e1));
}
