/* 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);
}
/* $e<- a*b$ */
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 gf33m_assign(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;
element_set(e0, a0);
element_set(e1, a1);
element_set(e2, a2);
}
// 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 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;
}
void point_set_xy(EC_POINT p, const Element x, const Element y)
{
element_set(p->x, x);
element_set(p->y, y);
element_set_one(p->z);
p->isinfinity = FALSE;
}
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);
}
}
/* $c <- a*b$ */
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);
}
/* $e <- a^{-1}$ */
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);
}
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;
}
static void sn_set(element_ptr c, element_ptr a) {
point_ptr r = c->data, p = a->data;
if (p->inf_flag) {
r->inf_flag = 1;
return;
}
r->inf_flag = 0;
element_set(r->x, p->x);
element_set(r->y, p->y);
}
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);
}
static void record(element_t asum, element_t bsum, element_t snark,
darray_t hole, mpz_t counter) {
snapshot_ptr ss = pbc_malloc(sizeof(struct snapshot_s));
element_init_same_as(ss->a, asum);
element_init_same_as(ss->b, bsum);
element_init_same_as(ss->snark, snark);
element_set(ss->a, asum);
element_set(ss->b, bsum);
element_set(ss->snark, snark);
darray_append(hole, ss);
element_printf("snark %Zd: %B\n", counter, snark);
}
/* $e <- a^3$ */
static void gf32m_cubic(element_t e, element_t a) {
element_ptr a0 = GF32M(a)->_0, a1 = GF32M(a)->_1, e0 = GF32M(e)->_0, e1 =
GF32M(e)->_1;
field_ptr base = BASE(a);
element_t c0, c1;
element_init(c0, base);
element_init(c1, base);
element_cubic(c0, a0);
element_cubic(c1, a1);
element_neg(c1, c1); // c1 == -(a1^3)
element_set(e0, c0);
element_set(e1, c1);
element_clear(c0);
element_clear(c1);
}
// USER JOIN PHASE 4 - user key generation (Join)
int xsgs_user_join_phase4(XSGS_PUBLIC_KEY* gpk, XSGS_USER_DB_ENTRY* udbe,
XSGS_JOIN_PHASE3* jpd3, XSGS_JOIN_PHASE4* jpd4, char* upk_pem_filename) {
int ret;
pairing_ptr pairing = gpk->pairing;
field_ptr Fp = pairing->Zr;
DWORD msg_len = element_length_in_bytes(udbe->UCert.A);
BYTE* msg = (BYTE*) malloc(msg_len);
element_to_bytes(msg, udbe->UCert.A);
/* TODO Verify_PK_CA(cert_user) */
ret = xsgs_rsa_verify(upk_pem_filename, msg, msg_len, jpd3->S.sig,
jpd3->S.len);
free(msg);
udbe->S.len = jpd3->S.len;
udbe->S.sig = (BYTE*) malloc(udbe->S.len);
memcpy(udbe->S.sig, jpd3->S.sig, udbe->S.len);
element_init(jpd4->x, Fp);
element_set(jpd4->x, udbe->UCert.x);
return ret;
}
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);
}
void CipherText::compute_node(element_t& v, Node* node){//v amounts to s
if(node->getType() == LEAF){
Leaf* leaf = (Leaf*)node;
leaf->compute(&v, this->pub, this->p);
// printf("leaf: %d, %d, computed\n", leaf->getK(), leaf->getNum());
} else if (node->getType() == INTERNAL_NODE){
InternalNode* internalNode = (InternalNode*)node;
int num = internalNode->getNum();
int k = internalNode->getK();
Node** sons = internalNode->getSons();//??
// printf("internal Node: %d, %d\n", k, num);
element_t* ys = (element_t*)malloc(sizeof(element_t) * (num + 1));
element_init_Zr(ys[0], *(this->p));
element_set(ys[0], v); //set ys[0] to v
computePoints(ys, k, num); //compute other num point,
int i = 1;
for (i = 1; i <= num; i++){
compute_node(ys[i], sons[i - 1]);
}
}
}
/* 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);
}
static val_ptr eval_elem(tree_ptr t) {
// TODO: Write element_clone(), or at least element_new().
element_ptr e = (element_ptr)pbc_malloc(sizeof(*e));
element_init_same_as(e, t->elem);
element_set(e, t->elem);
return val_new_element(e);
}
void millertate(element_t z, element_t P, element_t Q)
{
element_t Z;
element_t z0;
element_init_same_as(Z, P);
element_init_same_as(z0, z);
element_set(Z, P);
do_tangent(z, Z, Q);
element_double(Z, Z);
do_vert(z0, Z, Q);
element_div(z, z, z0);
element_printf("presquare: z = %B\n", z);
element_square(z, z);
element_printf("square: z = %B\n", z);
do_tangent(z0, Z, Q);
element_mul(z, z, z0);
element_clear(z0);
element_clear(Z);
}
//Called in file encryption function to generate C0,C1,C0',C1' and EK
//returns CT,EK
void EK_CT_generate(char *gamma, int *shared_users, int num_users, unsigned char *pps, ct CT, element_t EK, char *t_str)
{
global_broadcast_params_t gbs;
element_t t;
int j;
//Global Setup of gbs params
setup_global_broadcast_params(&gbs, pps);
element_set_str(gbs->gamma, gamma, PBC_CONVERT_BASE); //it is important to set user gamma here else a random value will be used
//pick a random value of t from Zr
element_init_Zr(t, gbs->pairing);
element_random(t);
element_snprint(t_str,MAX_ELEMENT_LEN,t);
//compute C0=g^t
element_init(CT->OC0, gbs->pairing->G1);
element_pow_zn(CT->OC0, gbs->g, t);
//compute C1=(g^gamma)x(g[num_users+1-j]) for j in all shared users
element_init(CT->OC1, gbs->pairing->G1);
element_pow_zn(CT->OC1, gbs->g, gbs->gamma); //at this step C1 = g^gamma = v as given in paper
for(j=0;j<num_users;j++)
element_mul(CT->OC1, CT->OC1, gbs->gs[(gbs->num_users)-shared_users[j]]);
element_pow_zn(CT->OC1, CT->OC1, t);
//Duplicate C0'=C0
element_init(CT->C0, gbs->pairing->G1);
element_set(CT->C0,CT->OC0);
//Duplicate C1'=C1
element_init(CT->C1, gbs->pairing->G1);
element_set(CT->C1,CT->OC1);
//COMPUTE EK = e(g[n], g[1])^(t)
element_init(EK, gbs->pairing->GT);
element_pairing(EK, gbs->gs[0],gbs->gs[gbs->num_users-1]); //at this step EK = e(g[1],g[n])
element_pow_zn(EK,EK,t); //EK = e(g[1],g[n])^t
//free the memory for global broadcast params
element_clear(t);
FreeGBP(gbs);
return;
}
static void fi_square(element_ptr n, element_ptr a) {
eptr p = a->data;
eptr r = n->data;
element_t e0, e1;
element_init(e0, p->x->field);
element_init(e1, e0->field);
// Re(n) = x^2 - y^2 = (x+y)(x-y)
element_add(e0, p->x, p->y);
element_sub(e1, p->x, p->y);
element_mul(e0, e0, e1);
// Im(n) = 2xy
element_mul(e1, p->x, p->y);
element_add(e1, e1, e1);
element_set(r->x, e0);
element_set(r->y, e1);
element_clear(e0);
element_clear(e1);
}
void bn254_fp2_pow(Element z, const Element x, const mpz_t exp)
{
long t, i;
Element c;
element_init(c, field(z));
element_set(c, x);
t = (long)mpz_sizeinbase(exp, 2);
for (i = t - 2; i >= 0; i--)
{
element_sqr(c, c);
if (mpz_tstbit(exp, i)) { element_mul(c, c, x); }
}
element_set(z, c);
element_clear(c);
}
static void curve_invert(element_ptr c, element_ptr a) {
point_ptr r = (point_ptr)c->data, p = (point_ptr)a->data;
if (p->inf_flag) {
r->inf_flag = 1;
return;
}
r->inf_flag = 0;
element_set(r->x, p->x);
element_neg(r->y, p->y);
}
/* doing multiplication in GF(3^m)
* The function sets $e == a*b \in GF(3^m)$ */
static void gf3m_mult(element_t e, element_ptr a, element_t b) {
params *p = PARAM(a);
element_t aa, t, c;
element_init(aa, a->field);
element_set(aa, a);
a = aa; // clone $a$
element_init(t, a->field);
element_init(c, a->field);
unsigned i;
for (i = 0; i < p->m; i++) {
unsigned v = gf3m_get(b, i);
gf3m_f1(t, v, a); /* t == b[i]*a in GF(3^m) */
gf3m_add(c, c, t); /* c += b[i]*a in GF(3^m) */
gf3m_f2(a); /* a == a*x in GF(3^m) */
}
element_set(e, c);
element_clear(t);
element_clear(c);
element_clear(aa);
}
static val_ptr run_item(val_ptr v[]) {
mpz_t z;
mpz_init(z);
element_to_mpz(z, v[1]->elem);
int i = mpz_get_si(z);
mpz_clear(z);
element_ptr a = element_item(v[0]->elem, i);
element_ptr e = (element_ptr)pbc_malloc(sizeof(*e));
element_init_same_as(e, a);
element_set(e, a);
return val_new_element(e);
}
static void fq_square(element_ptr n, element_ptr a) {
eptr p = a->data;
eptr r = n->data;
element_ptr nqr = fq_nqr(n->field);
element_t e0, e1;
element_init(e0, p->x->field);
element_init(e1, e0->field);
element_square(e0, p->x);
element_square(e1, p->y);
element_mul(e1, e1, nqr);
element_add(e0, e0, e1);
element_mul(e1, p->x, p->y);
//TODO: which is faster?
//element_add(e1, e1, e1);
element_double(e1, e1);
element_set(r->x, e0);
element_set(r->y, e1);
element_clear(e0);
element_clear(e1);
}