status_t element_invert(element_t c, element_t a)
{
GroupType type = a->type;
EXIT_IF_NOT_SAME(a, c);
if(type == ZR) {
bn_t s;
bn_inits(s);
// compute c = (1 / a) mod n
bn_gcd_ext(s, c->bn, NULL, a->bn, a->order);
if(bn_sign(c->bn) == BN_NEG) bn_add(c->bn, c->bn, a->order);
bn_free(s);
}
else if(type == G1) {
g1_neg(c->g1, a->g1);
}
else if(type == G2) {
g2_neg(c->g2, a->g2);
}
else if(type == GT) {
gt_inv(c->gt, a->gt);
}
else {
return ELEMENT_INVALID_TYPES;
}
return ELEMENT_OK;
}
status_t element_div(element_t c, element_t a, element_t b)
{
GroupType type = a->type;
EXIT_IF_NOT_SAME(a, b);
LEAVE_IF(a->isInitialized != TRUE || b->isInitialized != TRUE || c->isInitialized != TRUE, "uninitialized arguments.");
LEAVE_IF( c->type != type, "result initialized but invalid type.");
if(type == ZR) {
if(bn_is_zero(b->bn)) return ELEMENT_DIV_ZERO;
// c = (1 / b) mod order
element_invert(c, b);
if(bn_is_one(a->bn)) return ELEMENT_OK;
// bn_div(c->bn, a->bn, b->bn);
// bn_mod(c->bn, c->bn, c->order);
// remainder of ((a * c) / order)
integer_t s;
bn_inits(s);
// c = (a * c) / order (remainder only)
bn_mul(s, a->bn, c->bn);
bn_div_rem(s, c->bn, s, a->order);
// if(bn_sign(c->bn) == BN_NEG) bn_add(c->bn, c->bn, a->order);
bn_free(s);
}
else if(type == G1) {
g1_sub(c->g1, a->g1, b->g1);
g1_norm(c->g1, c->g1);
}
else if(type == G2) {
g2_sub(c->g2, a->g2, b->g2);
g2_norm(c->g2, c->g2);
}
else if(type == GT) {
gt_t t;
gt_inits(t);
gt_inv(t, b->gt);
gt_mul(c->gt, a->gt, t);
gt_free(t);
}
else {
return ELEMENT_INVALID_TYPES;
}
return ELEMENT_OK;
}
status_t element_neg(element_t c, element_t a)
{
GroupType type = a->type;
EXIT_IF_NOT_SAME(a, c);
if(type == ZR) {
bn_neg(c->bn, a->bn);
}
else if(type == G1) {
g1_neg(c->g1, a->g1);
}
else if(type == G2) {
g2_neg(c->g2, a->g2);
}
else if(type == GT) {
gt_inv(c->gt, a->gt);
}
else {
return ELEMENT_INVALID_TYPES;
}
return ELEMENT_OK;
}
int cp_bgn_dec(dig_t *out, gt_t in[4], bgn_t prv) {
int i, result = STS_ERR;
g1_t g;
g2_t h;
gt_t t[4];
bn_t n, r, s;
bn_null(n);
bn_null(r);
bn_null(s);
g1_null(g);
g2_null(h);
TRY {
bn_new(n);
bn_new(r);
bn_new(s);
g1_new(g);
g2_new(h);
for (i = 0; i < 4; i++) {
gt_null(t[i]);
gt_new(t[i]);
}
gt_exp(t[0], in[0], prv->x);
gt_exp(t[0], t[0], prv->x);
gt_mul(t[1], in[1], in[2]);
gt_exp(t[1], t[1], prv->x);
gt_inv(t[1], t[1]);
gt_mul(t[3], in[3], t[1]);
gt_mul(t[3], t[3], t[0]);
gt_get_ord(n);
g1_get_gen(g);
g2_get_gen(h);
bn_mul(r, prv->x, prv->y);
bn_sqr(r, r);
bn_mul(s, prv->x, prv->y);
bn_mul(s, s, prv->z);
bn_sub(r, r, s);
bn_sub(r, r, s);
bn_sqr(s, prv->z);
bn_add(r, r, s);
bn_mod(r, r, n);
pc_map(t[1], g, h);
gt_exp(t[1], t[1], r);
gt_copy(t[2], t[1]);
if (gt_is_unity(t[3]) == 1) {
*out = 0;
result = STS_OK;
} else {
for (i = 0; i < INT_MAX; i++) {
if (gt_cmp(t[2], t[3]) == CMP_EQ) {
*out = i + 1;
result = STS_OK;
break;
}
gt_mul(t[2], t[2], t[1]);
}
}
} CATCH_ANY {
result = STS_ERR;
} FINALLY {
bn_free(n);
bn_free(r);
bn_free(s);
g1_free(g);
g2_free(h);
for (i = 0; i < 4; i++) {
gt_free(t[i]);
}
}
return result;
}