int eb_upk(eb_t r, const eb_t p) {
fb_t t0, t1;
int res = 0;
fb_null(t0);
fb_null(t1);
TRY {
fb_new(t0);
fb_new(t1);
eb_rhs(t1, p);
if (eb_curve_is_super()) {
/* t0 = c^2. */
fb_sqr(t0, eb_curve_get_c());
/* t0 = 1/c^2. */
fb_inv(t0, t0);
/* t0 = t1/c^2. */
fb_mul(t0, t0, t1);
res = (fb_trc(t0) == 0);
/* Solve t1^2 + t1 = t0. */
fb_slv(t1, t0);
/* If this is not the correct solution, try the other. */
if (fb_get_bit(t1, 0) != fb_get_bit(p->y, 0)) {
fb_add_dig(t1, t1, 1);
}
/* x3 = x1, y3 = t1 * c, z3 = 1. */
fb_mul(r->y, t1, eb_curve_get_c());
} else {
fb_sqr(t0, p->x);
/* t0 = 1/x1^2. */
fb_inv(t0, t0);
/* t0 = t1/x1^2. */
fb_mul(t0, t0, t1);
res = (fb_trc(t0) == 0);
/* Solve t1^2 + t1 = t0. */
fb_slv(t1, t0);
/* If this is not the correct solution, try the other. */
if (fb_get_bit(t1, 0) != fb_get_bit(p->y, 0)) {
fb_add_dig(t1, t1, 1);
}
/* x3 = x1, y3 = t1 * x1, z3 = 1. */
fb_mul(r->y, t1, p->x);
}
fb_copy(r->x, p->x);
fb_set_dig(r->z, 1);
r->norm = 1;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fb_free(t0);
fb_free(t1);
}
return res;
}
void eb_hlv(eb_t r, const eb_t p) {
fb_t l, t;
fb_null(l);
fb_null(t);
TRY {
fb_new(l);
fb_new(t);
/* Solve l^2 + l = u + a. */
switch (eb_curve_opt_a()) {
case RLC_ZERO:
fb_copy(t, p->x);
break;
case RLC_ONE:
fb_add_dig(t, p->x, (dig_t)1);
break;
case RLC_TINY:
fb_add_dig(t, p->x, eb_curve_get_a()[0]);
break;
default:
fb_add(t, p->x, eb_curve_get_a());
break;
}
fb_slv(l, t);
if (p->norm == 1) {
/* Compute t = v + u * lambda. */
fb_mul(t, l, p->x);
fb_add(t, t, p->y);
} else {
/* Compute t = u * (u + lambda_P + lambda). */
fb_add(t, l, p->y);
fb_add(t, t, p->x);
fb_mul(t, t, p->x);
}
/* If Tr(t) = 0 then lambda_P = lambda, u = sqrt(t + u). */
if (fb_trc(t) == 0) {
fb_copy(r->y, l);
fb_add(t, t, p->x);
fb_srt(r->x, t);
} else {
/* Else lambda_P = lambda + 1, u = sqrt(t). */
fb_add_dig(r->y, l, 1);
fb_srt(r->x, t);
}
fb_set_dig(r->z, 1);
r->norm = 2;
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fb_free(l);
fb_free(t);
}
}
void fb_slv_basic(fb_t c, const fb_t a) {
int i;
fb_t t0;
fb_null(t0);
TRY {
fb_new(t0);
fb_copy(t0, a);
fb_copy(c, a);
for (i = 0; i < (FB_BITS - 1) / 2; i++) {
fb_sqr(c, c);
fb_sqr(c, c);
fb_add(c, c, t0);
}
fb_add_dig(c, c, fb_trc(c));
}
CATCH_ANY {
THROW(ERR_CAUGHT);
}
FINALLY {
fb_free(t0);
}
}
void fb_slv_quick(fb_t c, const fb_t a) {
fb_slvn_low(c, a);
fb_add_dig(c, c, fb_trc(c));
}
