public int sign() {
if (isZero()) return 0;
if (field.isOrderOdd()) {
return BigIntegerUtils.isOdd(value) ? 1 : -1;
} else {
return value.add(value).compareTo(field.order);
}
}
public ZrElement sqrt() {
// Apply the Tonelli-Shanks Algorithm
Element e0 = field.newElement();
Element nqr = field.getNqr();
Element gInv = nqr.duplicate().invert();
// let q be the field.order of the field
// q - 1 = 2^s t, for some t odd
BigInteger t = field.order.subtract(BigInteger.ONE);
int s = BigIntegerUtils.scanOne(t, 0);
t = t.divide(BigInteger.valueOf(2 << (s - 1)));
BigInteger e = BigInteger.ZERO;
BigInteger orderMinusOne = field.order.subtract(BigInteger.ONE);
for (int i = 2; i <= s; i++) {
e0.set(gInv).pow(e);
e0.mul(this).pow(orderMinusOne.divide(BigInteger.valueOf(2 << (i - 1))));
if (!e0.isOne()) e = e.setBit(i - 1);
}
e0.set(gInv).pow(e);
e0.mul(this);
t = t.add(BigInteger.ONE);
t = t.divide(BigIntegerUtils.TWO);
e = e.divide(BigIntegerUtils.TWO);
// TODO(-):
// (suggested by Hovav Shacham) replace next three lines with
// element_pow2_mpz(x, e0, t, nqr, e);
// once sliding windows are implemented for pow2
e0.pow(t);
set(nqr).pow(e).mul(e0);
return this;
}
public ZrElement setToRandom() {
this.value = BigIntegerUtils.getRandom(field.order, field.getRandom());
return this;
}
public boolean isSqr() {
return BigInteger.ZERO.equals(value) || BigIntegerUtils.legendre(value, field.order) == 1;
}