public bool IsPointOnCurve(MyBigInteger x, MyBigInteger y)
{
var result = x.ModPow(3, Prime) + A * x + _b - y.ModPow(2, Prime);
if (result % Prime == new MyBigInteger(0f))
{
return(true);
}
throw new Exception();
}
public List <MyBigInteger> ModSqrt(MyBigInteger modulus)
{
if (modulus is null || modulus == 0 || modulus._value.Sign == -1)
{
return(null);
}
var result = new List <MyBigInteger>();
//If the indicators value is "modulus - 1" then there is no modular square root
var indicator = ModPow((modulus - 1) / 2, modulus);
if (indicator == modulus - 1)
{
return(result);
}
//Special case for faster solution
if (modulus % 4 == 3)
{
var exponant = (modulus + 1) / 4;
var firstResult = ModPow(exponant, modulus);
if (firstResult * firstResult % modulus == this)
{
result.Add(firstResult);
result.Add(firstResult.Negate());
}
return(result);
}
var q = modulus - 1;
MyBigInteger s = 0;
while (q.IsEven)
{
q = q / 2;
s++;
}
MyBigInteger z = 1;
while (z.ModPow((modulus - 1) / 2, modulus) != modulus - 1)
{
z++;
}
var m = s;
var c = z.ModPow(q, modulus);
var t = ModPow(q, modulus);
var r = ModPow((q + 1) / 2, modulus);
while (true)
{
if (t == 0)
{
return(result);
}
if (t == 1)
{
if (r * r % modulus != this)
{
return(result);
}
result.Add(r);
result.Add(r.Negate());
return(result);
}
MyBigInteger i = 1;
while (t.ModPow(MyConstants.Two ^ i, modulus) != 1 && i < m - 1)
{
i++;
}
var b = c.ModPow(MyConstants.Two.ModPow(m - i - 1, modulus), modulus);
m = i;
c = b.ModPow(MyConstants.Two, modulus);
t = t * c % modulus;
r = r * b % modulus;
}
}