public bool IsOnCurve(AffinePoint P)
{
var x = P.X;
var t = (x * (x * x + A) + B).ModPositive(this.P);
if (BigIntegerExtension.JacobiSymbol(t, this.P) == -1)
{
return(false);
}
return(true);
}
public AffinePoint GetRandomAffinePoint()
{
BigIntegerRandom rand = new BigIntegerRandom();
var start = rand.Next(0, P);
var x = start;
BigInteger t;
do
{
t = (x * (x * x + A) + B).ModPositive(P);
if (BigIntegerExtension.JacobiSymbol(t, P) != -1)
{
return(new AffinePoint(x, BigIntegerExtension.Sqrt(t).ModPositive(P), this));
}
if (x > P - 1)
{
x = -1;
}
x++;
}while (x != start);
return(GetInfiniteAffinePoint());
}