public void PositiveModuloShouldAlwaysBePositive()
{
var rand = new Random800_90();
for (var i = 0; i < 100; i++)
{
var a = rand.GetRandomBigInteger(BigInteger.Pow(2, 1024));
var b = rand.GetRandomBigInteger(BigInteger.Pow(2, 1024) + 1, BigInteger.Pow(2, 2048));
var c = rand.GetRandomBigInteger(BigInteger.Pow(2, 2048));
// b is always greater than a
var result = (a - b).PosMod(c);
var negativeResult = (a - b) % c;
Assert.GreaterOrEqual(result, BigInteger.Zero);
// result - negativeResult should be a multiple of c.
Assert.AreEqual(BigInteger.Zero, (result + BigInteger.Abs(negativeResult)) % c);
}
}
/// <summary>
/// C.3.1 Probabilistic Primality Check, Miller-Rabin Algorithm
/// </summary>
/// <param name="n">Number</param>
/// <param name="k">Iterations</param>
/// <returns>True if probably prime. False if composite.</returns>
public static bool MillerRabin(BigInteger n, int k)
{
if (n < 2)
{
return(false);
}
if (n.IsEven)
{
return(false);
}
var s = n - 1;
while (s.IsEven)
{
s >>= 1;
}
var rand = new Random800_90();
for (var i = 0; i < k; i++)
{
var a = rand.GetRandomBigInteger(n - 1) + 1;
var temp = s;
var mod = BigInteger.ModPow(a, temp, n);
while (temp != n - 1 && mod != 1 && mod != n - 1)
{
mod = (mod * mod) % n;
temp = temp * 2;
}
if (mod != n - 1 && temp.IsEven)
{
return(false);
}
}
return(true);
}