/**
* The Miller-Rabin primality test.
*
* @param n the input number to be tested.
* @param t the number of trials.
* @return {@code false} if the number is definitely compose, otherwise
* {@code true} with probability {@code 1 - 4<sup>(-t)</sup>}.
* @ar.org.fitc.ref "D. Knuth, The Art of Computer Programming Vo.2, Section
* 4.5.4., Algorithm P"
*/
private static bool MillerRabin(BigInteger n, int t, CancellationToken argCancelToken)
{
argCancelToken.ThrowIfCancellationRequested();
// PRE: n >= 0, t >= 0
BigInteger x; // x := UNIFORM{2...n-1}
BigInteger y; // y := x^(q * 2^j) mod n
BigInteger n_minus_1 = n - BigInteger.One; // n-1
int bitLength = n_minus_1.BitLength; // ~ log2(n-1)
// (q,k) such that: n-1 = q * 2^k and q is odd
int k = n_minus_1.LowestSetBit;
BigInteger q = n_minus_1 >> k;
Random rnd = new Random();
for (int i = 0; i < t; i++)
{
argCancelToken.ThrowIfCancellationRequested();
// To generate a witness 'x', first it use the primes of table
if (i < primes.Length)
{
x = BIprimes[i];
}
else
{/*
* It generates random witness only if it's necesssary. Note
* that all methods would call Miller-Rabin with t <= 50 so
* this part is only to do more robust the algorithm
*/
do
{
argCancelToken.ThrowIfCancellationRequested();
x = new BigInteger(bitLength, rnd);
} while ((x.CompareTo(n) >= BigInteger.EQUALS) || (x.Sign == 0) ||
x.IsOne);
}
y = BigMath.ModPow(x, q, n);
if (y.IsOne || y.Equals(n_minus_1))
{
continue;
}
for (int j = 1; j < k; j++)
{
argCancelToken.ThrowIfCancellationRequested();
if (y.Equals(n_minus_1))
{
continue;
}
y = (y * y) % n;
if (y.IsOne)
{
return(false);
}
}
if (!y.Equals(n_minus_1))
{
return(false);
}
}
return(true);
}