public static BigInteger FindSmallPrimes(int bits)
{
if (bits > 20)
{
throw new ArgumentException("bits > 20");
}
Log.MethodEnter("TrialDivision.CheckForSmallComposites", nameof(bits), bits);
BigInteger result = 0;
using (executionTimer.StartTimer())
{
long n = 0;
bool composite = true;
while (composite)
{
n = 1 << (bits - 1);
for (int i = 0; i < bits - 1; i++)
{
n |= CryptoRandomSingleton.Next(2) << i;
}
composite = !Eratosthenes.IsPrime(n);
}
result = n;
}
Log.MethodLeave();
return(result);
}
/// <summary>
/// Returns a probable prime of size bits and will search n rounds for a composite
/// </summary>
/// <param name="bitSize">Size of prime, in bits</param>
/// <param name="testCount">Number of different bases to use when testing probable prime for composites as evidence of primality</param>
/// <returns></returns>
public BigInteger GetProbablePrime(int bitSize, int testCount)
{
BigInteger result = 0;
//Log.Message(".");
Log.MethodEnter("ProvablePrime", nameof(bitSize), bitSize);
if (cancelToken.IsCancellationRequested)
{
Log.Message("ProvablePrime.CancellationToken.IsCancellationRequested();");
Log.MethodLeave();
return(-1);
}
if (bitSize <= 20)
{
Log.Message("***MAXIMUM RECURSION DEPT REACHED");
result = TrialDivision.FindSmallPrimes(bitSize);
Log.Message("***Hopeful prime: {0}", result);
}
else
{
//double c = 0.1;
int m = 20;
double r = 0.5;
if (bitSize > 2 * m)
{
double rnd = 0;
bool done = false;
while (!done)
{
rnd = CryptoRandomSingleton.NextDouble();
r = Math.Pow(2, rnd - 1);
done = (bitSize - r * bitSize) > m;
}
}
int newBits = (int)Math.Floor(r * bitSize) + 1;
BigInteger smallPrime = GetProbablePrime(newBits, testCount);
if (smallPrime == -1)
{
Log.MethodLeave();
return(-1);
}
Log.Message("After Recursion: Length = {0}", smallPrime.ToString().Length);
BigInteger pow = BigInteger.Pow(Two, bitSize - 1);
BigInteger Q = Two * smallPrime;
BigInteger I = pow / Q;
bool success = false;
while (!success)
{
if (cancelToken.IsCancellationRequested)
{
Log.Message("ProvablePrime.CancellationToken.IsCancellationRequested();");
Log.MethodLeave();
return(-1);
}
//LogMethod("Loop[{0}]: TestComposite({1})", _loopCount, result);
BigInteger J = I + 1;
BigInteger K = 2 * I;
BigInteger rand1 = CryptoRandomSingleton.RandomRange(J, K);
result = 2 * rand1;
result = result * smallPrime;
result = result + 1;
bool isPrime = false;
if (Eratosthenes.IsTooLarge(result))
{
isPrime = true;
}
else
{
isPrime = Eratosthenes.IsPrime(result);
}
if (isPrime)
{
//LogMethod("ProvablePrime.RandomRange(J: {0}, K: {1}) = {2}", J, K, rand1);
if (MillerRabin.IsProbablyPrime(result, testCount))
{
success = true;
string cert = MillerRabin.GetCertificateOfPrimality(result, rand1);
if (cert != null)
{
Log.Message(cert);
}
}
}
}
}
//Log.Message(".");
Log.MethodLeave();
return(result);
}