private bool LucasStrongTestHelper(BigInteger thisVal)
{
long D = 5, sign = -1, dCount = 0;
bool done = false;
while (!done)
{
int Jresult = Jacobi(D, thisVal);
if (Jresult == -1)
done = true;
else
{
if (Jresult == 0 && Math.Abs(D) < thisVal)
return false;
if (dCount == 20)
{
BigInteger root = thisVal.Sqrt();
if (root * root == thisVal)
return false;
}
D = (Math.Abs(D) + 2) * sign;
sign = -sign;
}
dCount++;
}
long Q = (1 - D) >> 2;
BigInteger p_add1 = thisVal + 1;
int s = 0;
for (int index = 0; index < p_add1.DataLength; index++)
{
uint mask = 0x01;
for (int i = 0; i < 32; i++)
{
if ((p_add1._data[index] & mask) != 0)
{
index = p_add1.DataLength;
break;
}
mask <<= 1;
s++;
}
}
BigInteger t = p_add1 >> s;
BigInteger constant = new BigInteger();
int nLen = thisVal.DataLength << 1;
constant._data[nLen] = 0x00000001;
constant.DataLength = nLen + 1;
constant = constant / thisVal;
BigInteger[] lucas = LucasSequenceHelper(1, Q, t, thisVal, constant, 0);
bool isPrime = false;
if ((lucas[0].DataLength == 1 && lucas[0]._data[0] == 0) ||
(lucas[1].DataLength == 1 && lucas[1]._data[0] == 0))
{
isPrime = true;
}
for (int i = 1; i < s; i++)
{
if (!isPrime)
{
lucas[1] = thisVal.BarrettReduction(lucas[1] * lucas[1], thisVal, constant);
lucas[1] = (lucas[1] - (lucas[2] << 1)) % thisVal;
lucas[1] = ((lucas[1] * lucas[1]) - (lucas[2] << 1)) % thisVal;
if ((lucas[1].DataLength == 1 && lucas[1]._data[0] == 0))
isPrime = true;
}
lucas[2] = thisVal.BarrettReduction(lucas[2] * lucas[2], thisVal, constant);
}
if (isPrime)
{
BigInteger g = thisVal.Gcd(Q);
if (g.DataLength == 1 && g._data[0] == 1)
{
if ((lucas[2]._data[MAX_LENGTH - 1] & 0x80000000) != 0)
lucas[2] += thisVal;
BigInteger temp = (Q * BigInteger.Jacobi(Q, thisVal)) % thisVal;
if ((temp._data[MAX_LENGTH - 1] & 0x80000000) != 0)
temp += thisVal;
if (lucas[2] != temp)
isPrime = false;
}
}
return isPrime;
}
/// <summary>
/// Probabilistic prime test based on Rabin-Miller's test.
/// </summary>
/// <param name="confidence">The amount of times/iterations to check the primality of the current instance.</param>
/// <returns>true if the current instance is a strong pseudo-prime to randomly chosen bases, otherwise false if not prime.</returns>
public bool RabinMillerTest(int confidence)
{
BigInteger thisVal;
if ((_data[MAX_LENGTH - 1] & 0x80000000) != 0)
thisVal = -this;
else
thisVal = this;
if (thisVal.DataLength == 1)
{
if (thisVal._data[0] == 0 || thisVal._data[0] == 1)
return false;
else if (thisVal._data[0] == 2 || thisVal._data[0] == 3)
return true;
}
if ((thisVal._data[0] & 0x1) == 0)
return false;
BigInteger p_sub1 = thisVal - (new BigInteger(1));
int s = 0;
for (int index = 0; index < p_sub1.DataLength; index++)
{
uint mask = 0x01;
for (int i = 0; i < 32; i++)
{
if ((p_sub1._data[index] & mask) != 0)
{
index = p_sub1.DataLength;
break;
}
mask <<= 1;
s++;
}
}
BigInteger t = p_sub1 >> s;
int bits = thisVal.BitCount();
BigInteger a = new BigInteger();
Random rand = new Random();
for (int round = 0; round < confidence; round++)
{
bool done = false;
while (!done)
{
int testBits = 0;
while (testBits < 2)
testBits = (int)(rand.NextDouble() * bits);
a.GenRandomBits(testBits, rand);
int byteLen = a.DataLength;
if (byteLen > 1 || (byteLen == 1 && a._data[0] != 1))
done = true;
}
BigInteger gcdTest = a.Gcd(thisVal);
if (gcdTest.DataLength == 1 && gcdTest._data[0] != 1)
return false;
BigInteger b = a.ModPow(t, thisVal);
bool result = false;
if (b.DataLength == 1 && b._data[0] == 1)
result = true;
for (int j = 0; result == false && j < s; j++)
{
if (b == p_sub1)
{
result = true;
break;
}
b = (b * b) % thisVal;
}
if (result == false)
return false;
}
return true;
}