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;
}
private static BigInteger[] LucasSequenceHelper(BigInteger P, BigInteger Q, BigInteger k, BigInteger n, BigInteger constant, int s)
{
BigInteger[] result = new BigInteger[3];
if ((k._data[0] & 0x00000001) == 0)
throw (new ArgumentException("Argument k must be odd."));
int numbits = k.BitCount();
uint mask = (uint)0x1 << ((numbits & 0x1F) - 1);
BigInteger v = 2 % n, Q_k = 1 % n,
v1 = P % n, u1 = Q_k;
bool flag = true;
for (int i = k.DataLength - 1; i >= 0; i--)
{
while (mask != 0)
{
if (i == 0 && mask == 0x00000001)
break;
if ((k._data[i] & mask) != 0)
{
u1 = (u1 * v1) % n;
v = ((v * v1) - (P * Q_k)) % n;
v1 = n.BarrettReduction(v1 * v1, n, constant);
v1 = (v1 - ((Q_k * Q) << 1)) % n;
if (flag)
flag = false;
else
Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);
Q_k = (Q_k * Q) % n;
}
else
{
u1 = ((u1 * v) - Q_k) % n;
v1 = ((v * v1) - (P * Q_k)) % n;
v = n.BarrettReduction(v * v, n, constant);
v = (v - (Q_k << 1)) % n;
if (flag)
{
Q_k = Q % n;
flag = false;
}
else
Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);
}
mask >>= 1;
}
mask = 0x80000000;
}
u1 = ((u1 * v) - Q_k) % n;
v = ((v * v1) - (P * Q_k)) % n;
if (flag)
flag = false;
else
Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);
Q_k = (Q_k * Q) % n;
for (int i = 0; i < s; i++)
{
u1 = (u1 * v) % n;
v = ((v * v) - (Q_k << 1)) % n;
if (flag)
{
Q_k = Q % n;
flag = false;
}
else
Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);
}
result[0] = u1;
result[1] = v;
result[2] = Q_k;
return result;
}