private OmgNum _Carmichael(OmgNum phiP, OmgNum phiQ)
{
OmgNum pq = OmgOp.Multiply(phiP, phiQ);
OmgNum pqGCD = OmgOp.Gcd(phiP, phiQ);
OmgNum lcm = OmgOp.Div(pq, pqGCD);
pq.Release();
pqGCD.Release();
return(lcm);
}
private OmgNum _SelectExponent(OmgNum carmN)
{
OmgNum candidate = ((1 << 16) + 1).ToOmgNum();
OmgNum gcd = OmgOp.Gcd(candidate, carmN);
while (!gcd.IsOne())
{
gcd = OmgOp.Gcd(candidate.Inc(), carmN);
}
gcd.Release();
return(candidate);
}
public OmgNum FindFactor(OmgNum n, int maxIterations = -1)
{
m_iterations = 0;
m_current = n;
OmgNum x = OmgOp.Random(1.ToOmgNum(), OmgOp.Subtract(n, 2.ToOmgNum()));
OmgNum y = 1.ToOmgNum();
OmgNum i = 0.ToOmgNum();
OmgNum stage = 2.ToOmgNum();
OmgNum sub = OmgOp.Subtract(x, y).MakeAbs();
OmgNum gcd = OmgOp.Gcd(n, sub);
sub.Release();
while (gcd.IsOne())
{
if (maxIterations >= 0 && m_iterations++ > maxIterations)
{
return(null);
}
if (OmgOp.Equal(i, stage))
{
y.Release();
y = new OmgNum(x);
stage.MultByTwo();
}
OmgNum xSquare = OmgOp.Multiply(x, x).Inc();
x.Release();
x = OmgOp.Mod(xSquare, n);
xSquare.Release();
i.Inc();
sub = OmgOp.Subtract(x, y).MakeAbs();
gcd.Release();
gcd = OmgOp.Gcd(n, sub);
sub.Release();
}
return(gcd);
}