/// <summary>
/// Checks if <c>this</c> is irreducible, according to IEEE P1363, A.5.5, p103.
/// <para>Note: The algorithm from IEEE P1363, A5.5 can be used to check a polynomial with coefficients in GF(2^r) for irreducibility.
/// As this class only represents polynomials with coefficients in GF(2), the algorithm is adapted to the case r=1.</para>
/// </summary>
///
/// <returns>Returns true if <c>this</c> is irreducible</returns>
public bool IsIrreducible()
{
if (IsZero())
return false;
GF2Polynomial f = new GF2Polynomial(this);
int d, i;
GF2Polynomial u, g;
GF2Polynomial dummy;
f.ReduceN();
d = f._length - 1;
u = new GF2Polynomial(f._length, "X");
for (i = 1; i <= (d >> 1); i++)
{
u.SquareThisPreCalc();
u = u.Remainder(f);
dummy = u.Add(new GF2Polynomial(32, "X"));
if (!dummy.IsZero())
{
g = f.Gcd(dummy);
if (!g.IsOne())
return false;
}
else
{
return false;
}
}
return true;
}