/// <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;
}
/// <summary>
/// Returns the greatest common divisor of <c>this</c> and <c>G</c> in a new GF2Polynomial
/// </summary>
///
/// <param name="G">A GF2Polynomial != 0</param>
///
/// <returns>Returns a new GF2Polynomial gcd(<c>this</c>,<c>g</c>)</returns>
public GF2Polynomial Gcd(GF2Polynomial G)
{
if (IsZero() && G.IsZero())
throw new ArithmeticException("Both operands of gcd equal zero.");
if (IsZero())
return new GF2Polynomial(G);
if (G.IsZero())
return new GF2Polynomial(this);
GF2Polynomial a = new GF2Polynomial(this);
GF2Polynomial b = new GF2Polynomial(G);
GF2Polynomial c;
while (!b.IsZero())
{
c = a.Remainder(b);
a = b;
b = c;
}
return a;
}
