/// <summary>
/// Creates a new PolynomialGF2n from the given Bitstring <c>G</c> over the GF2nField <c>B1</c>
/// </summary>
///
/// <param name="G">The Bitstring to use</param>
/// <param name="B1">The field</param>
public GF2nPolynomial(GF2Polynomial G, GF2nField B1)
{
_size = B1.Degree + 1;
_coeff = new GF2nElement[_size];
int i;
if (B1 is GF2nONBField)
{
for (i = 0; i < _size; i++)
{
if (G.TestBit(i))
_coeff[i] = GF2nONBElement.One((GF2nONBField)B1);
else
_coeff[i] = GF2nONBElement.Zero((GF2nONBField)B1);
}
}
else if (B1 is GF2nPolynomialField)
{
for (i = 0; i < _size; i++)
{
if (G.TestBit(i))
_coeff[i] = GF2nPolynomialElement.One((GF2nPolynomialField)B1);
else
_coeff[i] = GF2nPolynomialElement.Zero((GF2nPolynomialField)B1);
}
}
else
{
throw new ArgumentException("GF2nPolynomial: PolynomialGF2n(Bitstring, GF2nField): B1 must be an instance of GF2nONBField or GF2nPolynomialField!");
}
}
/// <summary>
/// Creates a new GF2nField of degree <c>i</c> and uses the given <c>G</c> as field polynomial.
/// <para>The <c>G</c> is checked whether it is irreducible. This can take some time if <c>Degree</c> is huge!</para>
/// </summary>
///
/// <param name="Degree">The degree of the GF2nField</param>
/// <param name="G">The field polynomial to use</param>
public GF2nPolynomialField(int Degree, GF2Polynomial G)
{
if (Degree < 3)
throw new ArgumentException("degree must be at least 3");
if (G.Length != Degree + 1)
throw new Exception();
if (!G.IsIrreducible())
throw new Exception();
DegreeN = Degree;
// fieldPolynomial = new Bitstring(polynomial);
FieldPoly = G;
ComputeSquaringMatrix();
int k = 2; // check if the polynomial is a trinomial or pentanomial
for (int j = 1; j < FieldPoly.Length - 1; j++)
{
if (FieldPoly.TestBit(j))
{
k++;
if (k == 3)
_tc = j;
if (k <= 5)
_pc[k - 3] = j;
}
}
if (k == 3)
_isTrinomial = true;
if (k == 5)
_isPentanomial = true;
Fields = new ArrayList();
Matrices = new ArrayList();
}
/// <summary>
/// Calculates the multiplicative inverse of <c>this</c> using the modified almost inverse algorithm and returns the result in a new GF2nPolynomialElement
/// </summary>
///
/// <returns>Returns <c>this</c>^(-1)</returns>
public GF2nPolynomialElement InvertMAIA()
{
if (IsZero())
{
throw new ArithmeticException();
}
GF2Polynomial b = new GF2Polynomial(mDegree, "ONE");
GF2Polynomial c = new GF2Polynomial(mDegree);
GF2Polynomial u = GetGF2Polynomial();
GF2Polynomial v = mField.FieldPolynomial;
GF2Polynomial h;
while (true)
{
while (!u.TestBit(0))
{ // x|u (x divides u)
u.ShiftRightThis(); // u = u / x
if (!b.TestBit(0))
{
b.ShiftRightThis();
}
else
{
b.AddToThis(mField.FieldPolynomial);
b.ShiftRightThis();
}
}
if (u.IsOne())
return new GF2nPolynomialElement((GF2nPolynomialField)mField, b);
u.ReduceN();
v.ReduceN();
if (u.Length < v.Length)
{
h = u;
u = v;
v = h;
h = b;
b = c;
c = h;
}
u.AddToThis(v);
b.AddToThis(c);
}
}