/// <summary>
/// Calculates <c>this</c> to the power of <c>K</c> and returns the result in a new GF2nPolynomialElement
/// </summary>
///
/// <param name="K">The power</param>
///
/// <returns>Returns <c>this</c>^<c>K</c> in a new GF2nPolynomialElement</returns>
public GF2nPolynomialElement Power(int K)
{
if (K == 1)
{
return(new GF2nPolynomialElement(this));
}
GF2nPolynomialElement result = GF2nPolynomialElement.One((GF2nPolynomialField)mField);
if (K == 0)
{
return(result);
}
GF2nPolynomialElement x = new GF2nPolynomialElement(this);
x.polynomial.ExpandN((x.mDegree << 1) + 32); // increase performance
x.polynomial.ReduceN();
for (int i = 0; i < mDegree; i++)
{
if ((K & (1 << i)) != 0)
{
result.MultiplyThisBy(x);
}
x.Square();
}
return(result);
}
/// <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>
/// Computes the change-of-basis matrix for basis conversion according to 1363.
/// The result is stored in the lists fields and matrices.
/// </summary>
///
/// <param name="B1">The GF2nField to convert to</param>
public override void ComputeCOBMatrix(GF2nField B1)
{
// we are in B0 here!
if (DegreeN != B1.Degree)
{
throw new ArgumentException("GF2nPolynomialField.computeCOBMatrix: B1 has a different degree and thus cannot be coverted to!");
}
if (B1 is GF2nONBField)
{
// speedup (calculation is done in PolynomialElements instead of ONB)
B1.ComputeCOBMatrix(this);
return;
}
int i, j;
GF2nElement[] gamma;
GF2nElement u;
GF2Polynomial[] COBMatrix = new GF2Polynomial[DegreeN];
for (i = 0; i < DegreeN; i++)
{
COBMatrix[i] = new GF2Polynomial(DegreeN);
}
// find Random Root
do
{
// u is in representation according to B1
u = B1.RandomRoot(FieldPoly);
}while (u.IsZero());
// build gamma matrix by multiplying by u
if (u is GF2nONBElement)
{
gamma = new GF2nONBElement[DegreeN];
gamma[DegreeN - 1] = GF2nONBElement.One((GF2nONBField)B1);
}
else
{
gamma = new GF2nPolynomialElement[DegreeN];
gamma[DegreeN - 1] = GF2nPolynomialElement.One((GF2nPolynomialField)B1);
}
gamma[DegreeN - 2] = u;
for (i = DegreeN - 3; i >= 0; i--)
{
gamma[i] = (GF2nElement)gamma[i + 1].Multiply(u);
}
if (B1 is GF2nONBField)
{
// convert horizontal gamma matrix by vertical Bitstrings
for (i = 0; i < DegreeN; i++)
{
for (j = 0; j < DegreeN; j++)
{
// TODO remember: ONB treats its Bits in reverse order !!!
if (gamma[i].TestBit(DegreeN - j - 1))
{
COBMatrix[DegreeN - j - 1].SetBit(DegreeN - i - 1);
}
}
}
}
else
{
// convert horizontal gamma matrix by vertical Bitstrings
for (i = 0; i < DegreeN; i++)
{
for (j = 0; j < DegreeN; j++)
{
if (gamma[i].TestBit(j))
{
COBMatrix[DegreeN - j - 1].SetBit(DegreeN - i - 1);
}
}
}
}
// store field and matrix for further use
Fields.Add(B1);
Matrices.Add(COBMatrix);
// store field and inverse matrix for further use in B1
B1.Fields.Add(this);
B1.Matrices.Add(InvertMatrix(COBMatrix));
}