/// <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>
/// Tests random polynomials of degree (n+1) until an irreducible is found and stores the result in <c>field polynomial</c>.
/// This can take very long for huge degrees.
/// </summary>
///
/// <returns>Returns true</returns>
private bool TestRandom()
{
int l;
bool done = false;
FieldPoly = new GF2Polynomial(DegreeN + 1);
l = 0;
while (!done)
{
l++;
FieldPoly.Randomize();
FieldPoly.SetBit(DegreeN);
FieldPoly.SetBit(0);
if (FieldPoly.IsIrreducible())
{
done = true;
return done;
}
}
return done;
}
/// <summary>
/// Tests all trinomials of degree (n+1) until a irreducible is found and stores the result in <c>field polynomial</c>.
/// Returns false if no irreducible trinomial exists in GF(2^n). This can take very long for huge degrees.
/// </summary>
///
/// <returns>Returns true if an irreducible trinomial is found</returns>
private bool TestTrinomials()
{
int i, l;
bool done = false;
l = 0;
FieldPoly = new GF2Polynomial(DegreeN + 1);
FieldPoly.SetBit(0);
FieldPoly.SetBit(DegreeN);
for (i = 1; (i < DegreeN) && !done; i++)
{
FieldPoly.SetBit(i);
done = FieldPoly.IsIrreducible();
l++;
if (done)
{
_isTrinomial = true;
_tc = i;
return done;
}
FieldPoly.ResetBit(i);
done = FieldPoly.IsIrreducible();
}
return done;
}
/// <summary>
/// Tests all pentanomials of degree (n+1) until a irreducible is found and stores the result in <c>field polynomial</c>.
/// Returns false if no irreducible pentanomial exists in GF(2^n).
/// This can take very long for huge degrees.
/// </summary>
///
/// <returns>Returns true if an irreducible pentanomial is found</returns>
private bool TestPentanomials()
{
int i, j, k, l;
bool done = false;
l = 0;
FieldPoly = new GF2Polynomial(DegreeN + 1);
FieldPoly.SetBit(0);
FieldPoly.SetBit(DegreeN);
for (i = 1; (i <= (DegreeN - 3)) && !done; i++)
{
FieldPoly.SetBit(i);
for (j = i + 1; (j <= (DegreeN - 2)) && !done; j++)
{
FieldPoly.SetBit(j);
for (k = j + 1; (k <= (DegreeN - 1)) && !done; k++)
{
FieldPoly.SetBit(k);
if (((DegreeN & 1) != 0) | ((i & 1) != 0) | ((j & 1) != 0)
| ((k & 1) != 0))
{
done = FieldPoly.IsIrreducible();
l++;
if (done)
{
_isPentanomial = true;
_pc[0] = i;
_pc[1] = j;
_pc[2] = k;
return done;
}
}
FieldPoly.ResetBit(k);
}
FieldPoly.ResetBit(j);
}
FieldPoly.ResetBit(i);
}
return done;
}