/// <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);
}
/// <summary>
/// Squares this GF2nPolynomialElement using GF2nFields squaring matrix.
/// <para>This is supposed to be fast when using a polynomial (no tri- or pentanomial) as fieldpolynomial.
/// Use SquarePreCalc when using a tri- or pentanomial as fieldpolynomial instead.</para>
/// </summary>
public void SquareThisMatrix()
{
GF2Polynomial result = new GF2Polynomial(mDegree);
for (int i = 0; i < mDegree; i++)
{
if (polynomial.VectorMult(((GF2nPolynomialField)mField).SquaringMatrix[mDegree - i - 1]))
{
result.SetBit(i);
}
}
polynomial = result;
}
/// <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 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 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;
}
/// <summary>
/// Squares this GF2nPolynomialElement using GF2nFields squaring matrix.
/// <para>This is supposed to be fast when using a polynomial (no tri- or pentanomial) as fieldpolynomial.
/// Use SquarePreCalc when using a tri- or pentanomial as fieldpolynomial instead.</para>
/// </summary>
public void SquareThisMatrix()
{
GF2Polynomial result = new GF2Polynomial(mDegree);
for (int i = 0; i < mDegree; i++)
{
if (polynomial.VectorMult(((GF2nPolynomialField)mField).SquaringMatrix[mDegree - i - 1]))
result.SetBit(i);
}
polynomial = result;
}
/// <summary>
/// Converts the given element in representation according to this field to a new element in
/// representation according to B1 using the change-of-basis matrix calculated by computeCOBMatrix.
/// </summary>
///
/// <param name="Elem">The GF2nElement to convert</param>
/// <param name="Basis">The basis to convert <c>Elem</c> to</param>
///
/// <returns>Returns <c>Elem</c> converted to a new element representation according to <c>basis</c></returns>
public GF2nElement Convert(GF2nElement Elem, GF2nField Basis)
{
if (Basis == this)
return (GF2nElement)Elem.Clone();
if (FieldPoly.Equals(Basis.FieldPoly))
return (GF2nElement)Elem.Clone();
if (DegreeN != Basis.DegreeN)
throw new Exception("GF2nField.Convert: B1 has a different degree and thus cannot be coverted to!");
int i;
GF2Polynomial[] COBMatrix;
i = Fields.IndexOf(Basis);
if (i == -1)
{
ComputeCOBMatrix(Basis);
i = Fields.IndexOf(Basis);
}
COBMatrix = (GF2Polynomial[])Matrices[i];
GF2nElement elemCopy = (GF2nElement)Elem.Clone();
if (elemCopy is GF2nONBElement)
((GF2nONBElement)elemCopy).ReverseOrder();
GF2Polynomial bs = new GF2Polynomial(DegreeN, elemCopy.ToFlexiBigInt());
bs.ExpandN(DegreeN);
GF2Polynomial result = new GF2Polynomial(DegreeN);
for (i = 0; i < DegreeN; i++)
{
if (bs.VectorMult(COBMatrix[i]))
result.SetBit(DegreeN - 1 - i);
}
if (Basis is GF2nPolynomialField)
{
return new GF2nPolynomialElement((GF2nPolynomialField)Basis, result);
}
else if (Basis is GF2nONBField)
{
GF2nONBElement res = new GF2nONBElement((GF2nONBField)Basis, result.ToFlexiBigInt());
res.ReverseOrder();
return res;
}
else
{
throw new Exception("GF2nField.convert: B1 must be an instance of GF2nPolynomialField or GF2nONBField!");
}
}
/// <summary>
/// Converts the given element in representation according to this field to a new element in
/// representation according to B1 using the change-of-basis matrix calculated by computeCOBMatrix.
/// </summary>
///
/// <param name="Elem">The GF2nElement to convert</param>
/// <param name="Basis">The basis to convert <c>Elem</c> to</param>
///
/// <returns>Returns <c>Elem</c> converted to a new element representation according to <c>basis</c></returns>
public GF2nElement Convert(GF2nElement Elem, GF2nField Basis)
{
if (Basis == this)
{
return((GF2nElement)Elem.Clone());
}
if (FieldPoly.Equals(Basis.FieldPoly))
{
return((GF2nElement)Elem.Clone());
}
if (DegreeN != Basis.DegreeN)
{
throw new Exception("GF2nField.Convert: B1 has a different degree and thus cannot be coverted to!");
}
int i;
GF2Polynomial[] COBMatrix;
i = Fields.IndexOf(Basis);
if (i == -1)
{
ComputeCOBMatrix(Basis);
i = Fields.IndexOf(Basis);
}
COBMatrix = (GF2Polynomial[])Matrices[i];
GF2nElement elemCopy = (GF2nElement)Elem.Clone();
if (elemCopy is GF2nONBElement)
{
((GF2nONBElement)elemCopy).ReverseOrder();
}
GF2Polynomial bs = new GF2Polynomial(DegreeN, elemCopy.ToFlexiBigInt());
bs.ExpandN(DegreeN);
GF2Polynomial result = new GF2Polynomial(DegreeN);
for (i = 0; i < DegreeN; i++)
{
if (bs.VectorMult(COBMatrix[i]))
{
result.SetBit(DegreeN - 1 - i);
}
}
if (Basis is GF2nPolynomialField)
{
return(new GF2nPolynomialElement((GF2nPolynomialField)Basis, result));
}
else if (Basis is GF2nONBField)
{
GF2nONBElement res = new GF2nONBElement((GF2nONBField)Basis, result.ToFlexiBigInt());
res.ReverseOrder();
return(res);
}
else
{
throw new Exception("GF2nField.convert: B1 must be an instance of GF2nPolynomialField or GF2nONBField!");
}
}
