/// <summary>
/// Creates a new GF2nPolynomialElement using the given field <c>Gf</c> and int[] <c>Is</c> as value
/// </summary>
///
/// <param name="Gf">The GF2nField to use</param>
/// <param name="Is">The integer string to assign to this GF2nPolynomialElement</param>
public GF2nPolynomialElement(GF2nPolynomialField Gf, int[] Is)
{
mField = Gf;
mDegree = mField.Degree;
polynomial = new GF2Polynomial(mDegree, Is);
polynomial.ExpandN(Gf.Degree);
}
/// <summary>
/// Creates a new GF2nPolynomialElement using the given field <c>f</c> and byte[] <c>os</c> as value.
/// <para>The conversion is done according to 1363.</para>
/// </summary>
///
/// <param name="Gf">The GF2nField to use</param>
/// <param name="Os">The octet string to assign to this GF2nPolynomialElement</param>
public GF2nPolynomialElement(GF2nPolynomialField Gf, byte[] Os)
{
mField = Gf;
mDegree = mField.Degree;
polynomial = new GF2Polynomial(mDegree, Os);
polynomial.ExpandN(mDegree);
}
/// <summary>
/// Creates a new GF2nPolynomialElement using the given field and Bitstring
/// </summary>
///
/// <param name="Gf">The GF2nPolynomialField to use</param>
/// <param name="Gp">The desired value as Bitstring</param>
public GF2nPolynomialElement(GF2nPolynomialField Gf, GF2Polynomial Gp)
{
mField = Gf;
mDegree = mField.Degree;
polynomial = new GF2Polynomial(Gp);
polynomial.ExpandN(mDegree);
}
/// <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>
/// Reduces this GF2nPolynomialElement modulo the field-polynomial
/// </summary>
private void ReduceThis()
{
if (polynomial.Length > mDegree)
{ // really reduce ?
if (((GF2nPolynomialField)mField).IsTrinomial)
{ // fieldpolonomial
// is trinomial
int tc;
try
{
tc = ((GF2nPolynomialField)mField).Tc;
}
catch (Exception NATExc)
{
throw new Exception("GF2nPolynomialElement.Reduce: the field polynomial is not a trinomial!");
}
// do we have to use slow bitwise reduction ?
if (((mDegree - tc) <= 32) || (polynomial.Length > (mDegree << 1)))
{
ReduceTrinomialBitwise(tc);
return;
}
polynomial.ReduceTrinomial(mDegree, tc);
return;
}
else if (((GF2nPolynomialField)mField).IsPentanomial) // fieldpolynomial is pentanomial
{
int[] pc;
try
{
pc = ((GF2nPolynomialField)mField).Pc;
}
catch (Exception NATExc)
{
throw new Exception("GF2nPolynomialElement.Reduce: the field polynomial is not a pentanomial!");
}
// do we have to use slow bitwise reduction ?
if (((mDegree - pc[2]) <= 32) || (polynomial.Length > (mDegree << 1)))
{
ReducePentanomialBitwise(pc);
return;
}
polynomial.ReducePentanomial(mDegree, pc);
return;
}
else
{ // fieldpolynomial is something else
polynomial = polynomial.Remainder(mField.FieldPolynomial);
polynomial.ExpandN(mDegree);
return;
}
}
if (polynomial.Length < mDegree)
polynomial.ExpandN(mDegree);
}
/// <summary>
/// Returns the absolute quotient of <c>this</c> divided by <c>G</c> in a new GF2Polynomial
/// </summary>
///
/// <param name="G">A GF2Polynomial != 0</param>
///
/// <returns>Returns a new GF2Polynomial |_ <c>this</c> / <c>G</c></returns>
public GF2Polynomial Quotient(GF2Polynomial G)
{
// a div b = q / r
GF2Polynomial q = new GF2Polynomial(_length);
GF2Polynomial a = new GF2Polynomial(this);
GF2Polynomial b = new GF2Polynomial(G);
GF2Polynomial j;
int i;
if (b.IsZero())
throw new Exception();
a.ReduceN();
b.ReduceN();
if (a._length < b._length)
return new GF2Polynomial(0);
i = a._length - b._length;
q.ExpandN(i + 1);
while (i >= 0)
{
j = b.ShiftLeft(i);
a.SubtractFromThis(j);
a.ReduceN();
q.XorBit(i);
i = a._length - b._length;
}
return q;
}
/// <summary>
/// Multiplies this GF2Polynomial with <c>B</c> and returns the result in a new GF2Polynomial.
/// This method does not reduce the result in GF(2^N).
/// This method uses Karatzuba multiplication.
/// </summary>
///
/// <param name="B"> GF2Polynomial</param>
///
/// <returns>Returns a new GF2Polynomial (<c>this</c> * <c>B</c>)</returns>
public GF2Polynomial Multiply(GF2Polynomial B)
{
int n = Math.Max(_length, B._length);
ExpandN(n);
B.ExpandN(n);
return KaraMult(B);
}
/// <summary>
/// Divides <c>this</c> by <c>G</c> and returns the quotient and remainder in a new GF2Polynomial[2], quotient in [0], remainder in [1]
/// </summary>
///
/// <param name="G">A GF2Polynomial != 0</param>
///
/// <returns>Returns a new GF2Polynomial[2] containing quotient and remainder</returns>
public GF2Polynomial[] Divide(GF2Polynomial G)
{
// a div b = q / r
GF2Polynomial[] result = new GF2Polynomial[2];
GF2Polynomial q = new GF2Polynomial(_length);
GF2Polynomial a = new GF2Polynomial(this);
GF2Polynomial b = new GF2Polynomial(G);
GF2Polynomial j;
int i;
if (b.IsZero())
throw new Exception();
a.ReduceN();
b.ReduceN();
if (a._length < b._length)
{
result[0] = new GF2Polynomial(0);
result[1] = a;
return result;
}
i = a._length - b._length;
q.ExpandN(i + 1);
while (i >= 0)
{
j = b.ShiftLeft(i);
a.SubtractFromThis(j);
a.ReduceN();
q.XorBit(i);
i = a._length - b._length;
}
result[0] = q;
result[1] = a;
return result;
}