/// <summary>
/// Computes the field polynomial for a ONB according to IEEE 1363 A.7.2
/// </summary>
protected override void ComputeFieldPolynomial()
{
if (m_Type == 1)
{
FieldPoly = new GF2Polynomial(DegreeN + 1, "ALL");
}
else if (m_Type == 2)
{
// 1. q = 1
GF2Polynomial q = new GF2Polynomial(DegreeN + 1, "ONE");
// 2. p = t+1
GF2Polynomial p = new GF2Polynomial(DegreeN + 1, "X");
p.AddToThis(q);
GF2Polynomial r;
int i;
// 3. for i = 1 to (m-1) do
for (i = 1; i < DegreeN; i++)
{
// r <- q
r = q;
// q <- p
q = p;
// p = tq+r
p = q.ShiftLeft();
p.AddToThis(r);
}
FieldPoly = p;
}
}
/// <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);
}
}
/// <summary>
/// Compute <c>this + addend</c> (overwrite <c>this</c>)
/// </summary>
///
/// <param name="Addend">The addend</param>
public override void AddToThis(IGFElement Addend)
{
if (!(Addend is GF2nPolynomialElement))
{
throw new Exception();
}
if (!mField.Equals(((GF2nPolynomialElement)Addend).mField))
{
throw new Exception();
}
polynomial.AddToThis(((GF2nPolynomialElement)Addend).polynomial);
}
/// <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);
}
}
/// <summary>
/// Computes the field polynomial for a ONB according to IEEE 1363 A.7.2
/// </summary>
protected override void ComputeFieldPolynomial()
{
if (_mType == 1)
{
FieldPoly = new GF2Polynomial(DegreeN + 1, "ALL");
}
else if (_mType == 2)
{
// 1. q = 1
GF2Polynomial q = new GF2Polynomial(DegreeN + 1, "ONE");
// 2. p = t+1
GF2Polynomial p = new GF2Polynomial(DegreeN + 1, "X");
p.AddToThis(q);
GF2Polynomial r;
int i;
// 3. for i = 1 to (m-1) do
for (i = 1; i < DegreeN; i++)
{
// r <- q
r = q;
// q <- p
q = p;
// p = tq+r
p = q.ShiftLeft();
p.AddToThis(r);
}
FieldPoly = p;
}
}
