/// <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>
/// Calculates the multiplicative inverse of <c>this</c> and returns the result in a new GF2nPolynomialElement
/// </summary>
///
/// <returns>Returns <c>this</c>^(-1)</returns>
public GF2nPolynomialElement InvertEEA()
{
if (IsZero())
{
throw new ArithmeticException();
}
GF2Polynomial b = new GF2Polynomial(mDegree + 32, "ONE");
b.ReduceN();
GF2Polynomial c = new GF2Polynomial(mDegree + 32);
c.ReduceN();
GF2Polynomial u = GetGF2Polynomial();
GF2Polynomial v = mField.FieldPolynomial;
GF2Polynomial h;
int j;
u.ReduceN();
while (!u.IsOne())
{
u.ReduceN();
v.ReduceN();
j = u.Length - v.Length;
if (j < 0)
{
h = u;
u = v;
v = h;
h = b;
b = c;
c = h;
j = -j;
c.ReduceN(); // this increases the performance
}
u.ShiftLeftAddThis(v, j);
b.ShiftLeftAddThis(c, j);
}
b.ReduceN();
return(new GF2nPolynomialElement((GF2nPolynomialField)mField, b));
}
/// <summary>
/// Tests if the GF2nPolynomialElement has 'one' as value
/// </summary>
///
/// <returns>Returns true if <c>this</c> equals one (this == 1)</returns>
public override bool IsOne()
{
return(polynomial.IsOne());
}