/// <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;
}
}
/// <summary>
/// Does the recursion for Karatzuba multiplication
/// </summary>
///
/// <param name="B">A GF2Polynomial</param>
///
/// <returns><c>this * B</c></returns>
private GF2Polynomial KaraMult(GF2Polynomial B)
{
GF2Polynomial result = new GF2Polynomial(_length << 1);
if (_length <= 32)
{
result._value = Mult32(_value[0], B._value[0]);
return result;
}
if (_length <= 64)
{
result._value = Mult64(_value, B._value);
return result;
}
if (_length <= 128)
{
result._value = Mult128(_value, B._value);
return result;
}
if (_length <= 256)
{
result._value = Mult256(_value, B._value);
return result;
}
if (_length <= 512)
{
result._value = Mult512(_value, B._value);
return result;
}
int n = BigMath.FloorLog(_length - 1);
n = _bitMask[n];
GF2Polynomial a0 = Lower(((n - 1) >> 5) + 1);
GF2Polynomial a1 = Upper(((n - 1) >> 5) + 1);
GF2Polynomial b0 = B.Lower(((n - 1) >> 5) + 1);
GF2Polynomial b1 = B.Upper(((n - 1) >> 5) + 1);
GF2Polynomial c = a1.KaraMult(b1); // c = a1*b1
GF2Polynomial e = a0.KaraMult(b0); // e = a0*b0
a0.AddToThis(a1); // a0 = a0 + a1
b0.AddToThis(b1); // b0 = b0 + b1
GF2Polynomial d = a0.KaraMult(b0); // d = (a0+a1)*(b0+b1)
result.ShiftLeftAddThis(c, n << 1);
result.ShiftLeftAddThis(c, n);
result.ShiftLeftAddThis(d, n);
result.ShiftLeftAddThis(e, n);
result.AddToThis(e);
return result;
}
