/// <summary>
/// Shifts left <c>this</c> by <c>N</c> and stores the result in <c>this</c> PolynomialGF2n
/// </summary>
///
/// <param name="N">The amount the amount to shift the coefficients</param>
public void ShiftThisLeft(int N)
{
if (N > 0)
{
int i;
int oldSize = _size;
GF2nField f = _coeff[0].GetField();
Enlarge(_size + N);
for (i = oldSize - 1; i >= 0; i--)
{
_coeff[i + N] = _coeff[i];
}
if (_coeff[0] is GF2nPolynomialElement)
{
for (i = N - 1; i >= 0; i--)
{
_coeff[i] = GF2nPolynomialElement.Zero((GF2nPolynomialField)f);
}
}
else if (_coeff[0] is GF2nONBElement)
{
for (i = N - 1; i >= 0; i--)
{
_coeff[i] = GF2nONBElement.Zero((GF2nONBField)f);
}
}
}
}
/// <summary>
/// Enlarges the size of this PolynomialGF2n to <c>k</c> + 1
/// </summary>
///
/// <param name="K">The new maximum degree</param>
public void Enlarge(int K)
{
if (K <= _size)
{
return;
}
int i;
GF2nElement[] res = new GF2nElement[K];
Array.Copy(_coeff, 0, res, 0, _size);
GF2nField f = _coeff[0].GetField();
if (_coeff[0] is GF2nPolynomialElement)
{
for (i = _size; i < K; i++)
{
res[i] = GF2nPolynomialElement.Zero((GF2nPolynomialField)f);
}
}
else if (_coeff[0] is GF2nONBElement)
{
for (i = _size; i < K; i++)
{
res[i] = GF2nONBElement.Zero((GF2nONBField)f);
}
}
_size = K;
_coeff = res;
}
/// <summary>
/// Computes a random root of the given polynomial
/// </summary>
///
/// <param name="P">A polynomial</param>
///
/// <returns>A random root of the polynomial</returns>
public override GF2nElement RandomRoot(GF2Polynomial P)
{
// We are in B1!!!
GF2nPolynomial c;
GF2nPolynomial ut;
GF2nElement u;
GF2nPolynomial h;
int hDegree;
// 1. Set g(t) <- f(t)
GF2nPolynomial g = new GF2nPolynomial(P, this);
int gDegree = g.Degree;
int i;
// 2. while deg(g) > 1
while (gDegree > 1)
{
do
{
// 2.1 choose random u (element of) GF(2^m)
u = new GF2nONBElement(this, m_secRand);
ut = new GF2nPolynomial(2, GF2nONBElement.Zero(this));
// 2.2 Set c(t) <- ut
ut.Set(1, u);
c = new GF2nPolynomial(ut);
// 2.3 For i from 1 to m-1 do
for (i = 1; i <= DegreeN - 1; i++)
{
// 2.3.1 c(t) <- (c(t)^2 + ut) mod g(t)
c = c.MultiplyAndReduce(c, g);
c = c.Add(ut);
}
// 2.4 set h(t) <- GCD(c(t), g(t))
h = c.Gcd(g);
// 2.5 if h(t) is constant or deg(g) = deg(h) then go to
// step 2.1
hDegree = h.Degree;
gDegree = g.Degree;
}while ((hDegree == 0) || (hDegree == gDegree));
// 2.6 If 2deg(h) > deg(g) then set g(t) <- g(t)/h(t) ...
if ((hDegree << 1) > gDegree)
{
g = g.Quotient(h);
}
else // ... else g(t) <- h(t)
{
g = new GF2nPolynomial(h);
}
gDegree = g.Degree;
}
// 3. Output g(0)
return(g.At(0));
}
/// <summary>
/// Creates a new PolynomialGF2n from the given Bitstring <c>G</c> over the GF2nField <c>B1</c>
/// </summary>
///
/// <param name="G">The Bitstring to use</param>
/// <param name="B1">The field</param>
public GF2nPolynomial(GF2Polynomial G, GF2nField B1)
{
_size = B1.Degree + 1;
_coeff = new GF2nElement[_size];
int i;
if (B1 is GF2nONBField)
{
for (i = 0; i < _size; i++)
{
if (G.TestBit(i))
{
_coeff[i] = GF2nONBElement.One((GF2nONBField)B1);
}
else
{
_coeff[i] = GF2nONBElement.Zero((GF2nONBField)B1);
}
}
}
else if (B1 is GF2nPolynomialField)
{
for (i = 0; i < _size; i++)
{
if (G.TestBit(i))
{
_coeff[i] = GF2nPolynomialElement.One((GF2nPolynomialField)B1);
}
else
{
_coeff[i] = GF2nPolynomialElement.Zero((GF2nPolynomialField)B1);
}
}
}
else
{
throw new ArgumentException("GF2nPolynomial: PolynomialGF2n(Bitstring, GF2nField): B1 must be an instance of GF2nONBField or GF2nPolynomialField!");
}
}