/// <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 InvertSquare()
{
GF2nPolynomialElement n;
GF2nPolynomialElement u;
int i, j, k, b;
if (IsZero())
{
throw new ArithmeticException();
}
// b = (n-1)
b = m_Field.Degree - 1;
// n = a
n = new GF2nPolynomialElement(this);
n.m_polynomial.ExpandN((m_Degree << 1) + 32); // increase performance
n.m_polynomial.ReduceN();
// k = 1
k = 1;
// for i = (r-1) downto 0 do, r=bitlength(b)
for (i = BigMath.FloorLog(b) - 1; i >= 0; i--)
{
// u = n
u = new GF2nPolynomialElement(n);
// for j = 1 to k do
for (j = 1; j <= k; j++)
{
u.SquareThisPreCalc(); // u = u^2
}
// n = nu
n.MultiplyThisBy(u);
// k = 2k
k <<= 1;
// if b(i)==1
if ((b & m_bitMask[i]) != 0)
{
// n = n^2 * b
n.SquareThisPreCalc();
n.MultiplyThisBy(this);
// k = k+1
k += 1;
}
}
// outpur n^2
n.SquareThisPreCalc();
return(n);
}
/// <summary>
/// Calculates <c>this</c> to the power of <c>K</c> and returns the result in a new GF2nPolynomialElement
/// </summary>
///
/// <param name="K">The power</param>
///
/// <returns>Returns <c>this</c>^<c>K</c> in a new GF2nPolynomialElement</returns>
public GF2nPolynomialElement Power(int K)
{
if (K == 1)
{
return(new GF2nPolynomialElement(this));
}
GF2nPolynomialElement result = GF2nPolynomialElement.One((GF2nPolynomialField)m_Field);
if (K == 0)
{
return(result);
}
GF2nPolynomialElement x = new GF2nPolynomialElement(this);
x.m_polynomial.ExpandN((x.m_Degree << 1) + 32); // increase performance
x.m_polynomial.ReduceN();
for (int i = 0; i < m_Degree; i++)
{
if ((K & (1 << i)) != 0)
{
result.MultiplyThisBy(x);
}
x.Square();
}
return(result);
}
/// <summary>
/// Compute the product of this element and <c>factor</c>
/// </summary>
///
/// <param name="Factor">he factor</param>
///
/// <returns>Returns <c>this * factor</c> </returns>
public override IGFElement Multiply(IGFElement Factor)
{
GF2nPolynomialElement result = new GF2nPolynomialElement(this);
result.MultiplyThisBy(Factor);
return(result);
}
/// <summary>
/// Compute the product of this element and <c>factor</c>
/// </summary>
///
/// <param name="Factor">he factor</param>
///
/// <returns>Returns <c>this * factor</c> </returns>
public override IGFElement Multiply(IGFElement Factor)
{
GF2nPolynomialElement result = new GF2nPolynomialElement(this);
result.MultiplyThisBy(Factor);
return result;
}
/// <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 InvertSquare()
{
GF2nPolynomialElement n;
GF2nPolynomialElement u;
int i, j, k, b;
if (IsZero())
throw new ArithmeticException();
// b = (n-1)
b = mField.Degree - 1;
// n = a
n = new GF2nPolynomialElement(this);
n.polynomial.ExpandN((mDegree << 1) + 32); // increase performance
n.polynomial.ReduceN();
// k = 1
k = 1;
// for i = (r-1) downto 0 do, r=bitlength(b)
for (i = BigMath.FloorLog(b) - 1; i >= 0; i--)
{
// u = n
u = new GF2nPolynomialElement(n);
// for j = 1 to k do
for (j = 1; j <= k; j++)
u.SquareThisPreCalc(); // u = u^2
// n = nu
n.MultiplyThisBy(u);
// k = 2k
k <<= 1;
// if b(i)==1
if ((b & _bitMask[i]) != 0)
{
// n = n^2 * b
n.SquareThisPreCalc();
n.MultiplyThisBy(this);
// k = k+1
k += 1;
}
}
// outpur n^2
n.SquareThisPreCalc();
return n;
}