public override ECFieldElement Invert()
{
return(new SecT239FieldElement(
AbstractF2mCurve.Inverse(239, new int[] { 158 }, ToBigInteger())));
}
public override ECFieldElement Invert()
{
return(new SecT283FieldElement(
AbstractF2mCurve.Inverse(283, new int[] { 5, 7, 12 }, ToBigInteger())));
}
/**
* Computes the auxiliary values <code>s<sub>0</sub></code> and
* <code>s<sub>1</sub></code> used for partial modular reduction.
* @param curve The elliptic curve for which to compute
* <code>s<sub>0</sub></code> and <code>s<sub>1</sub></code>.
* @throws ArgumentException if <code>curve</code> is not a
* Koblitz curve (Anomalous Binary Curve, ABC).
*/
public static BigInteger[] GetSi(AbstractF2mCurve curve)
{
if(!curve.IsKoblitz)
throw new ArgumentException("si is defined for Koblitz curves only");
int m = curve.FieldSize;
int a = curve.A.ToBigInteger().IntValue;
sbyte mu = GetMu(a);
int shifts = GetShiftsForCofactor(curve.Cofactor);
int index = m + 3 - a;
BigInteger[] ui = GetLucas(mu, index, false);
if(mu == 1)
{
ui[0] = ui[0].Negate();
ui[1] = ui[1].Negate();
}
BigInteger dividend0 = BigInteger.One.Add(ui[1]).ShiftRight(shifts);
BigInteger dividend1 = BigInteger.One.Add(ui[0]).ShiftRight(shifts).Negate();
return new BigInteger[] { dividend0, dividend1 };
}
/**
* Returns the parameter <code>μ</code> of the elliptic curve.
* @param curve The elliptic curve from which to obtain <code>μ</code>.
* The curve must be a Koblitz curve, i.e. <code>a</code> Equals
* <code>0</code> or <code>1</code> and <code>b</code> Equals
* <code>1</code>.
* @return <code>μ</code> of the elliptic curve.
* @throws ArgumentException if the given ECCurve is not a Koblitz
* curve.
*/
public static sbyte GetMu(AbstractF2mCurve curve)
{
BigInteger a = curve.A.ToBigInteger();
sbyte mu;
if(a.SignValue == 0)
{
mu = -1;
}
else if(a.Equals(BigInteger.One))
{
mu = 1;
}
else
{
throw new ArgumentException("No Koblitz curve (ABC), TNAF multiplication not possible");
}
return mu;
}
public override ECFieldElement Invert()
{
return(new SecT571FieldElement(
AbstractF2mCurve.Inverse(571, new int[] { 2, 5, 10 }, ToBigInteger())));
}
public override ECFieldElement Invert()
{
return(new SecT163FieldElement(
AbstractF2mCurve.Inverse(163, new int[] { 3, 6, 7 }, ToBigInteger())));
}
public override ECFieldElement Invert()
{
return new SecT113FieldElement(
AbstractF2mCurve.Inverse(113, new int[]{ 9 }, ToBigInteger()));
}