public override ECFieldElement Add(
ECFieldElement b)
{
// No check performed here for performance reasons. Instead the
// elements involved are checked in ECPoint.F2m
// checkFieldElements(this, b);
IntArray iarrClone = (IntArray)this.x.Clone();
F2mFieldElement bF2m = (F2mFieldElement)b;
iarrClone.AddShifted(bF2m.x, 0);
return(new F2mFieldElement(m, k1, k2, k3, iarrClone));
}
public override ECFieldElement Invert()
{
// Inversion in F2m using the extended Euclidean algorithm
// Input: A nonzero polynomial a(z) of degree at most m-1
// Output: a(z)^(-1) mod f(z)
// u(z) := a(z)
IntArray uz = (IntArray)this.x.Clone();
// v(z) := f(z)
IntArray vz = new IntArray(t);
vz.SetBit(m);
vz.SetBit(0);
vz.SetBit(this.k1);
if (this.representation == Ppb) {
vz.SetBit(this.k2);
vz.SetBit(this.k3);
}
// g1(z) := 1, g2(z) := 0
IntArray g1z = new IntArray(t);
g1z.SetBit(0);
IntArray g2z = new IntArray(t);
// while u != 0
while (uz.GetUsedLength() > 0)
// while (uz.bitLength() > 1)
{
// j := deg(u(z)) - deg(v(z))
int j = uz.BitLength - vz.BitLength;
// If j < 0 then: u(z) <-> v(z), g1(z) <-> g2(z), j := -j
if (j < 0) {
IntArray uzCopy = uz;
uz = vz;
vz = uzCopy;
IntArray g1zCopy = g1z;
g1z = g2z;
g2z = g1zCopy;
j = -j;
}
// u(z) := u(z) + z^j * v(z)
// Note, that no reduction modulo f(z) is required, because
// deg(u(z) + z^j * v(z)) <= max(deg(u(z)), j + deg(v(z)))
// = max(deg(u(z)), deg(u(z)) - deg(v(z)) + deg(v(z))
// = deg(u(z))
// uz = uz.xor(vz.ShiftLeft(j));
// jInt = n / 32
int jInt = j >> 5;
// jInt = n % 32
int jBit = j & 0x1F;
IntArray vzShift = vz.ShiftLeft(jBit);
uz.AddShifted(vzShift, jInt);
// g1(z) := g1(z) + z^j * g2(z)
// g1z = g1z.xor(g2z.ShiftLeft(j));
IntArray g2zShift = g2z.ShiftLeft(jBit);
g1z.AddShifted(g2zShift, jInt);
}
return new F2mFieldElement(this.m, this.k1, this.k2, this.k3, g2z);
}
public override ECFieldElement Invert()
{
// Inversion in F2m using the extended Euclidean algorithm
// Input: A nonzero polynomial a(z) of degree at most m-1
// Output: a(z)^(-1) mod f(z)
// u(z) := a(z)
IntArray uz = (IntArray)this.x.Clone();
// v(z) := f(z)
IntArray vz = new IntArray(t);
vz.SetBit(m);
vz.SetBit(0);
vz.SetBit(this.k1);
if (this.representation == Ppb)
{
vz.SetBit(this.k2);
vz.SetBit(this.k3);
}
// g1(z) := 1, g2(z) := 0
IntArray g1z = new IntArray(t);
g1z.SetBit(0);
IntArray g2z = new IntArray(t);
// while u != 0
while (uz.GetUsedLength() > 0)
// while (uz.bitLength() > 1)
{
// j := deg(u(z)) - deg(v(z))
int j = uz.BitLength - vz.BitLength;
// If j < 0 then: u(z) <-> v(z), g1(z) <-> g2(z), j := -j
if (j < 0)
{
IntArray uzCopy = uz;
uz = vz;
vz = uzCopy;
IntArray g1zCopy = g1z;
g1z = g2z;
g2z = g1zCopy;
j = -j;
}
// u(z) := u(z) + z^j * v(z)
// Note, that no reduction modulo f(z) is required, because
// deg(u(z) + z^j * v(z)) <= max(deg(u(z)), j + deg(v(z)))
// = max(deg(u(z)), deg(u(z)) - deg(v(z)) + deg(v(z))
// = deg(u(z))
// uz = uz.xor(vz.ShiftLeft(j));
// jInt = n / 32
int jInt = j >> 5;
// jInt = n % 32
int jBit = j & 0x1F;
IntArray vzShift = vz.ShiftLeft(jBit);
uz.AddShifted(vzShift, jInt);
// g1(z) := g1(z) + z^j * g2(z)
// g1z = g1z.xor(g2z.ShiftLeft(j));
IntArray g2zShift = g2z.ShiftLeft(jBit);
g1z.AddShifted(g2zShift, jInt);
}
return(new F2mFieldElement(this.m, this.k1, this.k2, this.k3, g2z));
}