public override ECFieldElement Invert()
{
IntArray uz = (IntArray)this.x.Clone();
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);
}
IntArray g1z = new IntArray(t);
g1z.SetBit(0);
IntArray g2z = new IntArray(t);
while (uz.GetUsedLength() > 0)
{
int j = uz.BitLength - vz.BitLength;
if (j < 0)
{
IntArray uzCopy = uz;
uz = vz;
vz = uzCopy;
IntArray g1zCopy = g1z;
g1z = g2z;
g2z = g1zCopy;
j = -j;
}
int jInt = j >> 5;
int jBit = j & 0x1F;
IntArray vzShift = vz.ShiftLeft(jBit);
uz.AddShifted(vzShift, jInt);
IntArray g2zShift = g2z.ShiftLeft(jBit);
g1z.AddShifted(g2zShift, jInt);
}
return(new F2mFieldElement(this.m, this.k1, this.k2, this.k3, g2z));
}
public void AddShifted(IntArray other, int shift)
{
int usedLenOther = other.GetUsedLength();
int newMinUsedLen = usedLenOther + shift;
if (newMinUsedLen > m_ints.Length)
{
m_ints = resizedInts(newMinUsedLen);
//Console.WriteLine("Resize required");
}
for (int i = 0; i < usedLenOther; i++)
{
m_ints[i + shift] ^= other.m_ints[i];
}
}
public void AddShifted(IntArray other, int shift)
{
var usedLenOther = other.GetUsedLength();
var newMinUsedLen = usedLenOther + shift;
if (newMinUsedLen > _ints.Length)
{
_ints = ResizedInts(newMinUsedLen);
//Console.WriteLine("Resize required");
}
for (var i = 0; i < usedLenOther; i++)
{
_ints[i + shift] ^= other._ints[i];
}
}
public override bool Equals(object o)
{
if (!(o is IntArray))
{
return(false);
}
IntArray other = (IntArray)o;
int usedLen = GetUsedLength();
if (other.GetUsedLength() != usedLen)
{
return(false);
}
for (int i = 0; i < usedLen; i++)
{
if (m_ints[i] != other.m_ints[i])
{
return(false);
}
}
return(true);
}
public void AddShifted(IntArray other, int shift)
{
int usedLenOther = other.GetUsedLength();
int newMinUsedLen = usedLenOther + shift;
if (newMinUsedLen > m_ints.Length)
{
m_ints = resizedInts(newMinUsedLen);
//Console.WriteLine("Resize required");
}
for (int i = 0; i < usedLenOther; i++)
{
m_ints[i + shift] ^= other.m_ints[i];
}
}
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 void AddShifted(IntArray other, int shift)
{
var usedLenOther = other.GetUsedLength();
var newMinUsedLen = usedLenOther + shift;
if (newMinUsedLen > _ints.Length)
{
_ints = ResizedInts(newMinUsedLen);
//Console.WriteLine("Resize required");
}
for (var i = 0; i < usedLenOther; i++)
{
_ints[i + shift] ^= other._ints[i];
}
}
