private F2mFieldElement(int m, int k1, int k2, int k3, IntArray x)
{
t = (m + 31) >> 5;
this.x = x;
this.m = m;
this.k1 = k1;
this.k2 = k2;
this.k3 = k3;
if ((k2 == 0) && (k3 == 0))
{
this.representation = Tpb;
}
else
{
this.representation = Ppb;
}
}
/**
* Constructor for Ppb.
* @param m The exponent <code>m</code> of
* <code>F<sub>2<sup>m</sup></sub></code>.
* @param k1 The integer <code>k1</code> where <code>x<sup>m</sup> +
* x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
* represents the reduction polynomial <code>f(z)</code>.
* @param k2 The integer <code>k2</code> where <code>x<sup>m</sup> +
* x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
* represents the reduction polynomial <code>f(z)</code>.
* @param k3 The integer <code>k3</code> where <code>x<sup>m</sup> +
* x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
* represents the reduction polynomial <code>f(z)</code>.
* @param x The BigInteger representing the value of the field element.
*/
public F2mFieldElement(
int m,
int k1,
int k2,
int k3,
BigInteger x)
{
// t = m / 32 rounded up to the next integer
this.t = (m + 31) >> 5;
this.x = new IntArray(x, t);
if ((k2 == 0) && (k3 == 0))
{
this.representation = Tpb;
}
else
{
if (k2 >= k3)
throw new ArgumentException("k2 must be smaller than k3");
if (k2 <= 0)
throw new ArgumentException("k2 must be larger than 0");
this.representation = Ppb;
}
if (x.Sign < 0)
throw new ArgumentException("x value cannot be negative");
this.m = m;
this.k1 = k1;
this.k2 = k2;
this.k3 = k3;
}
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.Copy();
// 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 IntArray Square(int m)
{
// TODO make the table static readonly
int[] table = { 0x0, 0x1, 0x4, 0x5, 0x10, 0x11, 0x14, 0x15, 0x40,
0x41, 0x44, 0x45, 0x50, 0x51, 0x54, 0x55 };
int t = (m + 31) >> 5;
if (m_ints.Length < t)
{
m_ints = resizedInts(t);
}
IntArray c = new IntArray(t + t);
// TODO twice the same code, put in separate private method
for (int i = 0; i < t; i++)
{
int v0 = 0;
for (int j = 0; j < 4; j++)
{
v0 = (int)((uint) v0 >> 8);
int u = (int)((uint)m_ints[i] >> (j * 4)) & 0xF;
int w = table[u] << 24;
v0 |= w;
}
c.m_ints[i + i] = v0;
v0 = 0;
int upper = (int)((uint) m_ints[i] >> 16);
for (int j = 0; j < 4; j++)
{
v0 = (int)((uint) v0 >> 8);
int u = (int)((uint)upper >> (j * 4)) & 0xF;
int w = table[u] << 24;
v0 |= w;
}
c.m_ints[i + i + 1] = v0;
}
return c;
}
public IntArray Multiply(IntArray other, int m)
{
// Lenght of c is 2m bits rounded up to the next int (32 bit)
int t = (m + 31) >> 5;
if (m_ints.Length < t)
{
m_ints = resizedInts(t);
}
IntArray b = new IntArray(other.resizedInts(other.Length + 1));
IntArray c = new IntArray((m + m + 31) >> 5);
// IntArray c = new IntArray(t + t);
int testBit = 1;
for (int k = 0; k < 32; k++)
{
for (int j = 0; j < t; j++)
{
if ((m_ints[j] & testBit) != 0)
{
// The kth bit of m_ints[j] is set
c.AddShifted(b, j);
}
}
testBit <<= 1;
b.ShiftLeft();
}
return c;
}
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];
}
}
