public ECFieldElement add(final 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();
F2m bF2m = (F2m) b;
iarrClone.addShifted(bF2m.x, 0);
return new F2m(m, k1, k2, k3, iarrClone);
}
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.getLength() + 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 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.isZero())
// 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) {
final IntArray uzCopy = uz;
uz = vz;
vz = uzCopy;
final 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 ECFieldElement.F2m(this.m, this.k1, this.k2, this.k3, g2z);
}