/**
* Solves a quadratic equation <code>z<sup>2</sup> + z = beta</code>(X9.62
* D.1.6) The other solution is <code>z + 1</code>.
*
* @param beta
* The value to solve the qradratic equation for.
* @return the solution for <code>z<sup>2</sup> + z = beta</code> or
* <code>null</code> if no solution exists.
*/
private ECFieldElement solveQuadradicEquation(ECFieldElement beta)
{
if (beta.x.SignValue == 0)
{
return(new F2mFieldElement(
this.m, this.k1, this.k2, this.k3, BigInteger.Zero));
}
ECFieldElement z = null;
ECFieldElement gamma = new F2mFieldElement(this.m, this.k1,
this.k2, this.k3, BigInteger.Zero);
while (gamma.ToBigInteger().SignValue == 0)
{
ECFieldElement t = new F2mFieldElement(this.m, this.k1,
this.k2, this.k3, new BigInteger(m, new Random()));
z = new F2mFieldElement(this.m, this.k1, this.k2, this.k3,
BigInteger.Zero);
ECFieldElement w = beta;
for (int i = 1; i <= m - 1; i++)
{
ECFieldElement w2 = w.Square();
z = z.Square().Add(w2.Multiply(t));
w = w2.Add(beta);
}
if (w.x.SignValue != 0)
{
return(null);
}
gamma = z.Square().Add(z);
}
return(z);
}
/**
* Solves a quadratic equation <code>z<sup>2</sup> + z = beta</code>(X9.62
* D.1.6) The other solution is <code>z + 1</code>.
*
* @param beta
* The value to solve the qradratic equation for.
* @return the solution for <code>z<sup>2</sup> + z = beta</code> or
* <code>null</code> if no solution exists.
*/
private ECFieldElement solveQuadradicEquation(ECFieldElement beta)
{
if (beta.x.SignValue == 0)
{
return new F2mFieldElement(
this.m, this.k1, this.k2, this.k3, BigInteger.Zero);
}
ECFieldElement z = null;
ECFieldElement gamma = new F2mFieldElement(this.m, this.k1,
this.k2, this.k3, BigInteger.Zero);
while (gamma.ToBigInteger().SignValue == 0)
{
ECFieldElement t = new F2mFieldElement(this.m, this.k1,
this.k2, this.k3, new BigInteger(m, new Random()));
z = new F2mFieldElement(this.m, this.k1, this.k2, this.k3,
BigInteger.Zero);
ECFieldElement w = beta;
for (int i = 1; i <= m - 1; i++)
{
ECFieldElement w2 = w.Square();
z = z.Square().Add(w2.Multiply(t));
w = w2.Add(beta);
}
if (w.x.SignValue != 0)
{
return null;
}
gamma = z.Square().Add(z);
}
return z;
}