protected bool Equals(
F2mFieldElement other)
{
return(m == other.m &&
k1 == other.k1 &&
k2 == other.k2 &&
k3 == other.k3 &&
representation == other.representation &&
base.Equals(other));
}
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.Copy();
F2mFieldElement bF2m = (F2mFieldElement)b;
iarrClone.AddShifted(bF2m.x, 0);
return(new F2mFieldElement(m, k1, k2, k3, iarrClone));
}
public override ECFieldElement Multiply(
ECFieldElement b)
{
// Right-to-left comb multiplication in the IntArray
// Input: Binary polynomials a(z) and b(z) of degree at most m-1
// Output: c(z) = a(z) * b(z) mod f(z)
// No check performed here for performance reasons. Instead the
// elements involved are checked in ECPoint.F2m
// checkFieldElements(this, b);
F2mFieldElement bF2m = (F2mFieldElement)b;
IntArray mult = x.Multiply(bF2m.x, m);
mult.Reduce(m, new int[] { k1, k2, k3 });
return(new F2mFieldElement(m, k1, k2, k3, mult));
}
public override bool Equals(
object obj)
{
if (obj == this)
{
return(true);
}
F2mFieldElement other = obj as F2mFieldElement;
if (other == null)
{
return(false);
}
return(Equals(other));
}
/**
* Adds another <code>ECPoints.F2m</code> to <code>this</code> without
* checking if both points are on the same curve. Used by multiplication
* algorithms, because there all points are a multiple of the same point
* and hence the checks can be omitted.
* @param b The other <code>ECPoints.F2m</code> to add to
* <code>this</code>.
* @return <code>this + b</code>
*/
internal F2mPoint AddSimple(F2mPoint b)
{
if (this.IsInfinity)
{
return(b);
}
if (b.IsInfinity)
{
return(this);
}
F2mFieldElement x2 = (F2mFieldElement)b.X;
F2mFieldElement y2 = (F2mFieldElement)b.Y;
// Check if b == this or b == -this
if (this.x.Equals(x2))
{
// this == b, i.e. this must be doubled
if (this.y.Equals(y2))
{
return((F2mPoint)this.Twice());
}
// this = -other, i.e. the result is the point at infinity
return((F2mPoint)this.curve.Infinity);
}
ECFieldElement xSum = this.x.Add(x2);
F2mFieldElement lambda
= (F2mFieldElement)(this.y.Add(y2)).Divide(xSum);
F2mFieldElement x3
= (F2mFieldElement)lambda.Square().Add(lambda).Add(xSum).Add(this.curve.A);
F2mFieldElement y3
= (F2mFieldElement)lambda.Multiply(this.x.Add(x3)).Add(x3).Add(this.y);
return(new F2mPoint(curve, x3, y3, withCompression));
}
/**
* @param curve base curve
* @param x x point
* @param y y point
* @param withCompression true if encode with point compression.
*/
public F2mPoint(
ECCurve curve,
ECFieldElement x,
ECFieldElement y,
bool withCompression)
: base(curve, x, y, withCompression)
{
if ((x != null && y == null) || (x == null && y != null))
{
throw new ArgumentException("Exactly one of the field elements is null");
}
if (x != null)
{
// Check if x and y are elements of the same field
F2mFieldElement.CheckFieldElements(this.x, this.y);
// Check if x and a are elements of the same field
F2mFieldElement.CheckFieldElements(this.x, this.curve.A);
}
}
/* (non-Javadoc)
* @see Org.BouncyCastle.Math.EC.ECPoint#twice()
*/
public override ECPoint Twice()
{
// Twice identity element (point at infinity) is identity
if (this.IsInfinity)
{
return(this);
}
// if x1 == 0, then (x1, y1) == (x1, x1 + y1)
// and hence this = -this and thus 2(x1, y1) == infinity
if (this.x.ToBigInteger().Sign == 0)
{
return(this.curve.Infinity);
}
F2mFieldElement lambda = (F2mFieldElement)this.x.Add(this.y.Divide(this.x));
F2mFieldElement x2 = (F2mFieldElement)lambda.Square().Add(lambda).Add(this.curve.A);
ECFieldElement ONE = this.curve.FromBigInteger(BigInteger.One);
F2mFieldElement y2 = (F2mFieldElement)this.x.Square().Add(
x2.Multiply(lambda.Add(ONE)));
return(new F2mPoint(this.curve, x2, y2, withCompression));
}
protected bool Equals(
F2mFieldElement other)
{
return m == other.m
&& k1 == other.k1
&& k2 == other.k2
&& k3 == other.k3
&& representation == other.representation
&& base.Equals(other);
}
