protected bool Equals(
F2mFieldElement other)
{
return(m == other.m &&
k1 == other.k1 &&
k2 == other.k2 &&
k3 == other.k3 &&
representation == other.representation &&
base.Equals(other));
}
static F2mFieldElement halfTrace(F2mFieldElement x)
{
F2mFieldElement t = x;
for (int i = 1; i <= ((x.M - 1) / 2); i++)
{
t = (F2mFieldElement)t.Square().Square().Add(x);
}
return(t);
}
// 6.5 Вычисляем след элемента
static F2mFieldElement trace(F2mFieldElement x)
{
F2mFieldElement t = x;
for (int i = 1; i < x.M; i++)
{
t = (F2mFieldElement)t.Square().Add(x);
}
return(t);
}
/**
* Creates the points on the curve with literature values.
*/
internal static void createPoints()
{
for (int i = 0; i < pointSource.Length / 2; i++)
{
F2mFieldElement x = new F2mFieldElement(m, k1,
new BigInteger(pointSource[2 * i], 16));
F2mFieldElement y = new F2mFieldElement(m, k1,
new BigInteger(pointSource[2 * i + 1], 16));
p[i] = new F2mPoint(curve, x, y);
}
}
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.Clone();
F2mFieldElement bF2m = (F2mFieldElement)b;
iarrClone.AddShifted(bF2m.x, 0);
return(new F2mFieldElement(m, k1, k2, k3, iarrClone));
}
public override bool Equals(object obj)
{
if (obj == this)
{
return(true);
}
F2mFieldElement f2mFieldElement = obj as F2mFieldElement;
if (f2mFieldElement == null)
{
return(false);
}
return(Equals(f2mFieldElement));
}
public static int GetByteLength(
ECFieldElement fe)
{
if (fe is FpFieldElement)
{
FpFieldElement ep = (FpFieldElement)fe;
return((ep.Q.BitLength + 7) / 8);
}
F2mFieldElement em = (F2mFieldElement)fe;
return((em.M + 7) / 8);
}
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 static void CheckFieldElements(ECFieldElement a, ECFieldElement b)
{
if (!(a is F2mFieldElement) || !(b is F2mFieldElement))
{
throw new ArgumentException("Field elements are not both instances of F2mFieldElement");
}
F2mFieldElement f2mFieldElement = (F2mFieldElement)a;
F2mFieldElement f2mFieldElement2 = (F2mFieldElement)b;
if (f2mFieldElement.representation != f2mFieldElement2.representation)
{
throw new ArgumentException("One of the F2m field elements has incorrect representation");
}
if (f2mFieldElement.m != f2mFieldElement2.m || !Arrays.AreEqual(f2mFieldElement.ks, f2mFieldElement2.ks))
{
throw new ArgumentException("Field elements are not elements of the same field F2m");
}
}
// 6.8. Вычисление случайной точки эллиптической кривой
static F2mPoint computeRandomPoint(F2mCurve curve)
{
// 1. Вычислим случайный элемент основного поля
BigInteger u = RNG.GetRandomInteger(curve.M);
var u__element = new F2mFieldElement(curve.M, curve.K1, curve.K2, curve.K3, u);
var a__element = new F2mFieldElement(curve.M, curve.K1, curve.K2, curve.K3, curve.A.ToBigInteger());
var b__element = new F2mFieldElement(curve.M, curve.K1, curve.K2, curve.K3, curve.B.ToBigInteger());
var au__element = u__element.Multiply(u__element).Multiply(a__element);
// 2. Вычисляем элемент основного поля w = u ^ 3 + A u ^ 2 + B
var w__element = u__element.Multiply(u__element).Multiply(u__element).Add(au__element).Add(b__element);
// 3. Решаем квадратное уравнение z^2 + uz = w
var z__element = quadraticEquation(curve, u__element.ToBigInteger(), w__element.ToBigInteger());
// 5. Принимают x = u, y = z
var point = new F2mPoint(curve, u__element, z__element);
return(point);
}
protected bool Equals(
F2mFieldElement other)
{
return m == other.m
&& k1 == other.k1
&& k2 == other.k2
&& k3 == other.k3
&& representation == other.representation
&& base.Equals(other);
}
