protected internal ECPoint(
ECCurve curve,
ECFieldElement x,
ECFieldElement y,
bool withCompression)
{
if (curve == null)
throw new ArgumentNullException("curve");
this.curve = curve;
this.x = x;
this.y = y;
this.withCompression = withCompression;
}
public override ECFieldElement Add(
ECFieldElement b)
{
return new FpFieldElement(q, x.Add(b.ToBigInteger()).Mod(q));
}
protected bool Equals(
ECFieldElement other)
{
return ToBigInteger().Equals(other.ToBigInteger());
}
public abstract ECFieldElement Divide(ECFieldElement b);
public abstract ECFieldElement Multiply(ECFieldElement b);
/**
* 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.ToBigInteger().Sign == 0)
{
return FromBigInteger(BigInteger.Zero);
}
ECFieldElement z = null;
ECFieldElement gamma = FromBigInteger(BigInteger.Zero);
while (gamma.ToBigInteger().Sign == 0)
{
ECFieldElement t = FromBigInteger(new BigInteger(m, new Random()));
z = FromBigInteger(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.ToBigInteger().Sign != 0)
{
return null;
}
gamma = z.Square().Add(z);
}
return z;
}
/**
* @param curve base curve
* @param x x point
* @param y y point
*/
public F2mPoint(
ECCurve curve,
ECFieldElement x,
ECFieldElement y)
: this(curve, x, y, false)
{
}
public override ECFieldElement Divide(
ECFieldElement b)
{
// There may be more efficient implementations
ECFieldElement bInv = b.Invert();
return Multiply(bInv);
}
public override ECFieldElement Subtract(
ECFieldElement b)
{
// Addition and subtraction are the same in F2m
return Add(b);
}
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 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);
}
/**
* Checks, if the ECFieldElements <code>a</code> and <code>b</code>
* are elements of the same field <code>F<sub>2<sup>m</sup></sub></code>
* (having the same representation).
* @param a field element.
* @param b field element to be compared.
* @throws ArgumentException if <code>a</code> and <code>b</code>
* are not elements of the same field
* <code>F<sub>2<sup>m</sup></sub></code> (having the same
* representation).
*/
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 aF2m = (F2mFieldElement)a;
F2mFieldElement bF2m = (F2mFieldElement)b;
if ((aF2m.m != bF2m.m) || (aF2m.k1 != bF2m.k1)
|| (aF2m.k2 != bF2m.k2) || (aF2m.k3 != bF2m.k3))
{
throw new ArgumentException("Field elements are not "
+ "elements of the same field F2m");
}
if (aF2m.representation != bF2m.representation)
{
// Should never occur
throw new ArgumentException(
"One of the field "
+ "elements are not elements has incorrect representation");
}
}
public static int GetByteLength(
ECFieldElement fe)
{
return (fe.FieldSize + 7) / 8;
}
public override ECFieldElement Subtract(
ECFieldElement b)
{
return new FpFieldElement(q, x.Subtract(b.ToBigInteger()).Mod(q));
}
public override ECFieldElement Divide(
ECFieldElement b)
{
return new FpFieldElement(q, x.Multiply(b.ToBigInteger().ModInverse(q)).Mod(q));
}
protected internal ECPointBase(
ECCurve curve,
ECFieldElement x,
ECFieldElement y,
bool withCompression)
: base(curve, x, y, withCompression)
{
}
public abstract ECFieldElement Add(ECFieldElement b);
/**
* Create a point that encodes with or without point compresion.
*
* @param curve the curve to use
* @param x affine x co-ordinate
* @param y affine y co-ordinate
* @param withCompression if true encode with point compression
*/
public FpPoint(
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");
}
public abstract ECFieldElement Subtract(ECFieldElement b);
/**
* @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);
}
}
public X9FieldElement(
ECFieldElement f)
{
this.f = f;
}