public bool ValidatePublicKey()
{
if (_d == null || _Q == null)
{
return(true);
}
ECPoint point1 = _Q.Export();
ECPoint point2 = _domain.G.Multiply(_d).Export();
return(point1.X.CompareTo(point2.X) == 0 &&
point1.Y.CompareTo(point2.Y) == 0 &&
point1.Z.CompareTo(point2.Z) == 0);
}
/// <summary>
/// TODO: 未実装のValidationステップを実装する
/// </summary>
public bool Validate()
{
IFiniteField ff = _group.FiniteField;
// Step1: Check that p is an odd prime
// Step2: Check that a,b,Gx and Gy are integers in the interval [0, p - 1]
ECPoint ExportedG = _G.Export();
Number Gx = ff.ToElement(ExportedG.X);
Number Gy = ff.ToElement(ExportedG.Y);
if (A > P || B > P || Gx > P || Gy > P)
{
return(false);
}
// Step3: Check that 4*a^3 + 27*b^2 != 0 (mod p)
Number Apow3 = ff.Multiply(A, ff.Multiply(A, A));
Number Bpow2 = ff.Multiply(B, B);
Number ret = ff.Add(ff.Multiply(ff.ToElement(Number.Four), ff.ToElement(Apow3)), ff.Multiply(ff.ToElement(Number.TwentySeven), Bpow2));
if (ret.IsZero())
{
return(false);
}
// Step4: Gy^2 = Gx^3 + a*Gx + b
Number aGx = ff.Multiply(A, Gx);
Number Xpow3 = ff.Multiply(Gx, ff.Multiply(Gx, Gx));
Number Ypow2 = ff.Multiply(Gy, Gy);
ret = ff.Add(Xpow3, ff.Add(aGx, B));
if (ret.CompareTo(Ypow2) != 0)
{
return(false);
}
// Step5: Check that n is prime.
// Step6: Check that h <= 4, and that h = (sqrt(p)+1)^2 / n
// Step7: Check that nG = O
ECPoint nG = _G.Multiply(N).Export();
if (!nG.IsInifinity())
{
return(false);
}
// Step8: Check that q^B != 1 (mod n) for any 1 <= B <= 20, and that nh != p
Number p = Number.One;
Classical c = new Classical(N);
for (int i = 0; i <= 20; i++)
{
p = c.Multiply(p, P);
if (p.IsOne())
{
return(false);
}
}
if (c.Multiply(N, new Number(new uint[] { H }, 1)).CompareTo(P) == 0)
{
return(false);
}
return(true);
}
void PointCompressTest (int bits, ECGroup group, ECPoint p, int repeats, string name)
{
int bytes = (bits >> 3) + ((bits & 7) == 0 ? 0 : 1) + 1;
for (int i = 0; i < repeats; i ++) {
byte[] tmp = p.ToByteArray (true);
Assert.IsTrue (tmp.Length == bytes, name + " #1");
ECPoint x = new ECPoint (group, tmp).Export ();
ECPoint p2 = p.Export ();
Assert.IsTrue (x.X.CompareTo (p2.X) == 0, name + " #2");
Assert.IsTrue (x.Y.CompareTo (p2.Y) == 0, name + " #3");
p = p.Multiply (Number.CreateRandomElement (group.P));
}
}
