public void VerifyCert(StringBuilder sb, BackgroundWorker bw, Certificate cert)
{
BigInteger[] args = null;
ECPoint point = ECPoint.POINT_INFINITY;
ECPoint P = ECPoint.POINT_INFINITY;
EllipticCurve curve = null;
while ((args = cert.Read()) != null)
{
if (bw.CancellationPending)
{
return;
}
curve = new EllipticCurve(args[0], args[1], args[2], args[3]);
sb.AppendFormat("N = {0}\n", args[2].ToString());
sb.AppendFormat("a = {0}", args[0].ToString());
sb.AppendLine();
sb.AppendFormat("b = {0}", args[1].ToString());
sb.AppendLine();
sb.AppendFormat("m = {0}", args[3].ToString());
sb.AppendLine();
sb.AppendFormat("q = {0}", args[4].ToString());
sb.AppendLine();
point = new ECPoint(args[5], args[6]);
sb.AppendFormat("P = ({0}, {1})", point.GetAffineX().ToString(), point.GetAffineY().ToString());
sb.AppendLine();
P = ECMath.Multiply(curve, args[3] / args[4], point);
sb.AppendFormat("Q = ({0}, {1})", P.GetAffineX().ToString(), P.GetAffineY().ToString());
sb.AppendLine();
P = ECMath.Multiply(curve, args[4], P);
sb.Append("R = (0, 1)\n");
sb.AppendLine();
}
}
public int Start(BigInteger field, StringBuilder sb, BackgroundWorker bw, Certificate cert)
{
long D = 0;
int ID = 1;
int k = 0;
Random rng = new Random(Environment.TickCount);
BigInteger val = field;
ECPoint point = null;
EllipticCurve curve = null;
ECPoint P = null, Q = null;
Hilbert hp = new Hilbert();
BigInteger u = 0, v = 0;
BigInteger order = 0;
BigInteger factor = 0;
BigInteger a = 0, b = 0;
Hilbert.SetModulus(val);
BigInteger g = 1;
switch (ID)
{
case 1:
if (bw.CancellationPending)
{
return(-1);
}
D = hp.NextDiscriminant();
if (D == -1)
{
return(-2);
}
if (BigInteger.Jacobi(D, val) == -1)
{
goto case 1;
}
if (!ModifiedCornacchia(val, ref u, ref v, D))
{
goto case 1;
}
goto case 2;
case 2:
if (bw.CancellationPending)
{
return(-1);
}
if (D == -3)
{
order = val + 1 + (u + 3 * v);
factor = FindFactor(order);
if (factor != -1)
{
goto case 3;
}
order = val + 1 - (u + 3 * v);
factor = FindFactor(order);
if (factor != -1)
{
goto case 3;
}
order = val + 1 + (u - 3 * v);
factor = FindFactor(order);
if (factor != -1)
{
goto case 3;
}
order = val + 1 - (u - 3 * v);
factor = FindFactor(order);
if (factor != -1)
{
goto case 3;
}
}
else
if (D == -4)
{
order = val + 1 + 2 * v;
factor = FindFactor(order);
if (factor != -1)
{
goto case 3;
}
order = val + 1 - 2 * v;
factor = FindFactor(order);
if (factor != -1)
{
goto case 3;
}
}
else
{
order = val + 1 + u;
factor = FindFactor(order);
if (factor != -1)
{
goto case 3;
}
order = val + 1 - u;
factor = FindFactor(order);
if (factor != -1)
{
goto case 3;
}
}
goto case 1;
case 3:
if (bw.CancellationPending)
{
return(-1);
}
if (D == -3)
{
a = 0;
b = val - 1;
}
else
if (D == -4)
{
a = val - 1;
b = 0;
}
else
{
Polynomial poly = hp.GetHilbertPolynomial(D);
List <BigInteger> roots = new List <BigInteger>();
if (poly.Degree > 1)
{
poly.FindRoots(ref roots);
}
else
{
roots.Add(val - poly.coeffs[0]);
}
BigInteger J = roots[rng.Next(roots.Count)];
a = J - 1728;
BigInteger inv = a.Inverse(val);
BigInteger c = (J * inv) % val;
if (c == 0)
{
goto case 1;
}
a = (-3 * c) % val;
if (a < 0)
{
a += val;
}
b = (2 * c) % val;
}
goto case 4;
case 4:
if (bw.CancellationPending)
{
return(-1);
}
g = BigInteger.Next(rand, 1, val - 1);
if (D == -3)
{
if (BigInteger.Pow(g, (val - 1) / 3, val) == 1)
{
goto case 4;
}
}
else
{
if (BigInteger.Jacobi(g, val) != -1)
{
goto case 4;
}
}
k = 0;
goto case 5;
case 5:
if (bw.CancellationPending)
{
return(-1);
}
curve = new EllipticCurve(a, b, val, order);
point = curve.BasePoint;
goto case 6;
case 6:
P = ECMath.Multiply(curve, order / factor, point);
Q = ECMath.Multiply(curve, factor, P);
if (Q == ECPoint.POINT_INFINITY)
{
goto case 9;
}
goto case 7;
case 7:
if (bw.CancellationPending)
{
return(-1);
}
k++;
if (k >= w(D))
{
goto case 9;
}
if (D == -3)
{
b = (b * g) % val;
}
else
if (D == -4)
{
a = (a * g) % val;
}
else
{
BigInteger g2 = (g * g) % val;
a = (a * g2) % val;
g2 = (g2 * g) % val;
b = (b * g2) % val;
}
goto case 5;
case 8:
if (bw.CancellationPending)
{
return(-1);
}
point = curve.BasePoint;
P = ECMath.Multiply(curve, order / factor, point);
if (P == ECPoint.POINT_INFINITY)
{
goto case 8;
}
Q = ECMath.Multiply(curve, factor, P);
if (Q != ECPoint.POINT_INFINITY)
{
goto case 7;
}
goto case 9;
case 9:
if (bw.CancellationPending)
{
return(-1);
}
if (P == ECPoint.POINT_INFINITY)
{
goto case 8;
}
sb.AppendFormat("N = {0}", val.ToString());
sb.AppendLine();
sb.AppendFormat("a = {0}", a.ToString());
sb.AppendLine();
sb.AppendFormat("b = {0}", b.ToString());
sb.AppendLine();
sb.AppendFormat("m = {0}", order.ToString());
sb.AppendLine();
sb.AppendFormat("q = {0}", factor.ToString());
sb.AppendLine();
sb.AppendFormat("P = ({0}, {1})", point.GetAffineX().ToString(), point.GetAffineY().ToString());
sb.AppendLine();
sb.AppendFormat("Q = ({0}, {1})", P.GetAffineX().ToString(), P.GetAffineY().ToString());
sb.AppendLine();
sb.Append("R = (0, 1)\n");
sb.AppendLine();
cert.Write(a, b, val, order, factor, point.GetAffineX(), point.GetAffineY());
goto case 10;
case 10:
if (bw.CancellationPending)
{
return(-1);
}
val = factor;
Hilbert.SetModulus(val);
hp.Reset();
if (val.GetBits() <= 64)
{
return(1);
}
goto case 1;
}
return(0);
}