public CurvePoint(EllypticCurve curve, Point point, BigInteger?orderOfGroup = default(BigInteger?))
{
if (curve.IsOnCurve(point))
{
Console.WriteLine($"Point {point} is on curve {curve.Coefficient}, {curve.Constant}");
}
else
{
// throw new ArgumentException($"Point {point} is not on curve {curve.Coefficient}, {curve.Constant}");
Console.WriteLine($"Point {point} is not on curve {curve.Coefficient}, {curve.Constant}");
}
Curve = curve;
Point = point;
if (orderOfGroup.HasValue)
{
Order = orderOfGroup.Value;
}
else
{
Order = FindOrderOfGroup();
Console.WriteLine($"Order of group is calculated {Order}");
}
}
public static CurvePoint SimpleGenerator()
{
var curve = EllypticCurve.CreateWeierstrass(0, 7, new BigInteger(199));
var g = new Point(
new BigInteger(2),
new BigInteger(24));
return(new CurvePoint(curve, g));
}
public static CurvePoint BitCoinGenerator()
{
var curve = EllypticCurve.CreateWeierstrass(0, 7, Configurations.MathConfiguration.GenerateSECP256K1());
var g = new Point(
BigInteger.Parse("55066263022277343669578718895168534326250603453777594175500187360389116729240"),
BigInteger.Parse("32670510020758816978083085130507043184471273380659243275938904335757337482424"));
return(new CurvePoint(curve, g,
BigIntegerExtensions.FromBigEndianHexString("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141")));
}
public static CurvePoint NIST121P192Generator()
{
var curve = EllypticCurve.CreateWeierstrass(
new BigInteger(-3),
BigIntegerExtensions.FromBigEndianHexString("64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1"),
BigInteger.Parse("6277101735386680763835789423207666416083908700390324961279"));
var g = new Point(
BigIntegerExtensions.FromBigEndianHexString("188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012"),
BigIntegerExtensions.FromBigEndianHexString("07192b95ffc8da78631011ed6b24cdd573f977a11e794811"));
return(new CurvePoint(curve, g,
BigInteger.Parse("6277101735386680763835789423176059013767194773182842284081")));
}
public static Point CalculateAddition(this EllypticCurve curve, Point p1, Point p2)
{
var beta = default(BigInteger);
if (p1 != null && p1.Equals(p2))
{
beta = curve.CalculateBeta(p1);
}
else if (p1 != null && p2 != null)
{
beta = curve.CalculateBeta(p1, p2);
}
else
{
throw new ArgumentException();
}
var x = curve.CalculateAdditionXCoordinate(beta, p1, p2);
var y = curve.CalculateAdditionYCoordinate(beta, p1, x);
return(new Point(x.ToPositiveMod(curve.Modulo), y.ToPositiveMod(curve.Modulo)));
}
public static Point CalculateMultiplication(this EllypticCurve curve, Point g, BigInteger scalar)
{
var binary = scalar.ToBinaryString();
binary = binary.TrimStart('0');
var p = new Point(g.XCoordinate, g.YCoordinate);
for (var i = 1; i < binary.Length; i++)
{
bool add = binary[i] == '1';
p = curve.CalculateDoubling(p);
if (add)
{
p = curve.CalculateAddition(p, g);
}
}
return(p);
}
public static Point CalculateDoubling(this EllypticCurve curve, Point p)
{
return(curve.CalculateAddition(p, p));
}