public Field(BigInteger value, EllipticCurve curve)
{
if (value >= curve.Q)
{
throw new ArgumentOutOfRangeException(nameof(value));
}
Value = value;
Curve = curve;
}
public static Point FromX(BigInteger x, bool isOdd, EllipticCurve curve)
{
var pOverFour = curve.Q + BigInteger.One >> 2;
var alpha = (BigInteger.Pow(x, 3) + curve.A.Value * x + curve.B.Value).Mod(curve.Q);
var beta = BigInteger.ModPow(alpha, pOverFour, curve.Q);
var y = beta;
if (beta.IsEven ^ !isOdd)
{
y = curve.Q - y;
}
return(new Point(new Field(x, curve), new Field(y, curve), curve));
}
static EllipticCurve()
{
BigInteger q, a, b, n;
q = BigInteger.Parse("00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F", NumberStyles.AllowHexSpecifier);
a = BigInteger.Zero;
b = 7;
n = BigInteger.Parse("00FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141", NumberStyles.AllowHexSpecifier);
SECP256K1 = new EllipticCurve()
{
Q = q,
N = n
};
SECP256K1.A = new Field(a, SECP256K1);
SECP256K1.B = new Field(b, SECP256K1);
Field x = new Field("79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798".FromHex().ToInt256(), SECP256K1);
Field y = new Field("483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8".FromHex().ToInt256(), SECP256K1);
SECP256K1.G = new Point(x, y, SECP256K1);
SECP256K1.Infinity = new Point(null, null, SECP256K1);
q = BigInteger.Parse("00FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF", NumberStyles.AllowHexSpecifier);
a = BigInteger.Parse("00FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC", NumberStyles.AllowHexSpecifier);
b = BigInteger.Parse("005AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B", NumberStyles.AllowHexSpecifier);
n = BigInteger.Parse("00FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551", NumberStyles.AllowHexSpecifier);
SECP256R1 = new EllipticCurve()
{
Q = q,
N = n
};
SECP256R1.A = new Field(a, SECP256R1);
SECP256R1.B = new Field(b, SECP256R1);
x = new Field("6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296".FromHex().ToInt256(), SECP256R1);
y = new Field("4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5".FromHex().ToInt256(), SECP256R1);
SECP256R1.G = new Point(x, y, SECP256R1);
SECP256R1.Infinity = new Point(null, null, SECP256R1);
}
protected static Point RecoverPublicKey(byte[] hash, BigInteger r, BigInteger s, byte recoveryId, EllipticCurve curve)
{
var isYOdd = recoveryId & 1;
var isSecondKey = recoveryId >> 1;
var x = isSecondKey != 0 ? r + curve.N : r;
var R = Point.FromX(x, isYOdd != 0, EllipticCurve.SECP256K1);
var nR = R * curve.N;
var eNeg = BigInteger.Negate(hash.ToInt256()).Mod(curve.N);
var rInv = r.ModInverse(curve.N);
var q = R.MultiplyTwo(s, curve.G, eNeg) * rInv;
return(q);
}
public Point(Field x, Field y, EllipticCurve curve)
{
X = x;
Y = y;
Curve = curve;
}