ECDSA get public key in C#

Question

I can't figure this out it should be super simple.

I have both the C# and BouncyCastle (also C#) crypto libraries.

I just need to give a byte array as private key, specify the curve used and get the public key.

My curve is SEC-P-256-K1/secp256k1, but really if you can just help me navigate the sea of options and classes I don't need or care about I can set that myself.

Answer 1

Using Vasiliy's answer I was struggling to get the same results as this tutorial but finally got the correct results after changing his code by adding .Normalize():

public Tuple<byte[],byte[]> GetPublicKey(byte[] privateKey){
    BigInteger privKeyInt = new BigInteger(+1, privateKey);

    var parameters = SecNamedCurves.GetByName("secp256k1");
    ECPoint qa = parameters.G.Multiply(privKeyInt).Normalize();

    byte[] pubKeyX = qa.XCoord.ToBigInteger().ToByteArrayUnsigned();
    byte[] pubKeyY = qa.YCoord.ToBigInteger().ToByteArrayUnsigned();

    return Tuple.Create(pubKeyX, pubKeyY);
}

I'd add this as a comment but alas not enough reputation.

Answer 2

Martin's answer seems fine, but it might be done easier:

public Tuple<byte[],byte[]> GetPublicKey(byte[] privateKey)
{
    BigInteger privKeyInt = new BigInteger(+1, privateKey);

    var parameters = SecNamedCurves.GetByName("secp256k1");
    ECPoint qa = parameters.G.Multiply(privKeyInt);

    byte[] pubKeyX = qa.X.ToBigInteger().ToByteArrayUnsigned();
    byte[] pubKeyY = qa.Y.ToBigInteger().ToByteArrayUnsigned();

    return Tuple.Create(pubKeyX, pubKeyY);
}

Answer 3

This is the solution. I was confused by the Curve constructors taking a parameter 'q' which was actually supposed to be 'p' (the prime modulus of the field).

I also don't understand why I have to do so much myself such as the point multiplication to get public key. How will others who have not read EC math know to do that?

Why is there no "GetPubKey" method!?!

Oh well I hope this helps someone. User friendly is not what BouncyCastle is about I guess.

using Org.BouncyCastle.Security;
using Org.BouncyCastle.Math.EC;
using Org.BouncyCastle.Math;
using Org.BouncyCastle.Crypto.Parameters;
using System.Text.RegularExpressions;

public static Tuple<byte[], byte[]> GetSecp256k1PublicKey(byte[] privateKey)
        {
            //Secp256k1 curve variables - https://en.bitcoin.it/wiki/Secp256k1
            var privKeyInt = new BigInteger(+1, privateKey);
            var a = new BigInteger("0");
            var b = new BigInteger("7");
            var GX = new BigInteger(+1, HexStringToByteArray("79BE667E F9DCBBAC 55A06295 CE870B07 029BFCDB 2DCE28D9 59F2815B 16F81798"));
            var GY = new BigInteger(+1, HexStringToByteArray("483ADA77 26A3C465 5DA4FBFC 0E1108A8 FD17B448 A6855419 9C47D08F FB10D4B8"));
            var n = new BigInteger(+1, HexStringToByteArray("FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141"));
            var h = new BigInteger("1");
            var p = new BigInteger(+1, HexStringToByteArray("FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F"));
            var q = h.Multiply(n).Mod(p); //Is this right???
            //- http://en.wikipedia.org/wiki/Elliptic_curve_cryptography

            ECCurve curve = new Org.BouncyCastle.Math.EC.FpCurve(p, a, b);
            ECPoint G = new Org.BouncyCastle.Math.EC.FpPoint(curve, new FpFieldElement(p, GX), new FpFieldElement(p, GY));

            var Qa = G.Multiply(privKeyInt);

            byte[] PubKeyX = Qa.X.ToBigInteger().ToByteArrayUnsigned();
            byte[] PubKeyY = Qa.Y.ToBigInteger().ToByteArrayUnsigned();

            return Tuple.Create<byte[], byte[]>(PubKeyX, PubKeyY);
        }

        public static byte[] HexStringToByteArray(string hex)
        {
            if(String.IsNullOrWhiteSpace(hex))
                return new byte[0];

            hex = Regex.Replace(hex, "[\\s-\\{}]", "");

            if (hex.Length % 2 == 1)
                throw new Exception("The binary key cannot have an odd number of digits.");

            if (!Regex.IsMatch(hex, "(^|\\A)[0-9A-Fa-f]*(\\Z|$)"))
                throw new Exception("Not hex.");

            byte[] arr = new byte[hex.Length >> 1];

            hex = hex.ToUpper();

            for (int i = 0; i < hex.Length >> 1; ++i)
            {
                arr[i] = (byte)((GetHexVal(hex[i << 1]) << 4) + (GetHexVal(hex[(i << 1) + 1])));
            }

            return arr;
        }