Ed25519.cs

using System;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Security.Cryptography;

namespace Cryptographic
{
    /* Ported and refactored from Java to C# by Hans Wolff, 10/10/2013
     * Released to the public domain
     * /

    /* Java code written by k3d3
     * Source: https://github.com/k3d3/ed25519-java/blob/master/ed25519.java
     * Released to the public domain
     */

    public class Ed25519
    {
        private static byte[] ComputeHash(byte[] m)
        {
            using (var sha512 = SHA512Managed.Create())
            {
                return sha512.ComputeHash(m);
            }
        }

        private static BigInteger ExpMod(BigInteger number, BigInteger exponent, BigInteger modulo)
        {
            if (exponent.Equals(BigInteger.Zero))
            {
                return BigInteger.One;
            }
            BigInteger t = BigInteger.Pow(ExpMod(number, exponent / Two, modulo), 2).Mod(modulo);
            if (!exponent.IsEven)
            {
                t *= number;
                t = t.Mod(modulo);
            }
            return t;
        }

        private static BigInteger Inv(BigInteger x)
        {
            return ExpMod(x, Qm2, Q);
        }

        private static BigInteger RecoverX(BigInteger y)
        {
            BigInteger y2 = y * y;
            BigInteger xx = (y2 - 1) * Inv(D * y2 + 1);
            BigInteger x = ExpMod(xx, Qp3 / Eight, Q);
            if (!(x * x - xx).Mod(Q).Equals(BigInteger.Zero))
            {
                x = (x * I).Mod(Q);
            }
            if (!x.IsEven)
            {
                x = Q - x;
            }
            return x;
        }

        private static Tuple<BigInteger, BigInteger> Edwards(BigInteger px, BigInteger py, BigInteger qx, BigInteger qy)
        {
            BigInteger xx12 = px * qx;
            BigInteger yy12 = py * qy;
            BigInteger dtemp = D * xx12 * yy12;
            BigInteger x3 = (px * qy + qx * py) * (Inv(1 + dtemp));
            BigInteger y3 = (py * qy + xx12) * (Inv(1 - dtemp));
            return new Tuple<BigInteger, BigInteger>(x3.Mod(Q), y3.Mod(Q));
        }

        private static Tuple<BigInteger, BigInteger> EdwardsSquare(BigInteger x, BigInteger y)
        {
            BigInteger xx = x * x;
            BigInteger yy = y * y;
            BigInteger dtemp = D * xx * yy;
            BigInteger x3 = (2 * x * y) * (Inv(1 + dtemp));
            BigInteger y3 = (yy + xx) * (Inv(1 - dtemp));
            return new Tuple<BigInteger, BigInteger>(x3.Mod(Q), y3.Mod(Q));
        }
        private static Tuple<BigInteger, BigInteger> ScalarMul(Tuple<BigInteger, BigInteger> p, BigInteger e)
        {
            if (e.Equals(BigInteger.Zero))
            {
                return new Tuple<BigInteger, BigInteger>(BigInteger.Zero, BigInteger.One);
            }
            var q = ScalarMul(p, e / Two);
            q = EdwardsSquare(q.Item1, q.Item2);
            if (!e.IsEven) q = Edwards(q.Item1, q.Item2, p.Item1, p.Item2);
            return q;
        }

        public static byte[] EncodeInt(BigInteger y)
        {
            byte[] nin = y.ToByteArray();
            var nout = new byte[Math.Max(nin.Length, 32)];
            Array.Copy(nin, nout, nin.Length);
            return nout;
        }

        public static byte[] EncodePoint(BigInteger x, BigInteger y)
        {
            byte[] nout = EncodeInt(y);
            nout[nout.Length - 1] |= (x.IsEven ? (byte)0 : (byte)0x80);
            return nout;
        }

        private static int GetBit(byte[] h, int i)
        {
            return h[i / 8] >> (i % 8) & 1;
        }

        public static byte[] PublicKey(byte[] signingKey)
        {
            byte[] h = ComputeHash(signingKey);
            BigInteger a = TwoPowBitLengthMinusTwo;
            for (int i = 3; i < (BitLength - 2); i++)
            {
                var bit = GetBit(h, i);
                if (bit != 0)
                {
                    a += TwoPowCache[i];
                }
            }
            var bigA = ScalarMul(B, a);
            return EncodePoint(bigA.Item1, bigA.Item2);
        }

        private static BigInteger HashInt(byte[] m)
        {
            byte[] h = ComputeHash(m);
            BigInteger hsum = BigInteger.Zero;
            for (int i = 0; i < 2 * BitLength; i++)
            {
                var bit = GetBit(h, i);
                if (bit != 0)
                {
                    hsum += TwoPowCache[i];
                }
            }
            return hsum;
        }

        public static byte[] Signature(byte[] message, byte[] signingKey, byte[] publicKey)
        {
            byte[] h = ComputeHash(signingKey);
            BigInteger a = TwoPowBitLengthMinusTwo;
            for (int i = 3; i < (BitLength - 2); i++)
            {
                var bit = GetBit(h, i);
                if (bit != 0)
                {
                    a += TwoPowCache[i];
                }
            }

            BigInteger r;
            using (var rsub = new MemoryStream((BitLength / 8) + message.Length))
            {
                rsub.Write(h, BitLength / 8, BitLength / 4 - BitLength / 8);
                rsub.Write(message, 0, message.Length);
                r = HashInt(rsub.ToArray());
            }
            var bigR = ScalarMul(B, r);
            BigInteger s;
            var encodedBigR = EncodePoint(bigR.Item1, bigR.Item2);
            using (var stemp = new MemoryStream(32 + publicKey.Length + message.Length))
            {
                stemp.Write(encodedBigR, 0, encodedBigR.Length);
                stemp.Write(publicKey, 0, publicKey.Length);
                stemp.Write(message, 0, message.Length);
                s = (r+ HashInt(stemp.ToArray()) * a).Mod(L);
            }

            using (var nout = new MemoryStream(64))
            {
                nout.Write(encodedBigR, 0, encodedBigR.Length);
                var encodeInt = EncodeInt(s);
                nout.Write(encodeInt, 0, encodeInt.Length);
                return nout.ToArray();
            }
        }

        private static bool IsOnCurve(BigInteger x, BigInteger y)
        {
            BigInteger xx = x * x;
            BigInteger yy = y * y;
            BigInteger dxxyy = D * yy * xx;
            return (yy - xx - dxxyy - 1).Mod(Q).Equals(BigInteger.Zero);
        }

        private static BigInteger DecodeInt(byte[] s)
        {
            return new BigInteger(s) & Un;
        }

        private static Tuple<BigInteger, BigInteger> DecodePoint(byte[] pointBytes)
        {
            BigInteger y = new BigInteger(pointBytes) & Un;
            BigInteger x = RecoverX(y);
            if ((x.IsEven ? 0 : 1) != GetBit(pointBytes, BitLength - 1))
            {
                x = Q - x;
            }
            var point = new Tuple<BigInteger, BigInteger>(x, y);
            if (!IsOnCurve(x, y)) throw new ArgumentException("Decoding point that is not on curve");
            return point;
        }

        public static bool CheckValid(byte[] signature, byte[] message, byte[] publicKey)
        {
            if (signature.Length != BitLength / 4) throw new ArgumentException("Signature length is wrong");
            if (publicKey.Length != BitLength / 8) throw new ArgumentException("Public key length is wrong");

            byte[] rByte = Arrays.CopyOfRange(signature, 0, BitLength / 8);
            var r = DecodePoint(rByte);
            var a = DecodePoint(publicKey);

            byte[] sByte = Arrays.CopyOfRange(signature, BitLength / 8, BitLength / 4);
            BigInteger s = DecodeInt(sByte);
            BigInteger h;

            using (var stemp = new MemoryStream(32 + publicKey.Length + message.Length))
            {
                var encodePoint = EncodePoint(r.Item1, r.Item2);
                stemp.Write(encodePoint, 0, encodePoint.Length);
                stemp.Write(publicKey, 0, publicKey.Length);
                stemp.Write(message, 0, message.Length);
                h = HashInt(stemp.ToArray());
            }
            var ra = ScalarMul(B, s);
            var ah = ScalarMul(a, h);
            var rb = Edwards(r.Item1, r.Item2, ah.Item1, ah.Item2);
            if (!ra.Item1.Equals(rb.Item1) || !ra.Item2.Equals(rb.Item2))
                return false;
            return true;
        }

        private const int BitLength = 256;

        private static readonly BigInteger TwoPowBitLengthMinusTwo = BigInteger.Pow(2, BitLength - 2);
        private static readonly BigInteger[] TwoPowCache = Enumerable.Range(0, 2 * BitLength).Select(i => BigInteger.Pow(2, i)).ToArray();

        private static readonly BigInteger Q =
            BigInteger.Parse("57896044618658097711785492504343953926634992332820282019728792003956564819949");

        private static readonly BigInteger Qm2 =
            BigInteger.Parse("57896044618658097711785492504343953926634992332820282019728792003956564819947");

        private static readonly BigInteger Qp3 =
            BigInteger.Parse("57896044618658097711785492504343953926634992332820282019728792003956564819952");

        private static readonly BigInteger L =
            BigInteger.Parse("7237005577332262213973186563042994240857116359379907606001950938285454250989");

        private static readonly BigInteger D =
            BigInteger.Parse("-4513249062541557337682894930092624173785641285191125241628941591882900924598840740");

        private static readonly BigInteger I =
            BigInteger.Parse("19681161376707505956807079304988542015446066515923890162744021073123829784752");

        private static readonly BigInteger By =
            BigInteger.Parse("46316835694926478169428394003475163141307993866256225615783033603165251855960");

        private static readonly BigInteger Bx =
            BigInteger.Parse("15112221349535400772501151409588531511454012693041857206046113283949847762202");

        private static readonly Tuple<BigInteger, BigInteger> B = new Tuple<BigInteger, BigInteger>(Bx.Mod(Q), By.Mod(Q));

        private static readonly BigInteger Un =
            BigInteger.Parse("57896044618658097711785492504343953926634992332820282019728792003956564819967");

        private static readonly BigInteger Two = new BigInteger(2);
        private static readonly BigInteger Eight = new BigInteger(8);
    }

    internal static class Arrays
    {
        public static byte[] CopyOfRange(byte[] original, int from, int to)
        {
            int length = to - from;
            var result = new byte[length];
            Array.Copy(original, from, result, 0, length);
            return result;
        }
    }

    internal static class BigIntegerHelpers
    {
        public static BigInteger Mod(this BigInteger num, BigInteger modulo)
        {
            var result = num % modulo;
            return result < 0 ? result + modulo : result;
        }
    }
}