/// <summary> /// Decodes a point on the curve in accordance with §5.1.3 of RFC 8032. /// </summary> /// <param name="Encoded">Encoded point.</param> /// <param name="Curve">Elliptic curve</param> /// <returns>Point on curve.</returns> public static PointOnCurve Decode(byte[] Encoded, EdwardsCurveBase Curve) { int ScalarBits = Curve.CoordinateBits; int ScalarBytes = (ScalarBits + 9) >> 3; if (Encoded.Length != ScalarBytes) { throw new ArgumentException("Not encoded properly.", nameof(Encoded)); } bool x0 = (Encoded[ScalarBytes - 1] & 0x80) != 0; if (x0) { Encoded[ScalarBytes - 1] &= 0x7f; } BigInteger y = EllipticCurve.ToInt(Encoded); if (y >= Curve.Prime) { throw new ArgumentException("Not a valid point.", nameof(Encoded)); } if (x0) { Encoded[ScalarBytes - 1] |= 0x80; } BigInteger x = Curve.GetX(y, x0); return(new PointOnCurve(x, y)); }
/// <summary> /// Signs data using the EdDSA algorithm. /// </summary> /// <param name="Data">Data to be signed.</param> /// <param name="PrivateKey">Private key.</param> /// <param name="Prefix">Prefix</param> /// <param name="HashFunction">Hash function to use</param> /// <param name="Curve">Elliptic curve</param> /// <returns>Signature</returns> public static byte[] Sign(byte[] Data, byte[] PrivateKey, byte[] Prefix, HashFunction HashFunction, EdwardsCurveBase Curve) { // 5.1.6 of RFC 8032 int ScalarBytes = PrivateKey.Length; if (Prefix.Length != ScalarBytes) { throw new ArgumentException("Invalid prefix.", nameof(Prefix)); } BigInteger a = EllipticCurve.ToInt(PrivateKey); PointOnCurve P = Curve.ScalarMultiplication(PrivateKey, Curve.BasePoint, true); byte[] A = Encode(P, Curve); int c = Data.Length; byte[] Bin = new byte[ScalarBytes + c]; // dom2(F, C) = blank string Array.Copy(Prefix, 0, Bin, 0, ScalarBytes); // prefix Array.Copy(Data, 0, Bin, ScalarBytes, c); // PH(M)=M byte[] h = HashFunction(Bin); BigInteger r = BigInteger.Remainder(EllipticCurve.ToInt(h), Curve.Order); PointOnCurve R = Curve.ScalarMultiplication(r, Curve.BasePoint, true); byte[] Rs = Encode(R, Curve); Bin = new byte[(ScalarBytes << 1) + c]; // dom2(F, C) = blank string Array.Copy(Rs, 0, Bin, 0, ScalarBytes); Array.Copy(A, 0, Bin, ScalarBytes, ScalarBytes); Array.Copy(Data, 0, Bin, ScalarBytes << 1, c); // PH(M)=M h = HashFunction(Bin); BigInteger k = BigInteger.Remainder(EllipticCurve.ToInt(h), Curve.Order); BigInteger s = Curve.ModulusN.Add(r, Curve.ModulusN.Multiply(k, a)); Bin = s.ToByteArray(); if (Bin.Length != ScalarBytes) { Array.Resize <byte>(ref Bin, ScalarBytes); } byte[] Signature = new byte[ScalarBytes << 1]; Array.Copy(Rs, 0, Signature, 0, ScalarBytes); Array.Copy(Bin, 0, Signature, ScalarBytes, ScalarBytes); return(Signature); }
/// <summary> /// Verifies a signature of <paramref name="Data"/> made by the EdDSA algorithm. /// </summary> /// <param name="Data">Payload to sign.</param> /// <param name="PublicKey">Public Key of the entity that generated the signature.</param> /// <param name="HashFunction">Hash function to use.</param> /// <param name="Curve">Elliptic curve</param> /// <param name="Signature">Signature</param> /// <returns>If the signature is valid.</returns> public static bool Verify(byte[] Data, byte[] PublicKey, HashFunction HashFunction, EdwardsCurveBase Curve, byte[] Signature) { try { int ScalarBytes = Signature.Length; if ((ScalarBytes & 1) != 0) { return(false); } ScalarBytes >>= 1; byte[] R = new byte[ScalarBytes]; Array.Copy(Signature, 0, R, 0, ScalarBytes); PointOnCurve r = Decode(R, Curve); byte[] S = new byte[ScalarBytes]; Array.Copy(Signature, ScalarBytes, S, 0, ScalarBytes); BigInteger s = EllipticCurve.ToInt(S); if (s >= Curve.Order) { return(false); } int c = Data.Length; byte[] Bin = new byte[(ScalarBytes << 1) + c]; // dom2(F, C) = blank string Array.Copy(R, 0, Bin, 0, ScalarBytes); Array.Copy(PublicKey, 0, Bin, ScalarBytes, ScalarBytes); Array.Copy(Data, 0, Bin, ScalarBytes << 1, c); // PH(M)=M byte[] h = HashFunction(Bin); BigInteger k = BigInteger.Remainder(EllipticCurve.ToInt(h), Curve.Order); PointOnCurve P1 = Curve.ScalarMultiplication(s, Curve.BasePoint, false); PointOnCurve P2 = Curve.ScalarMultiplication(k, Curve.Decode(PublicKey), false); Curve.AddTo(ref P2, r); P1.Normalize(Curve); P2.Normalize(Curve); return(P1.Equals(P2)); } catch (ArgumentException) { return(false); } }
/// <summary> /// Gets a shared key using the Elliptic Curve Diffie-Hellman (ECDH) algorithm. /// </summary> /// <param name="LocalPrivateKey">Local private key.</param> /// <param name="RemotePublicKey">Public key of the remote party.</param> /// <param name="HashFunction">A Hash function is applied to the derived key to generate the shared secret. /// The derived key, as a byte array of equal size as the order of the prime field, ordered by most significant byte first, /// is passed on to the hash function before being returned as the shared key.</param> /// <param name="Curve">Elliptic curve used.</param> /// <returns>Shared secret.</returns> public static byte[] GetSharedKey(byte[] LocalPrivateKey, byte[] RemotePublicKey, HashFunction HashFunction, EllipticCurve Curve) { PointOnCurve PublicKey = Curve.Decode(RemotePublicKey); PointOnCurve P = Curve.ScalarMultiplication(LocalPrivateKey, PublicKey, true); byte[] B = P.X.ToByteArray(); if (B.Length != Curve.OrderBytes) { Array.Resize <byte>(ref B, Curve.OrderBytes); } Array.Reverse(B); // Most significant byte first. return(HashFunction(B)); }