/// <summary> /// Decodes a point on the curve in accordance with ยง5.1.3 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> /// 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(Stream Data, byte[] PublicKey, HashFunctionStream 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); byte[] h; if (s >= Curve.Order) { return(false); } using (TemporaryStream TempFile = new TemporaryStream()) // dom2(F, C) = blank string { TempFile.Write(R, 0, ScalarBytes); TempFile.Write(PublicKey, 0, ScalarBytes); Data.Position = 0; Data.CopyTo(TempFile); // PH(M)=M TempFile.Position = 0; h = HashFunction(TempFile); } 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> /// Verifies a signature of <paramref name="Data"/> made by the ECDSA 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="ScalarBytes">Number of bytes to use for scalars.</param> /// <param name="MsbMask">Mask for most significant byte.</param> /// <param name="Signature">Signature</param> /// <returns>If the signature is valid.</returns> public static bool Verify(byte[] Data, byte[] PublicKey, HashFunction HashFunction, int ScalarBytes, byte MsbMask, PrimeFieldCurve Curve, byte[] Signature) { int c = Signature.Length; if (c != ScalarBytes << 1) { return(false); } c >>= 1; byte[] Bin = new byte[c]; Array.Copy(Signature, 0, Bin, 0, c); BigInteger r = EllipticCurve.ToInt(Bin); Bin = new byte[c]; Array.Copy(Signature, c, Bin, 0, c); BigInteger s = EllipticCurve.ToInt(Bin); PointOnCurve PublicKeyPoint = Curve.Decode(PublicKey); if (!PublicKeyPoint.NonZero || r.IsZero || s.IsZero || r >= Curve.Order || s >= Curve.Order) { return(false); } BigInteger e = CalcE(Data, HashFunction, ScalarBytes, MsbMask); BigInteger w = Curve.ModulusN.Invert(s); BigInteger u1 = Curve.ModulusN.Multiply(e, w); BigInteger u2 = Curve.ModulusN.Multiply(r, w); PointOnCurve P2 = Curve.ScalarMultiplication(u1, Curve.BasePoint, true); PointOnCurve P3 = Curve.ScalarMultiplication(u2, PublicKeyPoint, true); Curve.AddTo(ref P2, P3); if (!P2.NonZero) { return(false); } P2.Normalize(Curve); BigInteger Compare = BigInteger.Remainder(P2.X, Curve.Order); if (Compare.Sign < 0) { Compare += Curve.Order; } return(Compare == r); }
/// <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, HashFunctionArray 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> /// Signs data using the ECDSA algorithm. /// </summary> /// <param name="Data">Data to be signed.</param> /// <param name="PrivateKey">Private key.</param> /// <param name="HashFunction">Hash function to use</param> /// <param name="ScalarBytes">Number of bytes to use for scalars.</param> /// <param name="MsbMask">Mask for most significant byte.</param> /// <param name="Curve">Elliptic curve</param> /// <returns>Signature</returns> public static byte[] Sign(byte[] Data, byte[] PrivateKey, HashFunction HashFunction, int ScalarBytes, byte MsbMask, PrimeFieldCurve Curve) { BigInteger e = CalcE(Data, HashFunction, ScalarBytes, MsbMask); BigInteger r, s, PrivateKeyInt = EllipticCurve.ToInt(PrivateKey); PointOnCurve P1; byte[] k; do { do { k = Curve.GenerateSecret(); P1 = Curve.ScalarMultiplication(k, Curve.BasePoint, true); }while (P1.IsXZero); r = BigInteger.Remainder(P1.X, Curve.Order); s = Curve.ModulusN.Divide(Curve.ModulusN.Add(e, Curve.ModulusN.Multiply(r, PrivateKeyInt)), EllipticCurve.ToInt(k)); }while (s.IsZero); if (r.Sign < 0) { r += Curve.Prime; } P1.Normalize(Curve); byte[] Signature = new byte[ScalarBytes << 1]; byte[] S = r.ToByteArray(); if (S.Length != ScalarBytes) { Array.Resize <byte>(ref S, ScalarBytes); } Array.Copy(S, 0, Signature, 0, ScalarBytes); S = s.ToByteArray(); if (S.Length != ScalarBytes) { Array.Resize <byte>(ref S, ScalarBytes); } Array.Copy(S, 0, Signature, ScalarBytes, ScalarBytes); return(Signature); }
private static BigInteger CalcE(byte[] Data, HashFunction HashFunction, int ScalarBytes, byte MsbMask) { byte[] Hash = HashFunction(Data); int c = Hash.Length; if (c != ScalarBytes) { Array.Resize <byte>(ref Hash, ScalarBytes); } Hash[ScalarBytes - 1] &= MsbMask; return(EllipticCurve.ToInt(Hash)); }
/// <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, HashFunctionArray 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> /// 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(Stream Data, byte[] PrivateKey, byte[] Prefix, HashFunctionStream 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); byte[] h; using (TemporaryStream TempFile = new TemporaryStream()) // dom2(F, C) = blank string { TempFile.Write(Prefix, 0, ScalarBytes); // prefix Data.Position = 0; Data.CopyTo(TempFile); // PH(M)=M TempFile.Position = 0; h = HashFunction(TempFile); } BigInteger r = BigInteger.Remainder(EllipticCurve.ToInt(h), Curve.Order); PointOnCurve R = Curve.ScalarMultiplication(r, Curve.BasePoint, true); byte[] Rs = Encode(R, Curve); using (TemporaryStream TempFile = new TemporaryStream()) // dom2(F, C) = blank string { TempFile.Write(Rs, 0, ScalarBytes); TempFile.Write(A, 0, ScalarBytes); Data.Position = 0; Data.CopyTo(TempFile); // PH(M)=M TempFile.Position = 0; h = HashFunction(TempFile); } BigInteger k = BigInteger.Remainder(EllipticCurve.ToInt(h), Curve.Order); BigInteger s = Curve.ModulusN.Add(r, Curve.ModulusN.Multiply(k, a)); byte[] 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); }