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Merge pull request #31 from TwoTenPvP/cryptography-2

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Cryptography 2
This commit is contained in:
Albin Corén 2018-03-31 02:06:11 +02:00 committed by GitHub
commit a27e4debe9
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GPG Key ID: 4AEE18F83AFDEB23
8 changed files with 541 additions and 17 deletions
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1
MLAPI/Data/NetworkedClient.cs
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@ -8,5 +8,6 @@ namespace MLAPI
public int ClientId;
public GameObject PlayerObject;
public List<NetworkedObject> OwnedObjects = new List<NetworkedObject>();
public byte[] AesKey;
}
}

15
MLAPI/Data/NetworkingConfiguration.cs
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@ -13,6 +13,7 @@ namespace MLAPI
public List<string> MessageTypes = new List<string>();
public List<string> PassthroughMessageTypes = new List<string>();
internal HashSet<ushort> RegisteredPassthroughMessageTypes = new HashSet<ushort>();
public HashSet<int> EncryptedChannels = new HashSet<int>();
public List<string> RegisteredScenes = new List<string>();
public int MessageBufferSize = 65535;
public int ReceiveTickrate = 64;
@ -28,11 +29,12 @@ namespace MLAPI
public byte[] ConnectionData = new byte[0];
public float SecondsHistory = 5;
public bool HandleObjectSpawning = true;
//TODO
public bool CompressMessages = false;
//Should only be used for dedicated servers and will require the servers RSA keypair being hard coded into clients in order to exchange a AES key
//TODO
public bool EncryptMessages = false;
public bool EnableEncryption = true;
public bool SignKeyExchange = true;
public string RSAPrivateKey = "<RSAKeyValue><Modulus>vBEvOQki/EftWOgwh4G8/nFRvcDJLylc8P7Dhz5m/hpkkNtAMzizNKYUrGbs7sYWlEuMYBOWrzkIDGOMoOsYc9uCi+8EcmNoHDlIhK5yNfZUexYBF551VbvZ625LSBR7kmBxkyo4IPuA09fYCHeUFm3prt4h6aTD0Hjc7ZsJHUU=</Modulus><Exponent>EQ==</Exponent><P>ydgcrq5qLJOdDQibD3m9+o3/dkKoFeCC110dnMgdpEteCruyBdL0zjGKKvjjgy3XTSSp43EN591NiXaBp0JtDw==</P><Q>7obHrUnUCsSHUsIJ7+JOrupcGrQ0XaYcQ+Uwb2v7d2YUzwZ46U4gI9snfD2J0tc3DGEh3v3G0Q8q7bxEe3H4aw==</Q><DP>L34k3c6vkgSdbHp+1nb/hj+HZx6+I0PijQbZyolwYuSOmR0a1DGjA1bzVWe9D86NAxevgM9OkOjG8yrxVIgZqQ==</DP><DQ>OB+2gyBuIKa2bdNNodrlVlVC2RtXnZB/HwjAGjeGdnJfP8VJoE6eJo3rLEq3BG7fxq1xYaUfuLhGVg4uOyngGQ==</DQ><InverseQ>o97PimYu58qH5eFmySRCIsyhBr/tK2GM17Zd9QQPJZRSorrhIJn1m6gwQ/G5aJLIM/3Yl04CoyqmQGsPXMzW2w==</InverseQ><D>CxAR1i22w4vCquB7U0Pd8Nl9R2Wxez6rHTwpnoszPB+rkAzlqKj7e5FMgpykhoQfciKPyWqQZKkAeTMIRbN56JinvpAt5POId/28HDd5xjGymHE81k3RzoHqzQXFIOF1TSYKUWzjPPF/TU4nn7auD4i6lOODATsMqtLr5DRBN/0=</D></RSAKeyValue>"; //CHANGE THESE FOR PRODUCTION!
public string RSAPublicKey = "<RSAKeyValue><Modulus>vBEvOQki/EftWOgwh4G8/nFRvcDJLylc8P7Dhz5m/hpkkNtAMzizNKYUrGbs7sYWlEuMYBOWrzkIDGOMoOsYc9uCi+8EcmNoHDlIhK5yNfZUexYBF551VbvZ625LSBR7kmBxkyo4IPuA09fYCHeUFm3prt4h6aTD0Hjc7ZsJHUU=</Modulus><Exponent>EQ==</Exponent></RSAKeyValue>"; //CHANGE THESE FOR PRODUCTION!
public bool AllowPassthroughMessages = true;
public bool EnableSceneSwitching = false;
@ -72,8 +74,7 @@ namespace MLAPI
}
}
writer.Write(HandleObjectSpawning);
writer.Write(CompressMessages);
writer.Write(EncryptMessages);
writer.Write(EnableEncryption);
writer.Write(AllowPassthroughMessages);
writer.Write(EnableSceneSwitching);
}

9
MLAPI/MLAPI.csproj
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@ -44,6 +44,9 @@
<GenerateSerializationAssemblies>Auto</GenerateSerializationAssemblies>
</PropertyGroup>
<ItemGroup>
<Reference Include="IntXLib, Version=1.0.0.0, Culture=neutral, PublicKeyToken=1744b76c74eaee1e, processorArchitecture=MSIL">
<HintPath>..\packages\IntX.1.0.1.0\lib\net20\IntXLib.dll</HintPath>
</Reference>
<Reference Include="System" />
<Reference Include="System.Core" />
<Reference Include="System.Xml.Linq" />
@ -62,6 +65,9 @@
<Compile Include="Data\TrackedPointData.cs" />
<Compile Include="MonoBehaviours\Prototyping\NetworkedAnimator.cs" />
<Compile Include="MonoBehaviours\Prototyping\NetworkedNavMeshAgent.cs" />
<Compile Include="NetworkingManagerComponents\CryptographyHelper.cs" />
<Compile Include="NetworkingManagerComponents\DiffieHellman.cs" />
<Compile Include="NetworkingManagerComponents\EllipticCurve.cs" />
<Compile Include="NetworkingManagerComponents\LagCompensationManager.cs" />
<Compile Include="MonoBehaviours\Core\NetworkedBehaviour.cs" />
<Compile Include="Data\NetworkedClient.cs" />
@ -79,5 +85,8 @@
<Compile Include="Data\ClientIdKey.cs" />
<Compile Include="NetworkingManagerComponents\MessageChunker.cs" />
</ItemGroup>
<ItemGroup>
<None Include="packages.config" />
</ItemGroup>
<Import Project="$(MSBuildToolsPath)\Microsoft.CSharp.targets" />
</Project>

186
MLAPI/MonoBehaviours/Core/NetworkingManager.cs
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@ -7,6 +7,7 @@ using System.IO;
using UnityEngine;
using UnityEngine.Networking;
using System.Linq;
using System.Security.Cryptography;
namespace MLAPI
{
@ -51,6 +52,10 @@ namespace MLAPI
public NetworkingConfiguration NetworkConfig;
private EllipticDiffieHellman clientDiffieHellman;
private Dictionary<int, byte[]> diffieHellmanPublicKeys;
private byte[] clientAesKey;
private void OnValidate()
{
if (SpawnablePrefabs != null)
@ -88,6 +93,7 @@ namespace MLAPI
pendingClients = new HashSet<int>();
connectedClients = new Dictionary<int, NetworkedClient>();
messageBuffer = new byte[NetworkConfig.MessageBufferSize];
diffieHellmanPublicKeys = new Dictionary<int, byte[]>();
MessageManager.channels = new Dictionary<string, int>();
MessageManager.messageTypes = new Dictionary<string, ushort>();
MessageManager.messageCallbacks = new Dictionary<ushort, Dictionary<int, Action<int, byte[]>>>();
@ -374,15 +380,29 @@ namespace MLAPI
}
else
{
byte[] diffiePublic = new byte[0];
if(NetworkConfig.EnableEncryption)
{
clientDiffieHellman = new EllipticDiffieHellman(EllipticDiffieHellman.DEFAULT_CURVE, EllipticDiffieHellman.DEFAULT_GENERATOR, EllipticDiffieHellman.DEFAULT_ORDER);
diffiePublic = clientDiffieHellman.GetPublicKey();
}
int sizeOfStream = 32;
if (NetworkConfig.ConnectionApproval)
sizeOfStream += 2 + NetworkConfig.ConnectionData.Length;
if (NetworkConfig.EnableEncryption)
sizeOfStream += 2 + diffiePublic.Length;
using (MemoryStream writeStream = new MemoryStream(sizeOfStream))
{
using (BinaryWriter writer = new BinaryWriter(writeStream))
{
writer.Write(NetworkConfig.GetConfig());
if (NetworkConfig.EnableEncryption)
{
writer.Write((ushort)diffiePublic.Length);
writer.Write(diffiePublic);
}
if (NetworkConfig.ConnectionApproval)
{
writer.Write((ushort)NetworkConfig.ConnectionData.Length);
@ -471,6 +491,14 @@ namespace MLAPI
ushort bytesToRead = reader.ReadUInt16();
byte[] incommingData = reader.ReadBytes(bytesToRead);
if(NetworkConfig.EncryptedChannels.Contains(channelId))
{
//Encrypted message
if (isServer)
incommingData = CryptographyHelper.Decrypt(incommingData, connectedClients[clientId].AesKey);
else
incommingData = CryptographyHelper.Decrypt(incommingData, clientAesKey);
}
if (isServer && isPassthrough && !NetworkConfig.RegisteredPassthroughMessageTypes.Contains(messageType))
{
@ -555,6 +583,14 @@ namespace MLAPI
DisconnectClient(clientId);
return;
}
byte[] aesKey = new byte[0];
if(NetworkConfig.EnableEncryption)
{
ushort diffiePublicSize = messageReader.ReadUInt16();
byte[] diffiePublic = messageReader.ReadBytes(diffiePublicSize);
diffieHellmanPublicKeys.Add(clientId, diffiePublic);
}
if (NetworkConfig.ConnectionApproval)
{
ushort bufferSize = messageReader.ReadUInt16();
@ -583,6 +619,30 @@ namespace MLAPI
sceneIndex = messageReader.ReadUInt32();
}
if (NetworkConfig.EnableEncryption)
{
ushort keyLength = messageReader.ReadUInt16();
byte[] serverPublicKey = messageReader.ReadBytes(keyLength);
clientAesKey = clientDiffieHellman.GetSharedSecret(serverPublicKey);
if (NetworkConfig.SignKeyExchange)
{
ushort signatureLength = messageReader.ReadUInt16();
byte[] publicKeySignature = messageReader.ReadBytes(signatureLength);
using (RSACryptoServiceProvider rsa = new RSACryptoServiceProvider())
{
rsa.PersistKeyInCsp = false;
rsa.FromXmlString(NetworkConfig.RSAPublicKey);
if(!rsa.VerifyData(serverPublicKey, new SHA512CryptoServiceProvider(), publicKeySignature))
{
//Man in the middle.
Debug.LogWarning("MLAPI: Signature doesnt match for the key exchange public part. Disconnecting");
StopClient();
return;
}
}
}
}
float netTime = messageReader.ReadSingle();
int remoteStamp = messageReader.ReadInt32();
int msDelay = NetworkTransport.GetRemoteDelayTimeMS(hostId, clientId, remoteStamp, out error);
@ -901,8 +961,18 @@ namespace MLAPI
writer.Write(orderId.Value);
writer.Write(true);
writer.Write(sourceId);
writer.Write((ushort)data.Length);
writer.Write(data);
if(NetworkConfig.EncryptedChannels.Contains(channelId))
{
//Encrypted message
byte[] encrypted = CryptographyHelper.Encrypt(data, connectedClients[targetId].AesKey);
writer.Write((ushort)encrypted.Length);
writer.Write(encrypted);
}
else
{
writer.Write((ushort)data.Length);
writer.Write(data);
}
}
NetworkTransport.QueueMessageForSending(hostId, targetId, channelId, stream.GetBuffer(), sizeOfStream, out error);
}
@ -951,8 +1021,25 @@ namespace MLAPI
writer.Write(isPassthrough);
if (isPassthrough)
writer.Write(clientId);
writer.Write((ushort)data.Length);
writer.Write(data);
if (NetworkConfig.EncryptedChannels.Contains(MessageManager.channels[channelName]))
{
//This is an encrypted message.
byte[] encrypted;
if (isServer)
encrypted = CryptographyHelper.Encrypt(data, connectedClients[clientId].AesKey);
else
encrypted = CryptographyHelper.Encrypt(data, clientAesKey);
writer.Write((ushort)encrypted.Length);
writer.Write(encrypted);
}
else
{
//Send in plaintext.
writer.Write((ushort)data.Length);
writer.Write(data);
}
}
if (isPassthrough)
clientId = serverClientId;
@ -965,7 +1052,12 @@ namespace MLAPI
internal void Send(int[] clientIds, string messageType, string channelName, byte[] data, uint? networkId = null, ushort? orderId = null)
{
int sizeOfStream = 6;
if (NetworkConfig.EncryptedChannels.Contains(MessageManager.channels[channelName]))
{
Debug.LogWarning("MLAPI: Cannot send messages over encrypted channel to multiple clients.");
return;
}
int sizeOfStream = 6;
if (networkId != null)
sizeOfStream += 4;
if (orderId != null)
@ -1007,6 +1099,12 @@ namespace MLAPI
internal void Send(List<int> clientIds, string messageType, string channelName, byte[] data, uint? networkId = null, ushort? orderId = null)
{
if (NetworkConfig.EncryptedChannels.Contains(MessageManager.channels[channelName]))
{
Debug.LogWarning("MLAPI: Cannot send messages over encrypted channel to multiple clients.");
return;
}
//2 bytes for messageType, 2 bytes for buffer length and one byte for target bool
int sizeOfStream = 6;
if (networkId != null)
@ -1050,6 +1148,12 @@ namespace MLAPI
internal void Send(string messageType, string channelName, byte[] data, uint? networkId = null, ushort? orderId = null)
{
if (NetworkConfig.EncryptedChannels.Contains(MessageManager.channels[channelName]))
{
Debug.LogWarning("MLAPI: Cannot send messages over encrypted channel to multiple clients.");
return;
}
//2 bytes for messageType, 2 bytes for buffer length and one byte for target bool
int sizeOfStream = 6;
if (networkId != null)
@ -1094,6 +1198,12 @@ namespace MLAPI
internal void Send(string messageType, string channelName, byte[] data, int clientIdToIgnore, uint? networkId = null, ushort? orderId = null)
{
if (NetworkConfig.EncryptedChannels.Contains(MessageManager.channels[channelName]))
{
Debug.LogWarning("MLAPI: Cannot send messages over encrypted channel to multiple clients.");
return;
}
//2 bytes for messageType, 2 bytes for buffer length and one byte for target bool
int sizeOfStream = 5;
if (networkId != null)
@ -1142,10 +1252,16 @@ namespace MLAPI
{
if (!isServer)
return;
if (pendingClients.Contains(clientId))
pendingClients.Remove(clientId);
if (connectedClients.ContainsKey(clientId))
connectedClients.Remove(clientId);
if (diffieHellmanPublicKeys.ContainsKey(clientId))
diffieHellmanPublicKeys.Remove(clientId);
NetworkTransport.Disconnect(hostId, clientId, out error);
}
@ -1188,9 +1304,34 @@ namespace MLAPI
//Inform new client it got approved
if (pendingClients.Contains(clientId))
pendingClients.Remove(clientId);
byte[] aesKey = new byte[0];
byte[] publicKey = new byte[0];
byte[] publicKeySignature = new byte[0];
if (NetworkConfig.EnableEncryption)
{
EllipticDiffieHellman diffieHellman = new EllipticDiffieHellman(EllipticDiffieHellman.DEFAULT_CURVE, EllipticDiffieHellman.DEFAULT_GENERATOR, EllipticDiffieHellman.DEFAULT_ORDER);
aesKey = diffieHellman.GetSharedSecret(diffieHellmanPublicKeys[clientId]);
publicKey = diffieHellman.GetPublicKey();
if (diffieHellmanPublicKeys.ContainsKey(clientId))
diffieHellmanPublicKeys.Remove(clientId);
if (NetworkConfig.SignKeyExchange)
{
using (RSACryptoServiceProvider rsa = new RSACryptoServiceProvider())
{
rsa.PersistKeyInCsp = false;
rsa.FromXmlString(NetworkConfig.RSAPrivateKey);
publicKeySignature = rsa.SignData(publicKeySignature, new SHA512CryptoServiceProvider());
}
}
}
NetworkedClient client = new NetworkedClient()
{
ClientId = clientId
ClientId = clientId,
AesKey = aesKey
};
connectedClients.Add(clientId, client);
@ -1200,18 +1341,26 @@ namespace MLAPI
GameObject go = SpawnManager.SpawnPlayerObject(clientId, networkId);
connectedClients[clientId].PlayerObject = go;
}
int sizeOfStream = 16 + ((connectedClients.Count - 1) * 4);
int amountOfObjectsToSend = SpawnManager.spawnedObjects.Values.Count(x => x.ServerOnly == false);
if(NetworkConfig.HandleObjectSpawning)
if (NetworkConfig.HandleObjectSpawning)
{
sizeOfStream += 4;
sizeOfStream += 14 * amountOfObjectsToSend;
}
if(NetworkConfig.EnableSceneSwitching)
if (NetworkConfig.EnableEncryption)
{
sizeOfStream += 2 + publicKey.Length;
if (NetworkConfig.SignKeyExchange)
{
sizeOfStream += 2 + publicKeySignature.Length;
}
}
if (NetworkConfig.EnableSceneSwitching)
{
sizeOfStream += 4;
}
@ -1225,8 +1374,21 @@ namespace MLAPI
{
writer.Write(NetworkSceneManager.CurrentSceneIndex);
}
if (NetworkConfig.EnableEncryption)
{
writer.Write((ushort)publicKey.Length);
writer.Write(publicKey);
if (NetworkConfig.SignKeyExchange)
{
writer.Write((ushort)publicKeySignature.Length);
writer.Write(publicKeySignature);
}
}
writer.Write(NetworkTime);
writer.Write(NetworkTransport.GetNetworkTimestamp());
writer.Write(connectedClients.Count - 1);
foreach (KeyValuePair<int, NetworkedClient> item in connectedClients)
{
@ -1292,6 +1454,10 @@ namespace MLAPI
{
if (pendingClients.Contains(clientId))
pendingClients.Remove(clientId);
if (diffieHellmanPublicKeys.ContainsKey(clientId))
diffieHellmanPublicKeys.Remove(clientId);
NetworkTransport.Disconnect(hostId, clientId, out error);
}
}

50
MLAPI/NetworkingManagerComponents/CryptographyHelper.cs Normal file
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@ -0,0 +1,50 @@
using System;
using System.Security.Cryptography;
using System.IO;
namespace MLAPI.NetworkingManagerComponents
{
public static class CryptographyHelper
{
public static byte[] Decrypt(byte[] encryptedBuffer, byte[] key)
{
byte[] iv = new byte[16];
Array.Copy(encryptedBuffer, 0, iv, 0, 16);
using (MemoryStream stream = new MemoryStream())
{
using (RijndaelManaged aes = new RijndaelManaged())
{
aes.IV = iv;
aes.Key = key;
using (CryptoStream cs = new CryptoStream(stream, aes.CreateDecryptor(), CryptoStreamMode.Write))
{
cs.Write(encryptedBuffer, 16, encryptedBuffer.Length - 16);
}
return stream.ToArray();
}
}
}
public static byte[] Encrypt(byte[] clearBuffer, byte[] key)
{
using (MemoryStream stream = new MemoryStream())
{
using (RijndaelManaged aes = new RijndaelManaged())
{
aes.Key = key;
aes.GenerateIV();
using (CryptoStream cs = new CryptoStream(stream, aes.CreateEncryptor(), CryptoStreamMode.Write))
{
cs.Write(clearBuffer, 0, clearBuffer.Length);
}
byte[] encrypted = stream.ToArray();
byte[] final = new byte[encrypted.Length + 16];
Array.Copy(aes.IV, final, 16);
Array.Copy(encrypted, 0, final, 16, encrypted.Length);
return final;
}
}
}
}
}

104
MLAPI/NetworkingManagerComponents/DiffieHellman.cs Normal file
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@ -0,0 +1,104 @@
using System;
using IntXLib;
using System.Text;
using System.Security.Cryptography;
namespace MLAPI.NetworkingManagerComponents
{
public class EllipticDiffieHellman
{
protected static readonly RNGCryptoServiceProvider rand = new RNGCryptoServiceProvider();
public static readonly IntX DEFAULT_PRIME = (new IntX(1) << 255) - 19;
public static readonly IntX DEFAULT_ORDER = (new IntX(1) << 252) + IntX.Parse("27742317777372353535851937790883648493");
public static readonly EllipticCurve DEFAULT_CURVE = new EllipticCurve(486662, 1, DEFAULT_PRIME, EllipticCurve.CurveType.Montgomery);
public static readonly CurvePoint DEFAULT_GENERATOR = new CurvePoint(9, IntX.Parse("14781619447589544791020593568409986887264606134616475288964881837755586237401"));
protected readonly EllipticCurve curve;
public readonly IntX priv;
protected readonly CurvePoint generator, pub;
public EllipticDiffieHellman(EllipticCurve curve, CurvePoint generator, IntX order, byte[] priv = null)
{
this.curve = curve;
this.generator = generator;
// Generate private key
if (priv == null)
{
byte[] max = order.ToArray();
do
{
byte[] p1 = new byte[5 /*rand.Next(max.Length) + 1*/];
rand.GetBytes(p1);
if (p1.Length == max.Length) p1[p1.Length - 1] %= max[max.Length - 1];
else p1[p1.Length - 1] &= 127;
this.priv = DHHelper.FromArray(p1);
} while (this.priv<2);
}
else this.priv = DHHelper.FromArray(priv);
// Generate public key
pub = curve.Multiply(generator, this.priv);
}
public byte[] GetPublicKey()
{
byte[] p1 = pub.X.ToArray();
byte[] p2 = pub.Y.ToArray();
byte[] ser = new byte[4 + p1.Length + p2.Length];
ser[0] = (byte)(p1.Length & 255);
ser[1] = (byte)((p1.Length >> 8) & 255);
ser[2] = (byte)((p1.Length >> 16) & 255);
ser[3] = (byte)((p1.Length >> 24) & 255);
Array.Copy(p1, 0, ser, 4, p1.Length);
Array.Copy(p2, 0, ser, 4 + p1.Length, p2.Length);
return ser;
}
public byte[] GetPrivateKey() => priv.ToArray();
public byte[] GetSharedSecret(byte[] pK)
{
byte[] p1 = new byte[pK[0] | (pK[1]<<8) | (pK[2]<<16) | (pK[3]<<24)]; // Reconstruct x-axis size
byte[] p2 = new byte[pK.Length - p1.Length - 4];
Array.Copy(pK, 4, p1, 0, p1.Length);
Array.Copy(pK, 4 + p1.Length, p2, 0, p2.Length);
CurvePoint remotePublic = new CurvePoint(DHHelper.FromArray(p1), DHHelper.FromArray(p2));
byte[] secret = curve.Multiply(remotePublic, priv).X.ToArray(); // Use the x-coordinate as the shared secret
// PBKDF2-HMAC-SHA1 (Common shared secret generation method)
return new Rfc2898DeriveBytes(secret, Encoding.UTF8.GetBytes("P1sN0R4inb0wPl5P1sPls"), 1000).GetBytes(32);
}
}
public static class DHHelper
{
public static byte[] ToArray(this IntX v)
{
v.GetInternalState(out uint[] digits, out bool negative);
byte[] b = DigitConverter.ToBytes(digits);
byte[] b1 = new byte[b.Length + 1];
Array.Copy(b, b1, b.Length);
b1[b.Length] = (byte)(negative ? 1 : 0);
return b1;
}
public static IntX FromArray(byte[] b)
{
if (b.Length == 0) return new IntX();
byte[] b1 = new byte[b.Length - 1];
Array.Copy(b, b1, b1.Length);
uint[] u = DigitConverter.FromBytes(b1);
return new IntX(u, b[b.Length - 1]==1);
}
public static bool BitAt(this uint[] data, long index) => (data[index / 32] & (1 << (int)(index % 32))) != 0;
public static IntX Abs(this IntX i) => i < 0 ? -i : i;
}
}

189
MLAPI/NetworkingManagerComponents/EllipticCurve.cs Normal file
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@ -0,0 +1,189 @@
using System;
using System.Collections.Generic;
using IntXLib;
namespace MLAPI.NetworkingManagerComponents
{
public class CurvePoint
{
public static readonly CurvePoint POINT_AT_INFINITY = new CurvePoint();
public IntX X { get; private set; }
public IntX Y { get; private set; }
private bool pai = false;
public CurvePoint(IntX x, IntX y)
{
X = x;
Y = y;
}
private CurvePoint() { pai = true; } // Accessing corrdinates causes undocumented behaviour
public override string ToString()
{
return pai ? "(POINT_AT_INFINITY)" : "(" + X + ", " + Y + ")";
}
}
public class EllipticCurve
{
public enum CurveType { Weierstrass, Montgomery }
protected readonly IntX a, b, modulo;
protected readonly CurveType type;
public EllipticCurve(IntX a, IntX b, IntX modulo, CurveType type = CurveType.Weierstrass)
{
if (
(type==CurveType.Weierstrass && (4 * a * a * a) + (27 * b * b) == 0) || // Unfavourable Weierstrass curves
(type==CurveType.Montgomery && b * (a * a - 4)==0) // Unfavourable Montgomery curves
) throw new Exception("Unfavourable curve");
this.a = a;
this.b = b;
this.modulo = modulo;
this.type = type;
}
public CurvePoint Add(CurvePoint p1, CurvePoint p2)
{
#if SAFE_MATH
CheckOnCurve(p1);
CheckOnCurve(p2);
#endif
// Special cases
if (p1 == CurvePoint.POINT_AT_INFINITY && p2 == CurvePoint.POINT_AT_INFINITY) return CurvePoint.POINT_AT_INFINITY;
else if (p1 == CurvePoint.POINT_AT_INFINITY) return p2;
else if (p2 == CurvePoint.POINT_AT_INFINITY) return p1;
else if (p1.X == p2.X && p1.Y == Inverse(p2).Y) return CurvePoint.POINT_AT_INFINITY;
IntX x3 = 0, y3 = 0;
if (type == CurveType.Weierstrass)
{
IntX slope = p1.X == p2.X && p1.Y == p2.Y ? Mod((3 * p1.X * p1.X + a) * MulInverse(2 * p1.Y)) : Mod(Mod(p2.Y - p1.Y) * MulInverse(p2.X - p1.X));
x3 = Mod((slope * slope) - p1.X - p2.X);
y3 = Mod(-((slope * x3) + p1.Y - (slope * p1.X)));
}
else if (type == CurveType.Montgomery)
{
if ((p1.X == p2.X && p1.Y == p2.Y))
{
IntX q = 3 * p1.X;
IntX w = q * p1.X;
IntX e = 2 * a;
IntX r = e * p1.X;
IntX t = 2 * b;
IntX y = t * p1.Y;
IntX u = MulInverse(y);
IntX o = w + e + 1;
IntX p = o * u;
}
IntX co = p1.X == p2.X && p1.Y == p2.Y ? Mod((3 * p1.X * p1.X + 2 * a * p1.X + 1) * MulInverse(2 * b * p1.Y)) : Mod(Mod(p2.Y - p1.Y) * MulInverse(p2.X - p1.X)); // Compute a commonly used coefficient
x3 = Mod(b * co * co - a - p1.X - p2.X);
y3 = Mod(((2 * p1.X + p2.X + a) * co) - (b * co * co * co) - p1.Y);
}
return new CurvePoint(x3, y3);
}
public CurvePoint Multiply(CurvePoint p, IntX scalar)
{
if (scalar <= 0) throw new Exception("Cannot multiply by a scalar which is <= 0");
if (p == CurvePoint.POINT_AT_INFINITY) return CurvePoint.POINT_AT_INFINITY;
CurvePoint p1 = new CurvePoint(p.X, p.Y);
scalar.GetInternalState(out uint[] u, out bool b);
long high_bit = -1;
for (int i = u.Length - 1; i>=0; --i)
if (u[i] != 0)
{
for(int j = 31; j>=0; --j)
if ((u[i] & (1<<j))!=0)
{
high_bit = j + i * 32;
goto Next;
}
}
Next:
// Double-and-add method
while(high_bit >= 0)
{
p1 = Add(p1, p1); // Double
if ((u.BitAt(high_bit)))
p1 = Add(p1, p); // Add
--high_bit;
}
return p1;
}
protected IntX MulInverse(IntX eq) => MulInverse(eq, modulo);
public static IntX MulInverse(IntX eq, IntX modulo)
{
eq = Mod(eq, modulo);
Stack<IntX> collect = new Stack<IntX>();
IntX v = modulo; // Copy modulo
IntX m;
while((m = v % eq) != 0)
{
collect.Push(-v/eq/*-(m.l_div)*/);
v = eq;
eq = m;
}
if (collect.Count == 0) return 1;
v = 1;
m = collect.Pop();
while (collect.Count > 0)
{
eq = m;
m = v + (m * collect.Pop());
v = eq;
}
return Mod(m, modulo);
}
public CurvePoint Inverse(CurvePoint p) => Inverse(p, modulo);
protected static CurvePoint Inverse(CurvePoint p, IntX modulo) => new CurvePoint(p.X, Mod(-p.Y, modulo));
public bool IsOnCurve(CurvePoint p)
{
try { CheckOnCurve(p); }
catch { return false; }
return true;
}
protected void CheckOnCurve(CurvePoint p)
{
if (
p!=CurvePoint.POINT_AT_INFINITY && // The point at infinity is asserted to be on the curve
(type == CurveType.Weierstrass && Mod(p.Y * p.Y) != Mod((p.X * p.X * p.X) + (p.X * a) + b)) || // Weierstrass formula
(type == CurveType.Montgomery && Mod(b * p.Y * p.Y) != Mod((p.X * p.X * p.X) + (p.X * p.X * a) + p.X)) // Montgomery formula
) throw new Exception("Point is not on curve");
}
protected IntX Mod(IntX b) => Mod(b, modulo);
private static IntX Mod(IntX x, IntX m)
{
IntX r = x.Abs() > m ? x % m : x;
return r < 0 ? r + m : r;
}
protected static IntX ModPow(IntX x, IntX power, IntX prime)
{
IntX result = 1;
bool setBit = false;
while(power > 0)
{
x %= prime;
setBit = (power & 1) == 1;
power >>= 1;
if (setBit) result *= x;
x *= x;
}
return result;
}
}
}

4
MLAPI/packages.config Normal file
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<?xml version="1.0" encoding="utf-8"?>
<packages>
<package id="IntX" version="1.0.1.0" targetFramework="net35" />
</packages>