private static async Task Client()
{
// Connect to the server using the named pipe.
using (var client = new NamedPipeClientStream(ServerName, PipeName, PipeDirection.InOut))
{
await client.ConnectAsync();
// Select the initial Noise protocol and configuration.
var initial = Protocol.Parse("Noise_NN_25519_ChaChaPoly_SHA256".AsSpan());
var config = new ProtocolConfig(initiator: true);
using (var noise = new NoiseSocket(initial, config, client))
{
// Send the initial handshake message to the server. In the real world the
// negotiation data would contain the initial protocol, supported protocols
// for the switch and retry cases, and maybe some other negotiation options.
await noise.WriteHandshakeMessageAsync(negotiationData : null);
// Receive the negotiation data from the server. In this example we will
// assume that the server decided to retry with Noise_XX_25519_AESGCM_BLAKE2b.
await noise.ReadNegotiationDataAsync();
// New protocol requires static key, so it's generated here.
using (var keyPair = KeyPair.Generate())
{
// The client again plays the role of the initiator.
config = new ProtocolConfig(initiator: true, s: keyPair.PrivateKey);
// Retry with a protocol different from the initial one.
noise.Retry(protocol, config);
// Ignore the empty handshake message.
await noise.IgnoreHandshakeMessageAsync();
// Finish the handshake using the new protocol.
await noise.WriteHandshakeMessageAsync();
await noise.ReadNegotiationDataAsync();
await noise.ReadHandshakeMessageAsync();
await noise.WriteHandshakeMessageAsync();
// Send the transport message to the server.
var request = Encoding.UTF8.GetBytes("I'm cooking MC's like a pound of bacon");
await noise.WriteMessageAsync(request);
// Receive the transport message from the
// server and print it to the standard output.
var response = await noise.ReadMessageAsync();
Console.WriteLine(Encoding.UTF8.GetString(response));
}
}
}
}
private static async Task Server()
{
// Listen for incoming TCP connections.
using (var socket = new Socket(AddressFamily.InterNetwork, SocketType.Stream, ProtocolType.Tcp))
{
socket.Bind(new IPEndPoint(IPAddress.Loopback, Port));
socket.Listen((int)SocketOptionName.MaxConnections);
// Generate the static key pair.
using (var keyPair = KeyPair.Generate())
{
var config = new ProtocolConfig(initiator: false, s: keyPair.PrivateKey);
// Accept the connection and initialize the NoiseSocket with its network stream.
using (var client = await socket.AcceptAsync())
using (var stream = new NetworkStream(client))
using (var noise = new NoiseSocket(initial, config, stream))
{
// Receive the negotiation data from the client. In the real world the
// negotiation data would contain the initial protocol, supported protocols
// for the switch and retry cases, and maybe some other negotiation options.
await noise.ReadNegotiationDataAsync();
try
{
await noise.ReadHandshakeMessageAsync();
}
catch (CryptographicException)
{
// The decryption of the initial handshake message failed
// because the client had an outdated remote static public key.
}
// The server decides to switch to a fallback protocol.
config = new ProtocolConfig(initiator: true, s: keyPair.PrivateKey);
noise.Switch(fallback, config);
// Send the first handshake message using the new protocol. In the
// real world the negotiation data would encode the details about
// the server's desicion to switch protocol.
await noise.WriteHandshakeMessageAsync(negotiationData : null, paddedLength : PaddedLength);
// Finish the handshake using the new protocol.
await noise.ReadNegotiationDataAsync();
await noise.ReadHandshakeMessageAsync();
// Receive the transport message from the client.
var request = await noise.ReadMessageAsync();
// Echo the message back to the client.
await noise.WriteMessageAsync(request, PaddedLength);
}
}
}
}
private static async Task Server()
{
// Listen for connections from TCP network clients.
var listener = new TcpListener(IPAddress.Loopback, Port);
listener.Start();
try
{
// Accept the connection from the TCP client.
using (var client = await listener.AcceptTcpClientAsync())
{
// Generate the static key pair.
using (var keyPair = KeyPair.Generate())
{
var config = new ProtocolConfig(initiator: false, s: keyPair.PrivateKey);
// Initialize the NoiseSocket with the network stream.
using (var stream = client.GetStream())
using (var noise = new NoiseSocket(stream))
{
// Receive the negotiation data from the client. In the real world the
// negotiation data would contain the initial protocol, supported protocols
// for the switch and retry cases, and maybe some other negotiation options.
await noise.ReadNegotiationDataAsync();
// Accept the offered protocol.
noise.Accept(protocol, config);
// Finish the handshake.
await noise.ReadHandshakeMessageAsync();
await noise.WriteHandshakeMessageAsync(paddedLength : PaddedLength);
await noise.ReadNegotiationDataAsync();
await noise.ReadHandshakeMessageAsync();
// Receive the transport message from the client.
var request = await noise.ReadMessageAsync();
// Echo the message back to the client.
await noise.WriteMessageAsync(request, PaddedLength);
}
}
}
}
finally
{
listener.Stop();
}
}
private static async Task Server()
{
// Create the named pipe and wait for the client to connect to it.
using (var server = new NamedPipeServerStream(PipeName, PipeDirection.InOut))
{
await server.WaitForConnectionAsync();
// Initialize the NoiseSocket.
using (var noise = new NoiseSocket(server))
{
// Receive the negotiation data from the client. In the real world the
// negotiation data would contain the initial protocol, supported protocols
// for the switch and retry cases, and maybe some other negotiation options.
await noise.ReadNegotiationDataAsync();
// Read the handshake message from the client, but without decrypting it.
await noise.IgnoreHandshakeMessageAsync();
// New protocol requires static key, so we generate it here.
using (var keyPair = KeyPair.Generate())
{
// The server decides to retry with a new protocol.
// It again plays the role of the responder.
var config = new ProtocolConfig(initiator: false, s: keyPair.PrivateKey);
noise.Retry(protocol, config);
// Request a retry from the client. In the real world the negotiation data
// would encode the details about the server's desicion to make a retry request.
await noise.WriteEmptyHandshakeMessageAsync(negotiationData : null);
// Receive the negotiation data from the client. The client will
// usually just confirm the server's choice of the retry protocol.
await noise.ReadNegotiationDataAsync();
// Finish the handshake using the new protocol.
await noise.ReadHandshakeMessageAsync();
await noise.WriteHandshakeMessageAsync();
await noise.ReadNegotiationDataAsync();
await noise.ReadHandshakeMessageAsync();
// Receive the transport message from the client.
var request = await noise.ReadMessageAsync();
// Echo the message back to the client.
await noise.WriteMessageAsync(request);
}
}
}
}
public async Task WriteEmptyHandshakeMessageAsync(NoiseSocket socket, byte[] negotiationData)
{
await socket.WriteEmptyHandshakeMessageAsync(negotiationData);
var message = new Message
{
NegotiationData = negotiationData,
Value = Utilities.ReadMessage(stream)
};
stream.Position = 0;
Messages.Add(message);
}
private static async Task Client()
{
// Connect to the server using the TCP socket.
using (var socket = new Socket(AddressFamily.InterNetwork, SocketType.Stream, ProtocolType.Tcp))
{
await socket.ConnectAsync(IPAddress.Loopback, Port);
// Generate the static key pair.
using (var keyPair = KeyPair.Generate())
{
// In this example the client has an outdated remote static public key. The server will
// fail to decrypt the initial handshake message, which will trigger a fallback.
var config = new ProtocolConfig(initiator: true, s: keyPair.PrivateKey, rs: new byte[32]);
// Initialize the NoiseSocket with the network stream.
using (var stream = new NetworkStream(socket))
using (var noise = new NoiseSocket(initial, config, stream))
{
// Send the initial handshake message to the server. In the real world the
// negotiation data would contain the initial protocol, supported protocols
// for the switch and retry cases, and maybe some other negotiation options.
await noise.WriteHandshakeMessageAsync(negotiationData : null, paddedLength : PaddedLength);
// Receive the negotiation data from the server. In this example we will
// assume that the server decided to switch to Noise_XX_25519_AESGCM_BLAKE2b.
await noise.ReadNegotiationDataAsync();
// The client now plays the role of the responder.
config = new ProtocolConfig(initiator: false, s: keyPair.PrivateKey);
// Switch to a protocol different from the initial one.
noise.Switch(fallback, config);
// Finish the handshake using the new protocol.
await noise.ReadHandshakeMessageAsync();
await noise.WriteHandshakeMessageAsync(paddedLength : PaddedLength);
// Send the padded transport message to the server.
var request = Encoding.UTF8.GetBytes("I'm cooking MC's like a pound of bacon");
await noise.WriteMessageAsync(request, PaddedLength);
// Receive the transport message from the
// server and print it to the standard output.
var response = await noise.ReadMessageAsync();
Console.WriteLine(Encoding.UTF8.GetString(response));
}
}
}
}
public async Task WriteMessageAsync(NoiseSocket socket, byte[] messageBody)
{
await socket.WriteMessageAsync(messageBody, paddedLength);
var message = new Message
{
MessageBody = messageBody,
PaddedLength = paddedLength,
Value = Utilities.ReadMessage(stream)
};
stream.Position = 0;
Messages.Add(message);
}
public async Task WriteHandshakeMessageAsync(NoiseSocket socket, byte[] negotiationData, byte[] messageBody)
{
bool isNextMessageEncrypted = socket.IsNextMessageEncrypted;
await socket.WriteHandshakeMessageAsync(negotiationData, messageBody, paddedLength);
var message = new Message
{
NegotiationData = negotiationData,
MessageBody = messageBody,
PaddedLength = isNextMessageEncrypted ? paddedLength : default(ushort),
Value = Utilities.ReadMessage(stream)
};
stream.Position = 0;
Messages.Add(message);
}
private static async Task Client()
{
// Open the TCP connection to the server.
using (var client = new TcpClient())
{
await client.ConnectAsync(IPAddress.Loopback, Port);
// Generate the static key pair.
using (var keyPair = KeyPair.Generate())
{
var config = new ProtocolConfig(initiator: true, s: keyPair.PrivateKey);
// Initialize the NoiseSocket with the network stream.
using (var stream = client.GetStream())
using (var noise = new NoiseSocket(protocol, config, stream))
{
// Send the initial handshake message to the server. In the real world the
// negotiation data would contain the initial protocol, supported protocols
// for the switch and retry cases, and maybe some other negotiation options.
await noise.WriteHandshakeMessageAsync(negotiationData : null, paddedLength : PaddedLength);
// Receive the negotiation data from the server. In this example we will
// assume that the server decided to accept the offered protocol.
await noise.ReadNegotiationDataAsync();
// Finish the handshake.
await noise.ReadHandshakeMessageAsync();
await noise.WriteHandshakeMessageAsync(paddedLength : PaddedLength);
// Send the padded transport message to the server.
var request = Encoding.UTF8.GetBytes("I'm cooking MC's like a pound of bacon");
await noise.WriteMessageAsync(request, PaddedLength);
// Receive the transport message from the
// server and print it to the standard output.
var response = await noise.ReadMessageAsync();
Console.WriteLine(Encoding.UTF8.GetString(response));
}
}
}
}
private static async Task Run()
{
using (var client = new TcpClient())
{
await client.ConnectAsync(IPAddress.Loopback, Port);
using (var keyPair = KeyPair.Generate())
{
var config = new ProtocolConfig(initiator: true, s: keyPair.PrivateKey);
using (var stream = client.GetStream())
using (var noise = new NoiseSocket(protocol, config, stream))
{
await noise.WriteHandshakeMessageAsync(negotiationData : clientNegotiationData, paddedLength : PaddedLength);
var serverNegotiationData = await noise.ReadNegotiationDataAsync();
if (serverNegotiationData.Length > 0)
{
throw new Exception("Unsupported Noise protocol.");
}
await noise.ReadHandshakeMessageAsync();
await noise.WriteHandshakeMessageAsync(paddedLength : PaddedLength);
var request = Encoding.UTF8.GetBytes("I'm cooking MC's like a pound of bacon");
await noise.WriteMessageAsync(request, PaddedLength);
var response = await noise.ReadMessageAsync();
Console.WriteLine(Encoding.UTF8.GetString(response));
}
}
}
}
public async Task TestVectors()
{
var s = File.ReadAllText("Vectors/noisesocket.json");
var json = JObject.Parse(s);
using (var stream = new MemoryStream())
{
foreach (var vector in json["vectors"])
{
var initialConfig = vector["initial"];
var switchConfig = vector["switch"];
var retryConfig = vector["retry"];
var alicePrologue = GetBytes(vector, "alice_prologue");
var alicePsks = GetPsks(vector, "alice_psks");
var bobPrologue = GetBytes(vector, "bob_prologue");
var bobPsks = GetPsks(vector, "bob_psks");
var handshakeHash = GetBytes(vector, "handshake_hash");
var config = vector["initial"].ToObject <Config>();
var aliceConfig = new ProtocolConfig(true, alicePrologue, config.AliceStatic, config.AliceRemoteStatic, alicePsks);
var bobConfig = new ProtocolConfig(false, bobPrologue, config.BobStatic, config.BobRemoteStatic, bobPsks);
var protocol = Protocol.Parse(config.ProtocolName.AsSpan());
var queue = ReadMessages(vector["messages"]);
var alice = new NoiseSocket(protocol, aliceConfig, stream, true);
var bob = new NoiseSocket(protocol, bobConfig, stream, true);
var aliceEphemeral = config.AliceEphemeral;
var bobEphemeral = config.BobEphemeral;
alice.SetInitializer(handshakeState => Utilities.SetDh(handshakeState, aliceEphemeral));
bob.SetInitializer(handshakeState => Utilities.SetDh(handshakeState, bobEphemeral));
var writer = alice;
var reader = bob;
if (switchConfig == null && retryConfig == null)
{
var message = queue.Dequeue();
stream.Position = 0;
await alice.WriteHandshakeMessageAsync(message.NegotiationData, message.MessageBody, message.PaddedLength);
Assert.Equal(message.Value, Utilities.ReadMessage(stream));
stream.Position = 0;
Assert.Equal(message.NegotiationData, await bob.ReadNegotiationDataAsync());
bob.Accept(protocol, bobConfig);
Assert.Equal(message.MessageBody, await bob.ReadHandshakeMessageAsync());
Utilities.Swap(ref writer, ref reader);
}
else if (switchConfig != null)
{
config = switchConfig.ToObject <Config>();
protocol = Protocol.Parse(config.ProtocolName.AsSpan());
aliceConfig = new ProtocolConfig(false, alicePrologue, config.AliceStatic, config.AliceRemoteStatic, alicePsks);
bobConfig = new ProtocolConfig(true, bobPrologue, config.BobStatic, config.BobRemoteStatic, bobPsks);
var message = queue.Dequeue();
stream.Position = 0;
await alice.WriteHandshakeMessageAsync(message.NegotiationData, message.MessageBody, message.PaddedLength);
Assert.Equal(message.Value, Utilities.ReadMessage(stream));
stream.Position = 0;
Assert.Equal(message.NegotiationData, await bob.ReadNegotiationDataAsync());
if ((protocol.Modifiers & PatternModifiers.Fallback) != 0)
{
await bob.ReadHandshakeMessageAsync();
bob.Switch(protocol, bobConfig);
message = queue.Dequeue();
stream.Position = 0;
await bob.WriteHandshakeMessageAsync(message.NegotiationData, message.MessageBody, message.PaddedLength);
Assert.Equal(message.Value, Utilities.ReadMessage(stream));
stream.Position = 0;
Assert.Equal(message.NegotiationData, await alice.ReadNegotiationDataAsync());
alice.Switch(protocol, aliceConfig);
Assert.Equal(message.MessageBody, await alice.ReadHandshakeMessageAsync());
}
else
{
bob.Switch(protocol, bobConfig);
bob.SetInitializer(handshakeState => Utilities.SetDh(handshakeState, config.BobEphemeral));
await bob.IgnoreHandshakeMessageAsync();
message = queue.Dequeue();
stream.Position = 0;
await bob.WriteHandshakeMessageAsync(message.NegotiationData, message.MessageBody, message.PaddedLength);
Assert.Equal(message.Value, Utilities.ReadMessage(stream));
stream.Position = 0;
Assert.Equal(message.NegotiationData, await alice.ReadNegotiationDataAsync());
alice.Switch(protocol, aliceConfig);
alice.SetInitializer(handshakeState => Utilities.SetDh(handshakeState, config.AliceEphemeral));
Assert.Equal(message.MessageBody, await alice.ReadHandshakeMessageAsync());
}
}
else if (retryConfig != null)
{
config = retryConfig.ToObject <Config>();
protocol = Protocol.Parse(config.ProtocolName.AsSpan());
aliceConfig = new ProtocolConfig(true, alicePrologue, config.AliceStatic, config.AliceRemoteStatic, alicePsks);
bobConfig = new ProtocolConfig(false, bobPrologue, config.BobStatic, config.BobRemoteStatic, bobPsks);
var message = queue.Dequeue();
stream.Position = 0;
await alice.WriteHandshakeMessageAsync(message.NegotiationData, message.MessageBody, message.PaddedLength);
Assert.Equal(message.Value, Utilities.ReadMessage(stream));
stream.Position = 0;
Assert.Equal(message.NegotiationData, await bob.ReadNegotiationDataAsync());
bob.Retry(protocol, bobConfig);
bob.SetInitializer(handshakeState => Utilities.SetDh(handshakeState, config.BobEphemeral));
await bob.IgnoreHandshakeMessageAsync();
message = queue.Dequeue();
stream.Position = 0;
await bob.WriteEmptyHandshakeMessageAsync(message.NegotiationData);
Assert.Equal(message.Value, Utilities.ReadMessage(stream));
stream.Position = 0;
Assert.Equal(message.NegotiationData, await alice.ReadNegotiationDataAsync());
alice.Retry(protocol, aliceConfig);
alice.SetInitializer(handshakeState => Utilities.SetDh(handshakeState, config.AliceEphemeral));
await alice.IgnoreHandshakeMessageAsync();
}
while (queue.Count > 0)
{
var message = queue.Dequeue();
if (writer.HandshakeHash.IsEmpty)
{
stream.Position = 0;
await writer.WriteHandshakeMessageAsync(message.NegotiationData, message.MessageBody, message.PaddedLength);
Assert.Equal(message.Value, Utilities.ReadMessage(stream));
stream.Position = 0;
Assert.Empty(await reader.ReadNegotiationDataAsync());
Assert.Equal(message.MessageBody, await reader.ReadHandshakeMessageAsync());
}
else
{
stream.Position = 0;
await writer.WriteMessageAsync(message.MessageBody, message.PaddedLength);
Assert.Equal(message.Value, Utilities.ReadMessage(stream));
stream.Position = 0;
Assert.Equal(message.MessageBody, await reader.ReadMessageAsync());
}
Utilities.Swap(ref writer, ref reader);
}
Assert.Equal(handshakeHash, writer.HandshakeHash.ToArray());
Assert.Equal(handshakeHash, reader.HandshakeHash.ToArray());
alice.Dispose();
bob.Dispose();
}
}
}
public static async Task <IEnumerable <Vector> > Generate()
{
var vectors = new List <Vector>();
using (var stream = new MemoryStream())
{
foreach (var test in GetTests())
{
var aliceConfig = new ProtocolConfig(
initiator: true,
prologue: PrologueRaw,
s: test.InitStaticRequired ? AliceStaticRaw : null,
rs: test.InitRemoteStaticRequired ? BobStaticPublicRaw : null,
psks: test.PsksRequired ? psksRaw : null
);
var bobConfig = new ProtocolConfig(
initiator: false,
prologue: PrologueRaw,
s: test.RespStaticRequired ? BobStaticRaw : null,
rs: test.RespRemoteStaticRequired ? AliceStaticPublicRaw : null,
psks: test.PsksRequired ? psksRaw : null
);
var alice = new NoiseSocket(test.Protocol, aliceConfig, stream, true);
var bob = new NoiseSocket(test.Protocol, bobConfig, stream, true);
alice.SetInitializer(handshakeState => Utilities.SetDh(handshakeState, AliceEphemeralRaw.ToArray()));
bob.SetInitializer(handshakeState => Utilities.SetDh(handshakeState, BobEphemeralRaw.ToArray()));
var proxy = new SocketProxy(stream, (ushort)test.PaddedLength);
var queue = new Queue <byte[]>(payloads);
var writer = alice;
var reader = bob;
if (test.Response == Response.Accept)
{
await proxy.WriteHandshakeMessageAsync(alice, InitialNegotiationData, queue.Dequeue());
await bob.ReadNegotiationDataAsync();
bob.Accept(test.Protocol, bobConfig);
await bob.ReadHandshakeMessageAsync();
stream.Position = 0;
Utilities.Swap(ref writer, ref reader);
}
else if (test.Response == Response.Switch)
{
await proxy.WriteHandshakeMessageAsync(alice, InitialNegotiationData, queue.Dequeue());
await bob.ReadNegotiationDataAsync();
if (test.Fallback != null)
{
await bob.ReadHandshakeMessageAsync();
stream.Position = 0;
bob.Switch(test.Fallback, new ProtocolConfig(true, PrologueRaw, BobStaticRaw));
await proxy.WriteHandshakeMessageAsync(bob, SwitchNegotiationData, queue.Dequeue());
await alice.ReadNegotiationDataAsync();
alice.Switch(test.Fallback, new ProtocolConfig(false, PrologueRaw, AliceStaticRaw));
await alice.ReadHandshakeMessageAsync();
stream.Position = 0;
}
else
{
bob.Switch(test.Protocol, aliceConfig);
bob.SetInitializer(handshakeState => Utilities.SetDh(handshakeState, AliceEphemeralRaw.ToArray()));
await bob.IgnoreHandshakeMessageAsync();
stream.Position = 0;
await proxy.WriteHandshakeMessageAsync(bob, SwitchNegotiationData, queue.Dequeue());
await alice.ReadNegotiationDataAsync();
alice.Switch(test.Protocol, bobConfig);
alice.SetInitializer(handshakeState => Utilities.SetDh(handshakeState, BobEphemeralRaw.ToArray()));
await alice.ReadHandshakeMessageAsync();
stream.Position = 0;
}
}
else if (test.Response == Response.Retry)
{
await proxy.WriteHandshakeMessageAsync(alice, InitialNegotiationData, queue.Dequeue());
await bob.ReadNegotiationDataAsync();
bob.Retry(test.Protocol, bobConfig);
await bob.IgnoreHandshakeMessageAsync();
stream.Position = 0;
await proxy.WriteEmptyHandshakeMessageAsync(bob, RetryNegotiationData);
await alice.ReadNegotiationDataAsync();
alice.Retry(test.Protocol, aliceConfig);
await alice.IgnoreHandshakeMessageAsync();
stream.Position = 0;
}
while (queue.Count > 0)
{
if (writer.HandshakeHash.IsEmpty)
{
await proxy.WriteHandshakeMessageAsync(writer, null, queue.Dequeue());
await reader.ReadNegotiationDataAsync();
await reader.ReadHandshakeMessageAsync();
stream.Position = 0;
}
else
{
await proxy.WriteMessageAsync(writer, queue.Dequeue());
}
Utilities.Swap(ref writer, ref reader);
}
var initialConfig = new Config
{
ProtocolName = Encoding.ASCII.GetString(test.Protocol.Name),
AliceStatic = aliceConfig.LocalStatic,
AliceEphemeral = AliceEphemeralRaw,
AliceRemoteStatic = aliceConfig.RemoteStatic,
BobStatic = bobConfig.LocalStatic,
BobEphemeral = BobEphemeralRaw,
BobRemoteStatic = bobConfig.RemoteStatic
};
var switchConfig = new Config
{
ProtocolName = Encoding.ASCII.GetString(test.Protocol.Name),
AliceStatic = bobConfig.LocalStatic,
AliceEphemeral = BobEphemeralRaw,
AliceRemoteStatic = bobConfig.RemoteStatic,
BobStatic = aliceConfig.LocalStatic,
BobEphemeral = AliceEphemeralRaw,
BobRemoteStatic = aliceConfig.RemoteStatic
};
if (test.Fallback != null)
{
switchConfig = new Config
{
ProtocolName = Encoding.ASCII.GetString(test.Fallback.Name),
AliceStatic = AliceStaticRaw,
AliceEphemeral = AliceEphemeralRaw,
BobStatic = BobStaticRaw,
BobEphemeral = BobEphemeralRaw
};
}
var vector = new Vector
{
Initial = initialConfig,
Switch = test.Response == Response.Switch ? switchConfig : null,
Retry = test.Response == Response.Retry ? initialConfig : null,
AlicePrologue = PrologueHex,
AlicePsks = test.PsksRequired ? psksHex : null,
BobPrologue = PrologueHex,
BobPsks = test.PsksRequired ? psksHex : null,
HandshakeHash = Hex.Encode(writer.HandshakeHash.ToArray()),
Messages = proxy.Messages
};
alice.Dispose();
bob.Dispose();
vectors.Add(vector);
}
}
return(vectors);
}
