How Does This VB.Net Program Implement Telegram Authorization Key Generation and Communication?

Here is a program in vb.Net that should help you implement the Telegram Authorization key generation and further communication you requested:

    'TCP Socket Event Handlers
    Public Shared Sub IO_Handler(sender As Object, e As SocketAsyncEventArgs)
        Log($"{e.LastOperation}:{e.SocketError}:{e.BytesTransferred}", ConsoleColor.Cyan)

        Select Case e.SocketError
            Case SocketError.Success
                Select Case e.LastOperation
                    Case SocketAsyncOperation.Connect 'A socket Connect operation.
                        Log("Connected to " & e.ConnectSocket.RemoteEndPoint.ToString, ConsoleColor.Green)
                        are.Set()

                    Case SocketAsyncOperation.Disconnect, SocketAsyncOperation.Connect
                        RaiseEvent Disconneted()

                    Case SocketAsyncOperation.Receive 'A socket Receive operation.
                        HandleData(e)
                End Select

            Case SocketError.ConnectionAborted
                RaiseEvent Disconneted()
        End Select
    End Sub

    'TCP Send data function
    Private Shared Sub SendData(b() As Byte, Optional read As Boolean = False)
        If Not IsConnected() Then
            Log("Connection Closed!", ConsoleColor.DarkRed)
            RaiseEvent Disconneted()
            Exit Sub
        End If

        b = TCPPack(b)

        Dim arg = New SocketAsyncEventArgs With {.RemoteEndPoint = ep}
        AddHandler arg.Completed, AddressOf IO_Handler
        arg.SetBuffer(b, 0, b.Length)

        Try
            If Not soc.SendAsync(arg) Then
                IO_Handler(soc, arg)
            End If
        
            If read Then
                ReadData()
            End If
        Catch ex As Exception
                Log("SendData: " & ex.ToString, ConsoleColor.Red)
        End Try

    End Sub

    'TCP Receive data function
    Private Shared Sub ReadData(Optional wait As Integer = 0)
        If Not IsConnected() Then
            Log("Connection Closed!", ConsoleColor.DarkRed)
            RaiseEvent Disconneted()
            Exit Sub
        End If

        Dim arg = New SocketAsyncEventArgs With {.RemoteEndPoint = ep}
        AddHandler arg.Completed, AddressOf IO_Handler

        Dim b(BUFFER_SIZE - 1) As Byte
        arg.SetBuffer(b, 0, BUFFER_SIZE)

        Try
            If Not soc.ReceiveAsync(arg) Then
                IO_Handler(soc, arg)
            End If
        Catch ex As Exception
            Log("ReadMessages: " & ex.ToString, ConsoleColor.Red)
        End Try
    End Sub


    Private Shared Function TCPPack(b As Byte()) As Byte()
        Dim a = New List(Of Byte)
        Dim len = CByte(b.Length / 4)

        If efSent = False Then --TCP abridged version
            efSent = True
            a.Add(&HEF)
        End If

        If len >= &H7F Then
            a.Add(&H7F)
            a.AddRange(BitConverter.GetBytes(len))
        Else
            a.Add(len)
        End If

        a.AddRange(b) --only data, no sequence number, no CRC32

        Return a.ToArray
    End Function

    Private Shared Sub HandleData(e As SocketAsyncEventArgs)
        If e.BytesTransferred = 0 Then --no pending data
            Log("The remote end has closed the connection.")
            Exit Sub
        End If

        Dim len As Integer = e.Buffer(0)
        Dim start = 1

        If len = &H7F Then
            len = e.Buffer(1)
            len += e.Buffer(2) << 8
            len += e.Buffer(3) << 16
            start = 4
        End If

        len = 4 * len

        Dim data(len - 1) As Byte
        Array.Copy(e.Buffer, start, data, 0, data.Length)


        ProcessResponse(data)

        ReadData()
    End Sub

    Private Shared Sub ProcessResponse(data As Byte())
        Try
            Dim r = New UnencryptedMessage(data)
            Log(r.ToString, ConsoleColor.Yellow, logTime:=False)

            Select Case r.message_type
                Case resPQ.Classid
                    RequestDHKeyExchange(New resPQ(r.message_data))
                Case server_DH_params_ok.Classid
                    RequestSetDH_params(New server_DH_params_ok(r.message_data), new_nonce)
                Case server_DH_params_fail.Classid
                    Log(New server_DH_params_fail(r.message_data).ToString, ConsoleColor.DarkMagenta)
                Case dh_gen_ok.Classid
                    Log(New dh_gen_ok(r.message_data).ToString, ConsoleColor.Green)
                Case dh_gen_retry.Classid
                    Log(New dh_gen_retry(r.message_data).ToString, ConsoleColor.DarkMagenta)
                Case dh_gen_fail.Classid
                    Log(New dh_gen_fail(r.message_data).ToString, ConsoleColor.DarkMagenta)
                Case Else
                    Log($&quot;Unhandled type: {r.message_type}&quot;, ConsoleColor.Magenta)
            End Select
        Catch ex As Exception
            Log($&quot;Error: {ex.ToString}&quot;, ConsoleColor.Red)
            Log(B2H(data), ConsoleColor.DarkRed, logTime:=False)
        End Try
    End Sub

    'Step 1 Request PQ
    Private Shared Sub RequestPQAuthorization()
        Send(MTProto.req_pq)
    End Sub

    'Step 2
    Shared Function req_pq(Optional nonce As Byte() = Nothing) As UnencryptedMessage
        --req_pq#60469778 
        --nonce:int128
        If nonce Is Nothing Then
            ReDim nonce(15)
            RND.NextBytes(nonce)
        End If

        Dim d = New List(Of Byte)
        d.AddRange({120, 151, 70, 96}) --60469778
        d.AddRange(nonce)

        Return New UnencryptedMessage(0, CreateMessageId, d.ToArray)
    End Function

    Private Shared Function CreateMessageId() As Int64
        Return CLng((Date.UtcNow.Ticks - ZERO_TICK) * 429.4967296)
    End Function

    'Step3
    Private Shared Sub RequestDHKeyExchange(r As resPQ)
        Log(r.ToString, ConsoleColor.Gray, logTime:=False)

        'decompose prime cofactors
        Dim pp = New PrimeProduct(r.pq)
        Log(pp.ToString, ConsoleColor.Gray, logTime:=False)

        'encrypted_data Generation
        Dim pq = New P_Q_inner_data(r.pq, pp.p, pp.q, r.nonce, r.server_nonce)
        new_nonce = pq.new_nonce

        'The serialization Of P_Q_inner_data produces some String data. This Is followed by encrypted_data
        'data_with_hash := SHA1(data) + data + (any random bytes); such that the length equal 255 
        Dim data_with_hash = New List(Of Byte)

        'SHA1(data) = xxx- 40 =20 bytes
        Using sha1 = New SHA1Managed
            Dim b = pq.ToBytes
            data_with_hash.AddRange(sha1.ComputeHash(b))
            data_with_hash.AddRange(b)
        End Using

        If data_with_hash.Count < 255 Then
            Dim pad(255 - data_with_hash.Count - 1) As Byte
            RND.NextBytes(pad)
            data_with_hash.AddRange(pad)
        End If

        'RSA(data_with_hash, server_public_key) = xxx - 512 = 256 bytes
        Dim key = i2H(r.fingerprints(0)) 'c3b42b026ce86b21
        Dim zb = Crypto.rsaEncrypt(data_with_hash.ToArray, key)
        Send(MTProto.req_DH_params(r.nonce, r.server_nonce, pp.p, pp.q, r.fingerprints(0), zb))
    End Sub

    'Step 4

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