How to implement an easy secure socket connection

I'm writing a simple client-server game in c#. my prototype works well with socket programming. i used socket class with SocketAsyncEventArgs for asyncing my code. now for alpha version i like (must) create a secure connection. but i don't have any background about security and SSL and TLS.

I found a class for this purpose: sslstream. but .Net docs are not understandable for me as a beginner. another problem is SocketAsyncEventArgs doesn't work by streams like TCPClient Class.

so can anyone guide me how to implement a simple secure connection with sockets? there is two requirements:
1- it should be fast an low-latency and I appreciate it supports non blocking (async) pattern.
2- it should support very small messages. my game commands are 10 bytes average. I don't like encrypted commands become 128 bytes!

because my server is not public and only my clients connect to it, i don't like to register and buy a certificate.

please provide a step-by-step answer. first how to create some keys (Public- private... i don't know) second how to authenticate client and third how to communicate securely.

sincerely Thanks for reading this question until end and previously thanks for your answers. best regards!

Solution

for those how are not familiar with cryptography like me, there is a very good start point for creating a secure scheme in the Microsoft docs. .NET Framework Cryptography Model

Creating a cryptographic scheme is not a trivial task! (Source)

but this tutorial is basic material about implementing a basic security system.

EDIT: Microsoft have deleted the page about creating a cryptographic scheme, so i paste a google chached version for you:

Creating a Cryptographic Scheme

The cryptographic components of the .NET Framework can be combined to create different schemes to encrypt and decrypt data.

A simple cryptographic scheme for encrypting and decrypting data might specify the following steps:

Each party generates a public/private key pair.

The parties exchange their public keys.

Each party generates a secret key for TripleDES encryption, for example, and encrypts the newly created key using the other's public key.

Each party sends the data to the other and combines the other's secret key with its own, in a particular order, to create a new secret key.

The parties then initiate a conversation using symmetric encryption.

Creating a cryptographic scheme is not a trivial task.