How could I create an Authentication process two Arduino?

What are you actually asking? If you want advice or help, in my experience of forums like this you're more likely to get help if you show in detail what you've done so far and explain where you got stuck. Then ask for help specifically on "this" or "that".

And forgive me for saying so, if it's a "university project" should you not be able to do this without resorting to a hobbyist forum?