How could I create an Authentication process two Arduino?

You are connecting two Arduino UNOs using Serial Port, probably, as per following diagram of Fig-1. Now, what you want for the UNOs to do? Will they exchnage data between them? For example: UNO-1 will send this message: "Hello! I am UNO-1 Sender." to UNO-2. In respones, UNO-2 will send this message to UNO-1: "Yes! I am UNO-2 Receiver."


Figure-1: