The prevalence of smart devices in our day-to-day activities increases the potential threat to our secret information. To counter these threats like unauthorized access and misuse of phones, only authorized users should be able to access the device. Authentication mechanism provide a secure way to safeguard the physical resources as well the information that is processed. Text-based passwords are the most common technique used for the authentication of devices, however, they are vulnerable to a certain type of attacks such as brute force, smudge and shoulder surfing attacks. Graphical Passwords (GPs) were introduced as an alternative for the conventional text-based authentication to overcome the potential threats. GPs use pictures and have been implemented in smart devices and workstations. Psychological studies reveal that humans can recognize images much easier and quicker than numeric and alphanumeric passwords, which become the basis for creating GPs. In this paper a novel Fractal-Based Authentication Technique (FBAT) has been proposed by implementing a Sierpinski triangle. In the FBAT scheme, the probability of password guessing is low making system resilient against abovementioned threats. Increasing fractal level makes the system stronger and provides security against attacks like shoulder surfing.