Graph theory towards designing graphical passwords for mobile devices

Graphical password schemes have been proposed as a possible alternative to text-based schemes. We show several methods for designing a particular class of graphical passwords by the idea of “topological structures plus number theory” in exploring new graphical passwords (Topsnut-GPWs), and focus on the Topsnut-GPWs that can be used to mobile devices with touch screen. We consider Topsnut as a “password language structure”, or a “language-platform”. We present our methods for mobile device Topsnut-GPWs with illustrations of pictures, such as Xu's novel technique “extending-contracting operation” by a special kind of configurations, called domino configurations, and Xu's Kempe equivalence of maximal planar graphs, as well as our offspring operation and splitting operation.