Mathematical Problems From Topological Graphic Passwords of Cryptography

Topological graphic passwords (Topsnut-gpws) differ from the existing graphical passwords (GPWs), and possess advantages such as, it is convenient to use, easy remember, high secure and individual; and it generates easily text-based passwords from Topsnut-gpws, and Topsnut-gpws are provable security because they are related many mathematical conjectures or NP-problems. Researching Topsnut-gpws produces new mathematical problems and new objects. More complex and highly secure Topsnut-gpws need mathematical support. We collect the problems from Topsnut-gpws and classify them in set theory, graph theory and algebra.