Algebraic Groups for Construction of Topological Graphic Passwords in Cryptography

Researchers discover that topological graphic passwords (Topsnut-gpws) can be easily remembered and run quickly in communication. We explore algebraic groups made by Topsnut-gpws and use them to encryption of networks. Some our algebraic groups are determined by the new graph labellings. More complex text-based passwords with longer byte can be easily obtained from the algebraic groups and new graph labellings. We show the technique of network-gpws for encrypting simple networks. Accordingly, the research bring new problems to mathematics.