Graphic Groups towards Cryptographic Systems Resisting Classical and Quantum Computers

Abstract

For building up new cryptographic systems of 'resisting classical computers and quantum computers', we introduce the every-zero mixed graphic group containing many every-zero graphic subgroups, and design a technique of encrypting networks by every-zero mixed graphic groups such that the encrypted networks form graphic group lattices. We show theoretical research for encrypting networks by every-zero mixed graphic groups, and provide particular graphic groups, such as planar graphic group, twin graphic group, dual coloring/labelling graphic group, matching graphic group, Topcode-matrix group and Topcode-string group. These groups are related many mathematical problems, in which some problems are NP-hard.