Graphic Lattices for Constructing High-Quality Networks

Since lattice-based cryptosystem is resisting classical computers and quantum computers, we, by means of graph operations and algebraic technique, will construct graphic lattices, graphic group lattices, Topcode-matrix lattices, matching-type graphic lattices, graphic lattice sequences in this article. Graphic lattices introduced here are various sets of Topsnut-gpws (topological structures plus number theory) in topological coding. We propose a way to realize connecting graphic lattices and traditional lattices. Clearly, these lattices are high-quality network sets, since dynamic graphs are just dynamic networks, meanwhile, these graphic lattices also lead to many new problems in mathematics.