探索整数格的拓扑图编码实现OA

In the post quantum era,lattice cryptography is featured as an interdisciplinary and diversified research method,and is most likely to become post quantum cryptography.The graphic lattice in topological coding is the product of interdisciplinary study.Graphs in graphic lattices are stored by matrices and run in the computer,the main theoretical technology of topological coding is originated from mathematical disciplines such as discrete mathematics,number theory and algebra.Because topological coding contains a lot of mathematical conjectures and NP-problems,the number-based strings generated by topological coding possess irreversibility and computational security.Some new labelings and colorings are defined in this paper,and the algorithms to realize these labelings and colorings are given,and the classes of graphs admitting these new labelings and colorings are determined.We establish graphic lattices based on graph operations and graphic lattice bases,for asymmetric cryptography,and show connections among caterpillar-graphic lattices,their complementary graphic lattices and integer lattices.The technical methods in this paper are shown by effective and feasible algorithms.