Topological Authentication Technique In Topologically Asymmetric Cryptosystem
This work addresses data protection and cryptography needs in the face of quantum computing, but it appears incremental as it builds on existing topological methods without clear breakthroughs.
The paper tackles the challenge of making topological authentication practical by leveraging graph theory and mathematical structures, resulting in a framework that includes various graph operations, matrices, and labelings to achieve computational and provable security.
Making topological authentication from theory to practical application is an important and challenging task. More and more researchers pay attention on coming quantum computation, privacy data protection, lattices and cryptography. Research show the advantages of topological authentications through graph operations, various matrices, graph colorings and graph labelings are: related with two or more different mathematical areas, be not pictures, there are huge number of colorings and labelings, rooted on modern mathematics, diversity of asymmetric ciphers, simplicity and convenience, easily created, irreversibility, computational security, provable security, and so on. Topological authentications based on various graph homomorphisms, degree-sequence homomorphisms, graph-set homomorphisms. Randomly topological coding and topological authentications are based on Hanzi authentication, randomly adding-edge-removing operation, randomly leaf-adding algorithms, graph random increasing techniques, operation graphic lattice and dynamic networked models and their spanning trees and maximum leaf spanning trees. Realization of topological authentication is an important topic, we study: number-based strings generated from colored graphs, particular graphs (complete graphs, trees, planar graphs), some methods of generating public-keys. some techniques of topologically asymmetric cryptosystem are: W-type matching labelings, dual-type labelings, reciprocal-type labelings, topological homomorphisms, indexed colorings, graphic lattices, degree-sequence lattices, every-zero Cds-matrix groups of degree-sequences, every-zero graphic groups, graphic lattices having coloring closure property, self-similar networked lattices.