Strings And Colorings Of Topological Coding Towards Asymmetric Topology Cryptography

TL;DR

This paper explores advanced topological cryptography techniques using various number-based strings and colorings, proposing new lattice structures and algorithms for network encryption and asymmetric topology cryptography.

Contribution

It introduces novel string-colorings, graphic lattices, and topological algorithms, addressing anti-quantum cryptography and NP-hard problems in network security.

Findings

Proposes new number-based string structures and colorings.

Introduces graphic lattices for network encryption.

Addresses NP-hard problems in topological cryptography.

Abstract

We, for anti-quantum computing, will discuss various number-based strings, such as number-based super-strings, parameterized strings, set-based strings, graph-based strings, integer-partitioned and integer-decomposed strings, Hanzi-based strings, as well as algebraic operations based on number-based strings. Moreover, we introduce number-based string-colorings, magic-constraint colorings, and vector-colorings and set-colorings related with strings. For the technique of encrypting the entire network at once, we propose graphic lattices related with number-based strings, Hanzi-graphic lattices, string groups, all-tree-graphic lattices. We study some topics of asymmetric topology cryptography, such as topological signatures, Key-pair graphs, Key-pair strings, one-encryption one-time and self-certification algorithms. Part of topological techniques and algorithms introduced here are closely related with NP-complete problems or NP-hard problems.