Topological Graphic Passwords And Their Matchings Towards Cryptography

TL;DR

This paper introduces topological graphic passwords (Topsnut-gpws) that utilize graph matchings and labellings for enhanced cryptographic security, emphasizing their computational efficiency and theoretical foundations.

Contribution

It presents new graph labellings and matching partitions, demonstrating their realizability in trees and spanning trees, and explores their applications in cryptography and graph theory.

Findings

Topsnut-gpws can be efficiently stored and run using classical matrices.

New graph labellings are realizable for trees and spanning trees.

Graph labellings relate to set matching problems in number theory.

Abstract

Graphical passwords (GPWs) are convenient for mobile equipments with touch screen. Topological graphic passwords (Topsnut-gpws) can be saved in computer by classical matrices and run quickly than the existing GPWs. We research Topsnut-gpws by the matching of view, since they have many advantages. We discuss: configuration matching partition, coloring/labelling matching partition, set matching partition, matching chain, etc. And, we introduce new graph labellings for enriching Topsnut-matchings and show that these labellings can be realized for trees or spanning trees of networks. In theoretical works we explore Graph Labelling Analysis, and show that every graph admits our extremal labellings and set-type labellings in graph theory. Many of the graph labellings mentioned are related with problems of set matching partitions to number theory, and yield new objects and new problems to graph theory.