Abstract:

In order to solve the problem of easy memory and security of passwords in traditional authentication methods, an elegant labeling algorithm for tree and unicyclic graphs was proposed, which was further used to construct a new type of graphical password based on elegant labeling. The algorithm combined graph structure and number theory, iteratively traversed the specified elegant solution space until the corresponding adjacency matrix satisfied the elegant objective function or finished when the corresponding elegant space traversal was completed. This paper presented the algorithm design steps and carried out the algorithm test and analysis. The results showed that almost all the tree and unicyclic graphs within the 16-point range were elegant. Only some of the graphs were non-elegant. According to the results, two theorems and one conjecture were obtained, which provided a basic data set based on elegant labeling for the new graphical password.

Key words: graphical password, tree and unicyclic graphs, elegant graph, elegant labeling, non-elegant graph, algorithm of elegant labeling