New Algebraic Groups Produced By Graphical Passwords Based On Colorings And Labellings

Hui Sun,Xiaohui Zhang,Bing Yao,Meimei Zhao,Bing Xu,Yinong Chen

doi:10.1051/matecconf/201713900152

Abstract

Safety of plain text passwords has been questioned in current researching information passwords. Graphical passwords are another way for alternative text-based passwords and to improve the user account security. As we are constructing Topsnut-graphical passwords that can be traced to an idea of “Graph structure plus the number theory” proposed first by Hongyu Wang with her colleagues, we find that some of Topsnut-graphical passwords can be composed of algebraic groups under the principle of Abelian additive finite group. We apply the odd-elegant labelling of graph theory to produce Topsnut-graphical passwords, and verify our Topsnut-graphical passwords can form algebraic groups, called labelling graphical groups . Our results can provide those users who have business in two or more banks, and our methods are easily transformed into algorithms with polynomial times.

Highlights

Everyone in today’s society has at least two or three passwords
Based on the new definition of graph coloring / labeling operations, we found the graph coloring / label constitute a algebraic group
In Theorem 1, we found that set Odde(H) and 2-element operation F(Hi) ⊕ k F(Hj) constitute a algebraic group for which we are in the same class label, converted from one label to another label provides a feasible method

Summary

Introduction

Everyone in today’s society has at least two or three passwords. Your password can ensure the safety of personal privacy, and provide a sense of security for the user. Alina goes to a bank for her business First of all, she is given six topological structures (six graphs) shown in Fig., and is asked for selecting a graph for making a key. She select the graph shown in Fig. (e) and Fig. (1) as the base of her key She labels each small circle of the graph shown in Fig. (2) with a positive integer, continuously, she labels each edge that joins two small circles with a positive integer, these two small circles are called the ends (vertices in graph theory) of the edge. She obtain her key shown in Fig. (3), this key is called a opsnutgraphical password.

Preliminary

A mixed labelling graphical group

Conclusion