The cryptography models designed by double odd labelling of trees

Abstract

Authenticating user is a core part of system security. We propose a new cryptographic model, lock-Trees and key-Trees, and our idea differs from current graphical passwords. Graphs and their double odd labellings are applied to establish the concepts of key-Trees and lock-Trees based on abundant of graphs having smaller orders and their corresponding double odd labellings. We put forward two methods, called Edge-Construction and Paste-Construction by So-DO-labellings, to construct trees of larger orders by some smaller trees such that the new trees have some set-ordered double odd labellings. Our results may be applied in information security and graph theory. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.