树与单圈图优雅标号算法的新型图形密码研究

为解决传统身份验证方法中密码易记忆性与安全性问题,文中提出了一种针对树图与单圈图的优雅标号算法,并将其应用于构建基于优雅标号的新型图形密码。该算法把图结构和数论相结合,递归遍历指定优雅解空间,直到对应邻接矩阵满足优雅目标函数或对应优雅空间遍历完成时结束。文中给出了算法设计步骤,并进行了算法测试分析。结果表明,16个点范围内所有树图与单圈图几乎都是优雅的,只有个别图是非优雅的。据此得到2个定理和一个猜想,为构建基于优雅标号的新型图形密码提供了基础数据。

New Type of Graphical Password Study Based on the Elegant Label Algorithm of Tree and Unicyclic Graph

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.