有限域上Chebyshev映射的周期性分析

The Periodic Analysis of Chebyshev Map Over the Finite Field

基于有限域上Chebyshev映射的公钥密码系统的安全性直接取决于Chebyshev映射的周期性。利用矩阵变换讨论有限域ZN上Chebyshev映射的周期性问题,并给出一种快速的寻找周期的方法,从而使得对有限域上Cheyshev公钥加密方案的攻击成为可能。

The security of public-key cryptosystem based on Chebyshev map is determined by the periodicity of Chebyshev map. In this paper, the period problem of Chebyshev map over the finite field ZN is analyzed, and a fast algorithm for period search is proposed, thus making the attack to the Chebyshev public-key cryptosystem possible.