计算机应用 ›› 2010, Vol. 30 ›› Issue (3): 680-684.

• 信息安全 • 上一篇    下一篇

TD-ERCS混沌系统的几个短周期轨道及其稳定性

贾伟尧1,盛利元2,陈亚丽3   

  1. 1. 西南大学物理科学与技术学院
    2. 中南大学物理科学与技术学院
    3. 漯河职业技术学院
  • 收稿日期:2009-09-06 修回日期:2009-11-01 发布日期:2010-03-14 出版日期:2010-03-01
  • 通讯作者: 贾伟尧
  • 基金资助:
    国家自然科学基金资助项目;西南大学青年基金项目

Several short periodic trajectories of TD-ERCS and their stabilities

  • Received:2009-09-06 Revised:2009-11-01 Online:2010-03-14 Published:2010-03-01
  • Contact: JIA WeiYao

摘要: 基于切延迟的椭圆反射腔系统(TD-ERCS)是一类为混沌加密而设计的混沌系统,虽然其具有全域混沌等优良的加密特性,但TD-ERCS包含大量的可能导致弱密钥的短周期轨道,对这些短周期轨道进行功率谱分析与Lyapunov计算,发现m=0时周期轨道是稳定的,m≥1时周期轨道是不稳定的,且这种不稳定性不依赖参数μ的选取,切延迟操作使得TD-ERCS系统从有序走向混沌,表明TD-ERCS在混沌加密中不会存在稳定的短周期轨道所导致的弱密钥。

关键词: 混沌加密, 基于切延迟的椭圆反射腔系统, 周期轨道, 稳定性

Abstract: TD-ERCS is a class of chaotic system designed for chaos encryption. Though it has good encryption properties such as being chaotic in all fields for encryption, Tangent-Delay Ellipse Reflecting Cavity map System (TD-ERCS) is comprises of quite a lot of short cycling trajectories, which may lead to weak keys. Power spectrum analysis and Lyapunov calculation of the periodic trajectories indicated that the periodic trajectories were stable under tangent-delay operation m=0 and instable under tangent-delay operation m≥1. And the instability was independent of parameter μ, TD-ERCS tended from order to chaos under tangent-delay operation. The results show that TD-ERCS does not have weak keys caused by the stable short-period Trajectories.

Key words: chaotic encryption, Tangent-Delay Ellipse Reflecting Cavity map System (TD-ERCS), periodic trajectory, stability