计算机科学

计算机科学 ›› 2022, Vol. 49 ›› Issue (4): 376-384.doi: 10.11896/jsjkx.210300116

所属专题： 密码学 虚拟专题

• 信息安全 • 上一篇    

基于离散动力学反控制的混沌序列密码算法

赵耿1,2, 李文健1,2, 马英杰2   

  1. 1 西安电子科技大学通信工程学院 西安 710071;
    2 北京电子科技学院密码系 北京 100070
  • 收稿日期:2021-03-11 修回日期:2021-07-22 发布日期:2022-04-01
  • 通讯作者: 李文健(594253850@qq.com)
  • 作者简介:(zg@besti.edu.cn)
  • 基金资助:
    国家自然科学基金面上项目(61772047); 2018-2021年北京市“高精尖”学科建设项目创新类项目(3201017)

Chaotic Sequence Cipher Algorithm Based on Discrete Anti-control

ZHAO Geng1,2, LI Wen-jian1,2, MA Ying-jie2   

  1. 1 School of Telecommunication Engineering, Xidian University, Xi'an 710071, China;
    2 Department of Cryptography, Beijing Electronic Science and Technology Institute, Beijing 100070, China
  • Received:2021-03-11 Revised:2021-07-22 Published:2022-04-01
  • About author:ZHAO Geng,born in 1964,Ph.D,professor,Ph.D supervisor,is a member of China Computer Federation.His main research interests include chaotic secure communication and information security.LI Wen-jian,born in 1996,postgra-duate.His main research interests include chaotic sequence and information secu-rity.
  • Supported by:
    This work was supported by the National Natural Science Foundation of China(61772047) and “High-Precision” Program Construction Project in Beijing Universities (3201017).

PDF (PC)

583

摘要： 针对离散混沌动力学系统在数字域上存在退化简并的问题,提出了一种可以配置系统的Lyapunov指数全部为正的算法,该算法基于混沌反控制原理,首先引入一个反馈矩阵,将该矩阵中的所有参数做了细致的规定设置,从理论角度证明了该算法能将Lyapunov指数配置为全正。随后对系统轨道的有界性和Lyapunov指数的有限性进行了证明,再通过几个算例对配置的数值进行仿真分析和性能比较,验证了所提算法能产生无简并的离散混沌系统,而且在数值准确性和算法运行时间方面存在一定的优势。再利用配置好的混沌系统生成序列然后量化,量化方案为取出序列有效数字组合,对该序列进行一些动态变换处理加强输出序列的随机性和序列的复杂性。将经过变换的输出序列转换为二进制序列,进行多项随机性和统计性测试,与一般混沌序列进行性能比较,测试结果表明该序列有着更好的随机特性,能够应用于混沌序列密码体制中。

关键词: Lyapunov指数, 反控制, 混沌系统, 序列密码

Abstract: Aiming at the degeneracy problem of discrete chaotic dynamics system in the digital domain, an algorithm that can configure the Lyapunov exponents of the system to be all positive is proposed.The algorithm is based on the principle of chaos anti-control.First, a feedback matrix is introduced.All the parameters in the set are specified carefully, and it is proved from a theore-tical point of view that the algorithm can configure the Lyapunov exponent to be fully positive.Subsequently, the boundedness of the system orbit and the finiteness of the Lyapunov exponent are proved, and the numerical simulation analysis and performance comparison of the configuration are carried out through several examples, so as to verify that the algorithm can produce a discrete chaotic system without degenerate.There are certain advantages in numerical accuracy and algorithm running time.The configured chaotic system is then used to generate the sequence and then quantized.The quantization scheme is to take out the effective digital combination of the sequence.Some dynamic transformation processing on the sequence can enhance the randomness and complexity of the output sequence.We convert the transformed output sequence into a binary sequence, perform a number of randomness and statistical tests, and compare the performance with the general chaotic sequence.The test results show that the sequence has better random characteristics and can be used in a chaotic sequence cipher system.

Key words: Anti-control, Chaotic system, Lyapunov exponent, Sequence cipher

中图分类号: 

  • TN918.91
[1] CUI J,WANG Y,ZHANG J.Full Session Key AgreementScheme Based on Chaotic Map in Vehicular Ad hoc Networks[J].IEEE Transactions on Vehicular Technology,2020,69(8):8914-8924.
[2] SURESHKUMAR V,AMIN R,OBAIDAT M S,et al.An enhanced mutual authentication and key establishment protocol for TMIS using chaotic map[J].Journal of Information Security and Applications,2020,53:102539.
[3] CHEN S K,YU S M,LÜ J H,et al.Design and FPGA-based realization of a chaotic secure video communication system[J].IEEE Transactions on Circuits and Systems for Video Techno-logy,2018,28(9):2359-2371.
[4] ZHOU S,WANG X Y.Simple estimation method for the largest Lyapunov exponent of continuous fractional-order differential equations[J].Physica A:Statistical Mechanics and its Applications,2021,563:125478.
[5] CHEN H K,LEE C I.Anti-control of chaos in rigid body motion[J].Chaos Solitons & Fractals,2004,21(4):957-965.
[6] CHEN G R,WANG X F.Chaos of Dynamical System—Theory,Method and Application [M].Shanghai:Shanghai Jiaotong University Press,2006.
[7] WANG C,FAN C,DING Q.Constructing Discrete Chaotic Systems with Positive Lyapunov Exponents[J].International Journal of Bifurcation & Chaos,2018,28(7):1850084.
[8] ZHANG L,TANG J S,OUYANG K J.Anti-control of perioddoubling bifurcation for a variable substitution model of Logistic map[J].Optik-International Journal for Light and Electron Optics,2017,130:1327-1332.
[9] YUAN C G,CHEN X.Generalized Chaos Control of Discrete Systems[J].Mathematics in Practice and Knowledge,2013,43(23):206-212.
[10] LIU N.Research on chaos anti-control of a class of linear systems[J].China Science and Technology Information,2012(12):60-61.
[11] ZHAO G,LI H,MA Y J,et al.Discrete dynamic system withoutdegradation-configuration of N positive Lyapunov exponents[J].Journal of Electronics and Information,2019,41(9):2280-2286.
[12] ZHAO L.Research on Anti-degradation Sequence Cipher[D].Xi’an:Xidian University,2020.
[13] XIANG H Y,LIU L F.A new perturbation-feedback hybridcontrol method for reducing the dynamic degradation of digital chaotic systems and its application in image encryption[J].Multimedia Tools and Applications,2021,80(1):1-25.
[14] WU T,JIN J G,WEI M J.A Hash function algorithm based on variable parameter cascade chaos[J].Computer Research and Development,2016,53(3):674-681.
[15] SHI J P,YANG L T.Design and circuit simulation of a switched chaotic system[J].Modern Electronic Technology,2019,42(8):59-62,67.
[16] YU S M,LU J H,CHEN G R.Anti-control method of power system and its application[M].Beijing:Science Press,2013.
[17] WEN H P,YU S M,LU J H.Encryption algorithm based on Hadoop big data platform and non-degenerate high-dimensional discrete hyperchaotic system[J].Acta Physica Sinica,2017,66(23):76-89.
[18] GAN Q Y.Voice chaotic secure communication based on multicast and WAN transmission and ARM implementation [D].Guangdong University of Technology,2016.
[19] OZKAYNAK F.Brief review on application of nonlinear dyna-mics in image encryption[J].Nonlinear Dynamics,2018,92(2):305-313.
[20] PREISHUBER M,HUTTER T,KATZENBEISSER S,et al.Depreciating motivation and empirical security analysis of chaos-based image and encryption[J].IEEE Transactions on Information Forensics And Security,2018,13(9):2137-2150.
[1] 王丽娟, 李国东, 吕冬梅.
基于动态参数控制的混沌系统图像加密算法
Chaotic System Image Encryption Algorithm Based on Dynamic Parameter Control
计算机科学, 2019, 46(11A): 469-472.
[2] 赵方正, 李成海, 刘晨, 宋亚飞.
超混沌彩色图像加密算法优化及安全性分析
Security Analysis and Optimization of Hyper-chaotic Color Image Encryption Algorithm
计算机科学, 2019, 46(11A): 483-487.
[3] 严波, 贺少波.
分数阶统一混沌系统动力学及其复杂度分析
Dynamics and Complexity Analysis of Fractional-order Unified Chaotic System
计算机科学, 2019, 46(11A): 539-543.
[4] 李修云,陈帅.
基于马尔科夫链理论的改进的最大Lyapunov指数混沌预测法
Improved Maximal Lyapunov Exponent Chaotic Forecasting Method Based on Markov Chain Theory
计算机科学, 2016, 43(4): 270-273. https://doi.org/10.11896/j.issn.1002-137X.2016.04.055
[5] 柴秀丽,甘志华.
基于超混沌系统的位级自适应彩色图像加密新算法
New Bit-level Self-adaptive Color Image Encryption Algorithm Based on Hyperchaotic System
计算机科学, 2016, 43(4): 134-139. https://doi.org/10.11896/j.issn.1002-137X.2016.04.027
[6] 柴秀丽,甘志华.
一种基于时空混沌系统的彩色图像自适应位级加密算法
Self-adaptive Bit-level Colour Image Encryption Algorithm Based on Spatiotemporal Chaotic System
计算机科学, 2015, 42(7): 204-209. https://doi.org/10.11896/j.issn.1002-137X.2015.07.045
[7] 柴秀丽,甘志华,王 俊.
一类时滞混沌系统的修正函数投影拟同步
Modified Function Projective Quasisynchronization of a Class of Delayed Chaotic System
计算机科学, 2015, 42(5): 169-172. https://doi.org/10.11896/j.issn.1002-137X.2015.05.034
[8] 成平广,马跃,黄军建,刘冀.
忆阻混沌系统的有限时间控制
Finite Time Control of Memristor Chaotic Systems
计算机科学, 2015, 42(2): 260-262. https://doi.org/10.11896/j.issn.1002-137X.2015.02.054
[9] 方颖,徐炳吉.
一种基于荷控忆阻器的混沌电路
Charge-controlled Memristor-based Chaotic Circuit
计算机科学, 2014, 41(Z11): 447-450.
[10] 柴秀丽,王玉璟,袁光耀,史春晓.
未知干扰下混沌系统的修正函数投影滞后同步
Modified Function Projective Lag Synchronization of Chaotic Systems Subject to Unknown Disturbance
计算机科学, 2014, 41(4): 283-286.
[11] 陈河山,吕珍珍,罗伟.
一个基于离散混沌加密的数字水印算法
Digital Image Watermarking Algorithm Based on Dispersed Chaotic Mapping System
计算机科学, 2014, 41(12): 48-52. https://doi.org/10.11896/j.issn.1002-137X.2014.12.011
[12] 张小红,王 伟.
异维异构混沌系统同步及其在保密通信中的应用
Synchronization between Different Hyperchaotic Systems and Dimensions and its Application in Secret Communication
计算机科学, 2012, 39(4): 220-222.
[13] 卢辉斌,孙艳.
基于新的超混沌系统的图像加密方案
Image Encryption Scheme Based on Novel Hyperchaotic System
计算机科学, 2011, 38(6): 149-152.
[14] 张向华.
一种改进的基于时空混沌系统的Hash函数构造方法
Modified Algorithm for Hash Function Based on the Spatiotemporal Chaotic System
计算机科学, 2009, 36(7): 252-255. https://doi.org/10.11896/j.issn.1002-137X.2009.07.062
[15] 邓绍江 李艳涛 张岱固 杨吉云.
一种基于混沌的JPEG2000图像加密算法

计算机科学, 2009, 36(5): 273-275.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
渝ICP备16013121号-4
地址：重庆市渝北区洪湖西路18号    邮编：401121  
电话：023-63500828（编辑部） 023-67039612（会议/专题） 023-67039623（财务/发票）
E-mail：jsjkx12@163.com
本系统由北京玛格泰克科技发展有限公司设计开发