Science China Information Sciences

, Volume 55, Issue 5, pp 1162–1171 | Cite as

Weak key analysis for chaotic cipher based on randomness properties

  • RuMing Yin
  • Jian Wang
  • Jian YuanEmail author
  • XiuMing Shan
  • XiQin Wang
Research Paper


Weak key analysis is a key issue in the design of chaotic ciphers. While most of the existing research focusing on the degradation of the chaotic sequences which causes weak keys, we point out that the parameters for which the chaotic sequences do not degrade are still possible to be weak keys. In this paper, we propose a new approach based on the rigorous statistical test to improve the weak key analysis. The weak keys of a specific chaotic cipher are investigated by using our method and a large number of new weak keys are detected. These results verify that our method is more effective. On the other hand, although statistical tests are now widely adopted to test the chaos-based bit sequences, there are few reports of analysis results on the weak keys or weak sequences of chaotic cipher. Thus our work may be helpful for current research on statistical tests of chaotic cipher.


chaos cryptography statistical test weak keys sequence randomness 


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  1. 1.
    Kocarev L. Chaos-based cryptography: a brief overview. IEEE Circ Syst Mag, 2001, 1: 6–21CrossRefGoogle Scholar
  2. 2.
    Zhang Y W, Wang Y M, Shen X B. Chaos-based image encryption algorithm using alternate structure. Sci China Ser F-Inf Sci, 2007, 50: 334–341MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Alvarez G, Li S. Some basic cryptographic requirements for chaos-based cryptosystems. Int J Bifurcat Chaos, 2006, 16: 2129–2151MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Biham E. Cryptanalysis of the chaotic-map cryptosystem suggested at EuroCrypt’91. In: Advances in Cryptology — EuroCrypt’91. Berlin: Springer, 1991. 532–534Google Scholar
  5. 5.
    Alvarez G, Montoya F, Romera M, et al. Cryptanalysis of a discrete chaotic cryptosystem using external key. Phys Lett A, 2003, 319: 334–339MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Skrobek A. Cryptanalysis of chaotic stream cipher. Phys Lett A, 2007, 363: 84–90CrossRefGoogle Scholar
  7. 7.
    Li S, Alvarez G, Chen G, et al. Breaking a chaos-noise-based secure communication scheme. Chaos, 2005, 15: 013703CrossRefGoogle Scholar
  8. 8.
    Li C, Li S, Alvarez G, et al. Cryptanalysis of a chaotic block cipher with external key and its improved version. Chaos Soliton Fract, 2008, 37: 299–307MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Schneier B. Applied Cryptography: Protocols, Algorithms, and Source Code in C. 2nd ed. Brisbane: John Wiley and Sons, 1996. 280–282zbMATHGoogle Scholar
  10. 10.
    Robinson R C. An introduction to Dynamical Systems: Continuous and Discrete. New Jersey: Pearson Prentice Hall, 2004. 303–366zbMATHGoogle Scholar
  11. 11.
    Tang K W, Tang K S, Man K F. A chaos-based pseudo-random number generator and its application in voice communications. Int J Bifurcat Chaos, 2007, 17: 923–933zbMATHCrossRefGoogle Scholar
  12. 12.
    Li C, Li S, Alvarez G, et al. Cryptanalysis of two chaotic encryption schemes based on circular bit shift and XOR operations. Phys Lett A, 2007, 369: 23–30zbMATHCrossRefGoogle Scholar
  13. 13.
    Lian S, Sun J, Wang J, et al. A chaotic stream cipher and the usage in video protection. Chaos Soliton Fract, 2007, 34: 851–859MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Li P, Li Z, Halang W A, et al. Analysis of a multiple-output pseudo-random-bit generator based on a spatiotemporal chaotic system. Int J Bifurcat Chaos, 2006, 16: 2949–2963CrossRefGoogle Scholar
  15. 15.
    Xiang T, Liao X, Tang G, et al. A novel block cryptosystem based on iterating a chaotic map. Phys Lett A, 2006, 349: 109–115zbMATHCrossRefGoogle Scholar
  16. 16.
    Li P, Li Z, Halang W A, et al. A multiple pseudorandom-bit generator based on a spatiotemporal chaotic map. Phys Lett A, 2006, 349: 467–473CrossRefGoogle Scholar
  17. 17.
    National Institute of Standards and Technology (NIST). Security Requirements for Cryptographic Modules. Federal Information Processing Standards Publication 140-2. 2001Google Scholar
  18. 18.
    Patidar V, Sud K K, Pareek N K. A pseudo random bit generator based on chaotic logistic map and its statistical testing. Informatica, 2009, 33: 441–452MathSciNetzbMATHGoogle Scholar
  19. 19.
    Soto J. Randomness Testing of the AES Candidate Algorithms. NIST Interagency Reports 6390. 1999Google Scholar
  20. 20.
    Soto J, Bassham L. Randomness Testing of the Advanced Encryption Standard Finalist Candidates. NIST Interagency Reports 6483. 2000Google Scholar
  21. 21.
    Turan M S, Doganaksoy A, Calik C. Detailed Statistical Analysis of Synchronous Stream Ciphers. eSTREAM report 2006/043. 2006Google Scholar
  22. 22.
    Rukhin A, Soto J, Nechvatal J, et al. A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications. NIST Special Publication 800-22. 2001Google Scholar
  23. 23.
    Li S. When chaos meets computers. arXiv: nlin.CD/0405038. 2004Google Scholar
  24. 24.
    Li S, Chen G, Mou X. On the dynamical degradation of digital piecewise linear chaotic maps. Int J Bifurcat Chaos, 2005, 15: 3119–3151MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Sang T, Wang R, Yan Y. Perturbance-based algorithm to expand cycle length of chaotic key stream. Electron Lett, 1998, 34: 873–877CrossRefGoogle Scholar
  26. 26.
    Park S K, Miller K W. Random number generators: good ones are hard to find. Commun ACM, 1988, 31: 1192–1201MathSciNetCrossRefGoogle Scholar
  27. 27.
    Kohda T, Tsuneda A. Statistics of chaotic binary sequences. IEEE Trans Inform Theory, 1997, 43: 104–112MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    Kohda T. Information sources using chaotic dynamics. Proc IEEE, 2002, 90: 641–661CrossRefGoogle Scholar
  29. 29.
    Tsuneda A. Design of binary sequences with tunable exponential autocorrelations and run statistics based on onedimensional chaotic maps. IEEE Trans Circ Syst-I, 2005, 52: 454–462MathSciNetCrossRefGoogle Scholar
  30. 30.
    Addabbo T, Fort A, Papini D, et al. Invariant measures of tunable chaotic sources: robustness analysis and efficient estimation. IEEE Trans Circ Syst-I, 2009, 56: 806–819MathSciNetCrossRefGoogle Scholar
  31. 31.
    Ergun S, Ozoguz S. Truly random number generators based on a non-autonomous chaotic oscillator. Int J Electron Commun, 2007, 61: 235–242CrossRefGoogle Scholar
  32. 32.
    Tomassini M, Sipper M, Perrenoud M. On the generation of high-quality random numbers by two-dimensional cellular automata. IEEE Trans Comput, 2000, 49: 1146–1151CrossRefGoogle Scholar
  33. 33.
    Addabbo T, Alioto M, Fort A, et al. A feedback strategy to improve the entropy of a chaos-based random bit generator. IEEE Trans Circ Syst-I, 2006, 53: 326–337MathSciNetCrossRefGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • RuMing Yin
    • 1
  • Jian Wang
    • 1
  • Jian Yuan
    • 1
    Email author
  • XiuMing Shan
    • 1
  • XiQin Wang
    • 1
  1. 1.Department of Electronic EngineeringTsinghua UniversityBeijingChina

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