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Statistical tests and chaotic synchronization based pseudorandom number generator for string bit sequences with application to image encryption

  • Regular Article
  • Chaos Based Image Encryption, Stream Cipher and Authentication
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Abstract

Recently, a stream encryption scheme using d-bit segment sequences has been proposed. This scheme may generate key avalanche effect. The randomness tests of d-bit segment pseudorandom number generator will be important for implementing such a scheme. Firstly this paper extends Beker and Piper’s binary pseudorandom sequence statistical test suite to d-bit segment sequences case. Secondly, a novel 3-dimensional polynomial discrete chaotic map (3DPDCM) is proposed. The calculated Lyapunov exponents of the 3DPCDM are 0.213, 0.125 and − 3.228. Using the 3DPDCM constructs a 6-dimensional generalized synchronization chaotic system. Based on this system, a 8-bit segment chaotic pseudorandom number generator (CPRNG) is introduced. Using the generalized test suite tests 100 key streams generated via the 8-bit PRNG with different initial conditions and perturbed system parameters. The tested results are similar to those of the key streams generated via RC4 PRNG. As an application, using the key streams generated via the CPRNG and the RC4 PRNG encrypts an RGB image Landscape. The results have shown that the encrypted RGB images have significant avalanche effects. This research suggests that the requirements for PRNGs are not as strict as those under the traditional avalanche criteria. Suitable designed chaos-based d-bit string PRNGs may be qualified candidates for the stream encryption scheme with avalanche effect.

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References

  1. C.L. Phillips, J.A. Anderson, S.C. Glotzer, J. Comput. Phys. 230, 7191 (2011)

    Article  ADS  MATH  Google Scholar 

  2. N. Ferguson, B. Schneier, T. Kohno, Cryptography Engineering: Design Principles and Practical Applications (Wiley Publishing, 2010)

  3. S. Banerjee, Chaos Synchronization and Cryptography for Secure Communications: Applications for Encryption (IGI Global, 2010)

  4. G. Marsaglia, Diehard test suite, 1996, http://www.stat.fsu.edu/pub/diehard/

  5. NIST, FIPS PUB 140-2, security requirements for cryptographic modules (NIST, Gaithersburg, MD, 2001)

  6. A. Rukhin, J. Soto, J. Nechvatal, et al., A Statistical Test Suite for Random and Pseudorandom Number Generator for Cryptographic Applications (NIST Special Publication, 2001)

  7. P.L. Ecuyer, R. Simard, ACM Trans. Math. Software 33, 1 (2007)

    Article  Google Scholar 

  8. H. Beker, F. Piper, Cipher systems: the protection of communications (van Nostrand Reinhold, New York, 1982)

  9. J.G. Spropt, Chaos and Time-Series Analysis (University Press, Oxford, 2003)

  10. R.A.J. Matthews, Cryptologia XIII(1), 29 (1989)

    Article  MathSciNet  Google Scholar 

  11. T. Stojanovski, L. Kocarev, IEEE Trans. Circ. Syst.-I: Fund. Theory Appl. 48, 281 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  12. B. Nana, P. Woafo, S. Domngang, Comm. Nonlinear Sci. Numer. Simul. 14, 2266 (2009)

    Article  ADS  Google Scholar 

  13. F. Sun, S. Liu, Chaos, Solitons Fractals 41, 2216 (2009)

    Article  ADS  Google Scholar 

  14. D.V. Senthilkumar, J. Kurths, Eur. Phys. J. Special Topics 187, 87 (2010)

    Article  ADS  Google Scholar 

  15. J.W. Yoon, H. Kim, Comm. Nonlinear Sci. Numer. Simul. 15, 3998 (2010)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  16. P. Shyamala, Comm. Comput. Info. Sci. 140, 312 (2011)

    Article  Google Scholar 

  17. A. Akhavan, A. Samsudin, A. Akhshani, J. Franklin Inst. 348, 1797 (2011)

    Article  MathSciNet  Google Scholar 

  18. S. Banerjee, S. Mukhopadhyay, Opt. Lasers Eng. 50, 950 (2012)

    Article  Google Scholar 

  19. A. Kanso, M. Ghebleh, Commun. Nonlinear Sci. Numer. Simulat. 17, 2943 (2012)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  20. S. Banerjee, M.R.K. Ariffin, Optics Laser Technol. 45, 435 (2013)

    Article  ADS  Google Scholar 

  21. S.J.S. Theesar, M.R.K. Ariffin, S. Banerjee, Optics Laser Technol. 54, 15 (2013)

    Article  ADS  Google Scholar 

  22. C.K. Volos, I.M. Kyprianidis, I.N. Stouboulos, Signal Proc. 93, 1328 (2013)

    Article  Google Scholar 

  23. J.S.A.E. Fouda, J.Y. Effa, S.L. Sabat, et al., Commun. Nonlinear Sci. Numer. Simulat. 19, 578 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  24. A. Kassem, H.A.H. Hassan, Y. Harkouss, Digital Signal Proc. 25, 266 (2014)

    Article  Google Scholar 

  25. L. Min, G. Chen, Euro. Phys. J. B 86, 459-1 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  26. L. Min, L. Hao,L. Zhang, Study on the Statistical Test for String Pseudorandom Number Generators, in Lecture Notes Artificial Intelligence, edited by D. Liu, et al., Vol. 7888 (Springer-Verlag, Berlin, 2013), p. 278

  27. S.W. Golomb, Shift Register Sequences (Laguna Hills, Aegean Park, CA, 1982)

  28. A. Menezes, P. Vanorschot, S. Vanstone, Handbook of Applied Cryptography (CRC Press, 1996)

  29. H. Zang, L. Min, G. Zhao, A generalized synchronization theorem for discrete-time chaos system with application in data encryption scheme, in Proc. of the 2007 Int. Conf. on Communications, Circuits and Systems, Vol. II (Kokura, Fukuoka, Japan, 2007), p. 1325

  30. L. Min, G. Chen, Int. J. Bifurcat. Chaos 23, 1350016-1 (2013)

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China

    Longjie Hao & Lequan Min

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  1. Longjie Hao
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  2. Lequan Min
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Correspondence to Lequan Min.

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Hao, L., Min, L. Statistical tests and chaotic synchronization based pseudorandom number generator for string bit sequences with application to image encryption. Eur. Phys. J. Spec. Top. 223, 1679–1697 (2014). https://doi.org/10.1140/epjst/e2014-02182-2

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  • DOI: https://doi.org/10.1140/epjst/e2014-02182-2

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