Advertisement

Cryptographic Properties of Some Cryptosystem with Modulation of the Chaotic Sequence Parameters

  • Stefan Berczyński
  • Yury A. Kravtsov
  • Jerzy Pejaś
  • Adrian Skrobek

Abstract

This paper discusses mixing of some non-linear chaotic maps, e.g. a logistic equation and a tent mapping, as simplified method for information encryption and decryption. A ciphertext is obtained by the iteration of defined mixing chaotic maps from an initial state. Because the secure control parameters of these chaotic mappings are modulated according to currently encrypted plaintext, the proposed cipher algorithm can be treated as some homophonic substitution cipher with encryption key defined by initial state of build-in chaotic maps and some additional parameters. The resulting cipher algorithm is investigated against typical attacks on classical encryption schemes. The objective of these attacks is to recover plaintext from ciphertext or to deduce the decryption key. In this paper we study the exhaustive key search attack and find that this attack is not efficient as a practical attack on proposed cipher. Similar conclusion concerns some classical attacks, e.g.: ciphertext-only attacks and a known-plaintext attacks.

Keywords

chaotic signals and sequence stream ciphers logistic equation secure data transmission chaotic cryptosystems cryptoanalysis 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

5 References

  1. [1]
    R. Schmitz Use of chaotic dynamical systems in cryptography, Journal of the Franklin Institute 338 (2001), pp.429–441zbMATHMathSciNetCrossRefGoogle Scholar
  2. [2]
    S. Papadimitriou, A. Bezerianos, T. Bountis, G. Pavlides Secure communication protocols with discrete nonlinear chaotic maps, Journal of Systems Architecture, 47 (2001), pp.61–72CrossRefGoogle Scholar
  3. [3]
    R.L. Devaney An Introduction to Chaotic Dynamical Systems, 2nd Edition, Addison-Wesley Publishing Company, Reading, MA, 1989Google Scholar
  4. [4]
    A.J. Menezes, P.C. van Oorschot, S.A. Vanstone Handbook of Applied Cryptography, CRC Press (1997)Google Scholar
  5. [5]
    L. Cappelletti An FPGA Implementation of a Chaotic Encryption Algorithm, Thesis, Università Degli Studi Di Padova, 2000Google Scholar
  6. [6]
    Z. Kotulski, J. Szczepński On the application of discrete chaotic dynamical systems to cryptography. DCC method, Biuletyn WAT, Rok XLVIII, Nr 10(566), pp.111–123, 1999Google Scholar
  7. [7]
    L. Kocarev, G. Jakimoski Logistic map as a block encryption algorithm, Physics Letters A 289 (2001), pp. 199–206MathSciNetCrossRefGoogle Scholar
  8. [8]
    E. Ott Chaos in Dynamical Systems, Cambridge University Press, Cambridge, MA, 1993Google Scholar
  9. [9]
    T.L. Carrol, L.M. Pecora Cascading synchronized chaotic systems, Physica D 67 (1993), pp.l26–140.Google Scholar
  10. [10]
    G. Álvarez, Shujun Li Cryptographic requirements for chaotic secure communications, eprint arXiv:nlin/0311039, November 2003, 13 pages, http://adsabs.harvard.edu/cgi-bin/nph-bib_query?2003nlin.....11039AGoogle Scholar
  11. [11]
    Ninan Sajeeth Philip, K. Babu Joseph Chaos for Stream Cipher, in Proceedings of ADCOM 2000, Tata McGraw Hill 2001Google Scholar
  12. [12]
    G. Álvarez, F. Montoya, M. Romera, G. Pastor Cryptanalysis of dynamic look-up table based chaotic cryptosystems, arXiv: nlin. CD/ 0311043 vl 20 Nov 2003Google Scholar
  13. [13]
    T. Guoning, W. Tang, W. Shihong, L. Huaping, H. Gang Chaos-based cryptograph incorporated with S-box algebraic operation, Physics Letters A, Vol.318, Issues 4–5, pp. 388–398, 17 November 2003MathSciNetGoogle Scholar
  14. [14]
    S. Berczyński, Yu. A. Kravtsov, J. Pejaś, E. D. Surovyatkina Secure Data Transmission via Modulation of the Chaotic Sequence Parameters, 10th Multi-Conference On Advanced Computer Systems. 22–24 October 2003, Międzyzdroje, PolandGoogle Scholar
  15. [15]
    N.K. Pareek, Vinod Patidar, K.K. Sud Discrete chaotic cryptography using external key, Physics Letters A 309 (2003), pp.75–82MathSciNetCrossRefGoogle Scholar
  16. [16]
    V.S. Anishchenko and A.N. Pavlov, Phys. Rev., 57 (1998), pp. 2455–2461.Google Scholar
  17. [17]
    V.S. Anishchenko, V.V. Astakhov, A.B. Neiman, T.E. Vadivasova and L. Schimansky-Geier Nonlinear Dynamics of Chaotic and Stochastic Systems. Tutorial and Modern Development, Springer, Berlin, Heidelberg, 2002.Google Scholar
  18. [18]
    S. G. Bilchinskaya, O. Ya. Butkovskii, M. V. Kapranov, Yu. A. Kravtsov, A. G. Morozov, E. D. Surovyatkina Signal reconstruction errors in data transmission using modulation of the parameters of chaotic sequences, J. Comm. Technol. Electron., 48 (2003), pp.284–292.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Stefan Berczyński
    • 1
  • Yury A. Kravtsov
    • 2
  • Jerzy Pejaś
    • 1
  • Adrian Skrobek
    • 1
  1. 1.Technical University of SzczecinPoland
  2. 2.Maritime University of SzczecinPoland

Personalised recommendations