A New Direction in Utilization of Chaotic Fractal Functions for Cryptosystems

  • M. R. K. AriffinEmail author
  • N. M. G. Al-Saidi
  • M. R. M. Said
  • Z. Mahad
  • M. A. Daud
Part of the Understanding Complex Systems book series (UCS)


Ever since Baptista in 1998 introduced his cryptographic scheme utilizing the only in online version. ergodic property of chaotic maps which is able to produce different cipher values for the same plaintext within the same message, intense scrutiny has been given upon the design. The capability to do the above mentioned output is akin to the Vigenere cipher and thus has the capacity to render an attacker with infinitely many choices (theoretically speaking) or in cryptographic terms would render an attacker to have a set off possible ciphertexts that could all have the possibility to just be mapped to a unique plaintext. This makes it computationally infeasible for the attacker to re-construct the correct plaintext. The Baptista design has been attacked and repaired many times. Alvarez noticed the characteristic of the cryptosystem that generates a sequence which can be exploited by an attacker. The attack which is dubbed the one-time pad attack is akin to an attack upon a One-Time-Pad (OTP) cryptosystem that reuses its key. Since then, attempts were made to redefine the cryptosystem such that it would be resistant towards the attack. Most of the attempts failed due to either the repaired cryptosystem still generates an exploitable sequence or it is not invertible. In this work we pair the Baptista design with a concept taken from the Iterated Function Systems (IFS). Although we did not encompass the whole concept of iterating the IFS, it could be seen that this could be easily done with the same desirable results. Four main outcomes are discussed. Beginning with the discussion on the infeasibility of Alvarez’s one-time pad attack on the design, we then discuss the quantitative properties of the design in discussing its cryptographic properties namely the Maximum Deviation Factor (MDF), Correlation Coefficient Factor (CCF) and the Strict Avalanche Criterion (SAC). Each experimental result shows promising results for this new design.


  1. 1.
    Alvarez, G., Montoya, F., Romera, M., Pastor, G.: Cryptanalysis of an ergodic chaotic cipher. Phys. Lett. A 311, 172–179 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Ariffin, M.R.K., Noorani, M.S.M.: Modified Baptista type chaotic cryptosystem via matrix secret key. Phys. Lett. A 327, 427–430 (2008)MathSciNetGoogle Scholar
  3. 3.
    Ariffin, M.R.K., Noorani, M.S.M.: Mathematical treatment for constructing a countermeasure against the one time pad attack. In: Chaos Synchronization and Cryptography for Secure Communications: Applications for Encryption, pp. 463–475, IGI Global, Hershey PA, USA, 2010Google Scholar
  4. 4.
    Baptista, M.: Cryptography with chaos. Phys. Lett. A 240, 50–54 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Barnsley, M.F.: Fractal Image Compression, Notices of The AMS, pp. 657–659, June 1996Google Scholar
  6. 6.
    Rhouma, R.: Comment on modified Baptista type chaotic cryptosystem via matrix secret key. Phys. Lett. A 373, 3398–3400 (2009)CrossRefGoogle Scholar
  7. 7.
    Vergili, I., Ycel, M.D.: Avalanche and bit independence properties for the ensembles of randomly chosen n×n S-Boxes. Turkish J. Electr. Eng. Comput. Sci. 9(2), 137–145 (2001)Google Scholar
  8. 8.
    Webster, A., Tavares S.: On the design of S-boxes. In: Advances in Cryptology. Proceedings of the CRYPTO_85, pp. 523–534. Springer, New York (1986)Google Scholar
  9. 9.
    Ziedan, I.E., Fouad, M.M., Salem, D.H.: Application of data encryption standard to bitmap and JPEG image. In: Proceedings of the Twentieth National Radio Science Conference, pp. 1–8, Cairo, Egypt, 2003Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • M. R. K. Ariffin
    • 1
    Email author
  • N. M. G. Al-Saidi
    • 1
  • M. R. M. Said
    • 1
  • Z. Mahad
    • 1
  • M. A. Daud
    • 1
  1. 1.Al-Kindi Cryptography Research Laboratory, Institute for Mathematical ResearchUniversiti Putra MalaysiaSerdangMalaysia

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