Secret Key Specification for a Variable-Length Cryptographic Cellular Automata Model

  • Gina M. B. Oliveira
  • Luiz G. A. Martins
  • Giordano B. Ferreira
  • Leonardo S. Alt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6239)


Reverse algorithm was previously evaluated as encryption method concluding that its simple adoption is unviable, since it does not assurance the pre-image existence. Variable-Length Encryption Method (VLE) was proposed where a alternative algorithm with extra bits is adopted when pre-image computation is not possible. If an adequate secret key is used with VLE it is expected that the final ciphertext length is close to plaintext size. Several CA static parameters were calculated for a set formed by all radius 2 right-toggle rules. A database was generated associating rules performance in VLE ciphering with its parameters. A genetic algorithm-based data mining was performed to discover an adequate key specification based on CA parameters. Using such specification, ciphertext length is short, encryption process returns high entropy and VLE has a good protection against differential cryptanalysis.


Cellular Automata cryptography pre-image computation genetic algorithm data mining 


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  1. 1.
    Wolfram, S.: Cryptography with cellular automata. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 429–432. Springer, Heidelberg (1986)Google Scholar
  2. 2.
    Tomassini, M., Perrenoud, M.: Stream Ciphers with One and Two-Dimensional Cellular Automata. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 722–731. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  3. 3.
    Seredynski, F., Bouvry, P., Zomaya, A.Y.: Secret key cryptography with cellular automata. In: Workshop on Nature Inspired Distributed Computing (2003)Google Scholar
  4. 4.
    Benkiniouar, M., Benmohamed, M.:: Cellular Automata for Cryptosystem. In: Proceedings of IEEE Conference Information and Communication Technologies: From Theory to Applications, pp. 423-424 (2004)Google Scholar
  5. 5.
    Kari, J.: Cryptosystem based on reversible cellular automata. Personal communication. Apud in (Seredynski, Bouvry and Zomaya, 2003) (1994)Google Scholar
  6. 6.
    Nandi, S., Kar, B., Chaudhuri, P.: Theory and Applications of CA Automata in Cryptography. IEEE Transactions on Computers 43, 1346–1357 (1994)CrossRefGoogle Scholar
  7. 7.
    Gutowitz, H.: Cryptography with Dynamical Systems. In: Goles, E., Boccara, N. (eds.) Cellular Automata and Cooperative Phenomena, vol. 1, pp. 237–274. Kluwer Acapdemic Press, Dordrecht (1995)Google Scholar
  8. 8.
    Oliveira, G., Coelho, A., e Monteiro, L.: Cellular Automata Cryptographic Model Based on Bi-Directional Toggle Rules. I. J. Modern Physics C 15, 1061–1068 (2004)zbMATHCrossRefGoogle Scholar
  9. 9.
    Oliveira, G., Macêdo, H., Branquinho, A., Lima, M.: A cryptographic model based on the pre-image computation of cellular automata. In: Automata-2008: Theory and Applications of Cellular Automata, pp. 139–155. Luniver Press (2008)Google Scholar
  10. 10.
    Oliveira, G.M.B., Martins, L.G.A., Alt, L.S., Ferreira, G.B.: Exhaustive Evaluation of Radius 2 Toggle Rules for a Variable-Length Cryptographic CA-Based Model. In: Int. Conf. on Cellular Automata for Research and Industry, Ascoli Piceno (2010)Google Scholar
  11. 11.
    Oliveira, G.M.B., Martins, L.G.A., Alt, L.S., Ferreira, G.B.:: Investigating a Cellular Automata-Based Cryptographic Model with a Variable-Length Ciphertext. In: CSC 2010, - International Conference on Scientific Computing, Las Vegas (2010)Google Scholar
  12. 12.
    Wuensche, A., Lesser, M.: Global Dynamics of Cellular Automata. Addison-Wesley, New Mexico (1992) ISBN: 0-201-55740-1zbMATHGoogle Scholar
  13. 13.
    Fidelis, M., Lopes, H., Freitas, A.: Discovery comprehensible classification rules with a genetic algorithm. In: C.Evolutionary Computation, CEC 2000, USA (2000)Google Scholar
  14. 14.
    Oliveira, G., de Oliveira, P., e Omar, N.: Definition and applications of a five-parameter characterization of 1D cellular automata rule space. Artificial Life 7(3), 277–301 (2001)CrossRefGoogle Scholar
  15. 15.
    Sen, S., Shaw, C., Chowdhuri, D., Ganguly, N., Chaudhuri, P.: Cellular Automata based Cryptosystem (CAC). In: Deng, R.H., Qing, S., Bao, F., Zhou, J. (eds.) ICICS 2002. LNCS, vol. 2513, pp. 303–314. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Gina M. B. Oliveira
    • 1
  • Luiz G. A. Martins
    • 1
  • Giordano B. Ferreira
    • 1
  • Leonardo S. Alt
    • 1
  1. 1.Faculdade de ComputaçãoUniversidade Federal de UberlândiaUberlândiaBrazil

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