Evolutionary Design of Resilient Substitution Boxes: From Coding to Hardware Implementation

  • Nadia Nedjah
  • Luiza de Macedo Mourelle
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4684)


S-boxes constitute a cornerstone component in symmetric-key cryptographic algorithms, such as DES and AES encryption systems. In block ciphers, they are typically used to obscure the relationship between the plaintext and the ciphertext. Non-linear and non-correlated S-boxes are the most secure against linear and differential cryptanalysis. In this paper, we focus on a two-fold objective: first, we evolve regular an S-box with high non-linearity and low auto-correlation properties using evolutionary computation; then automatically generate evolvable hardware for the obtained S-box. Targeting the former, we use the Nash equilibrium-based multi-objective evolutionary algorithm to optimise regularity, non-linearity and auto- correlation, which constitute the three main desired properties in resilient S-boxes. Pursuing the latter, we exploit genetic programming to automatically generate the evolvable hardware designs of substitution boxes that minimise hardware space, encryption/decryption time and dissipated power, which form the three main hardware characteristics. We compare our results against existing and well-known designs, which were produced by using conventional methods as well as through evolution.


Nash Equilibrium Crossover Operator Hardware Implementation Block Cipher Evolutionary Design 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Beauchamp, K.G.: Walsh Functions and Their Applications. Academic, New York (1975)zbMATHGoogle Scholar
  2. 2.
    Biham, E., Shamir, A.: Differential Cryptanalysis of DES-like Cryptosystems. In: Menezes, A.J., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 2–21. Springer, Heidelberg (1991)Google Scholar
  3. 3.
    Clark, J.A., Jacob, J.L., Stepney, S.: The Design of S-Boxes by Simulated Annealing. New Generation Computing 23(3), 219–231 (2005)zbMATHCrossRefGoogle Scholar
  4. 4.
    Dorigo, M., Maniezzo, M.: Parallel Genetic Algorithms: Introduction and Overview of Current Research. In: Stender, J. (ed.) Parallel Genetic Algorithms, IOS Press, Amsterdam (1993)Google Scholar
  5. 5.
    Haupt, R.L., Haupt, S.E.: Practical genetic algorithms. John Wiley, Chichester (1998)zbMATHGoogle Scholar
  6. 6.
    Kwan, M.: Reducing the gate count of bitslice DES (2000),
  7. 7.
    Matsui, M.: Linear cryptanalysis method for DES cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994)Google Scholar
  8. 8.
    Menezes, A.J., Van Oorschot, P.C., Vanstone, S.A.: Handbook of Applied Cryptography. CRC Press, Boca Raton, USA (1996)Google Scholar
  9. 9.
    Millan, W., Burnett, L., Cater, G., Clark, J.A., Dawson, E.: Evolutionary Heuristics for Finding Cryptographically Strong S-Boxes. In: Varadharajan, V., Mu, Y. (eds.) Information and Communication Security. LNCS, vol. 1726, pp. 263–274. Springer, Heidelberg (1999)Google Scholar
  10. 10.
    Monteiro, J., Devadas, D., Gosh, A., Keutzer, K., White, J.: Estimation of average switching activity in combinational logic circuits using symbolic simulation. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 16(1), 121–127 (1997)CrossRefGoogle Scholar
  11. 11.
    National Institute of Standard and Technology, Data Encryption Standard, Federal Information Processing Standards 46 (November 1977)Google Scholar
  12. 12.
    Nash, J.F.: Equilibrium points in n-person games. Proceedings of the National Academy of Sciences 36, 48–49 (1950)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Nash, J.N.: Non-cooperative game. Annals of Mathematics 54(2), 286–295 (1951)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Rhyne, V.T.: Fundamentals of digital systems design. Electrical Engineering Series. Prentice-Hall, Englewood Cliffs (1973)Google Scholar
  15. 15.
    Shanon, C.E.: Communication theory of secrecy systems. Bell Sys. Tech. J. 28(4), 656–715 (1949)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Nadia Nedjah
    • 1
  • Luiza de Macedo Mourelle
    • 2
  1. 1.Department of Electronics Engineering and Telecommunications 
  2. 2.Department of System Engineering and Computation, Engineering Faculty, State University of Rio de JaneiroBrazil

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