S-box, SET, Match: A Toolbox for S-box Analysis

  • Stjepan Picek
  • Lejla Batina
  • Domagoj Jakobović
  • Barış Ege
  • Marin Golub
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8501)


Boolean functions and substitution boxes (S-boxes) represent the only nonlinear part in many algorithms and therefore play the crucial role in their security. Despite the fact that some algorithms today reuse theoretically secure and carefully constructed S-boxes, there is a clear need for a tool that can analyze security properties of S-boxes and hence the corresponding primitives. This need is especially evident in the scenarios where the goal is to create new S-boxes. Even in the cases when some common properties of S-boxes are known, we believe it is prudent to exhaustively investigate all possible sets of cryptographic properties. In this paper we present a tool for the evaluation of Boolean functions and S-boxes suitable for cryptography.


Private-key Cryptography Boolean functions S-boxes Cryptographic Properties 


  1. 1.
    Matsui, M., Yamagishi, A.: A new method for known plaintext attack of FEAL cipher. In: Rueppel, R.A. (ed.) Advances in Cryptology - EUROCRYPT 1992. LNCS, vol. 658, pp. 81–91. Springer, Heidelberg (1993)Google Scholar
  2. 2.
    Biham, E., Shamir, A.: Differential Cryptanalysis of DES-like Cryptosystems. In: Menezes, A., Vanstone, S.A. (eds.) Advances in Cryptology - CRYPTO 1990. LNCS, vol. 537, pp. 2–21. Springer, Heidelberg (1991)Google Scholar
  3. 3.
    Team, R.C.: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2013) ISBN 3-900051-07-0Google Scholar
  4. 4.
    Lafitte, F.: The boolfun Package: Cryptographic Properties of Boolean Functions (2013)Google Scholar
  5. 5.
    Lafitte, F., Heule, D.V., Hamme, J.V.: Cryptographic Boolean Functions with R. The R Journal 3(1), 44–47 (2011)Google Scholar
  6. 6.
    Stein, W.A., et al.: Sage Mathematics Software (Version 5.10). The Sage Development Team (2013),
  7. 7.
    Alvarez-Cubero, J., Zufiria, P.: A c++ class for analysing vector boolean functions from a cryptographic perspective. In: Proceedings of the 2010 International Conference on Security and Cryptography (SECRYPT), pp. 1–9 (July 2010)Google Scholar
  8. 8.
    Knudsen, L.R., Robshaw, M.: The Block Cipher Companion. Information Security and Cryptography. Springer (2011)Google Scholar
  9. 9.
    Braeken, A.: Cryptographic Properties of Boolean Functions and S-Boxes. PhD thesis. Katholieke Universiteit Leuven (2006)Google Scholar
  10. 10.
    Crama, Y., Hammer, P.L.: Boolean Models and Methods in Mathematics, Computer Science, and Engineering, 1st edn. Cambridge University Press, New York (2010)CrossRefzbMATHGoogle Scholar
  11. 11.
    Guilley, S., Pacalet, R.: Differential Power Analysis Model and Some Results. In: Proceedings of CARDIS 2004, pp. 127–142. Kluwer Academic Publishers (2004)Google Scholar
  12. 12.
    Prouff, E.: DPA Attacks and S-Boxes. In: Gilbert, H., Handschuh, H. (eds.) FSE 2005. LNCS, vol. 3557, pp. 424–441. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  13. 13.
    Carlet, C.: On highly nonlinear S-boxes and their inability to thwart DPA attacks. In: Maitra, S., Veni Madhavan, C.E., Venkatesan, R. (eds.) INDOCRYPT 2005. LNCS, vol. 3797, pp. 49–62. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    Burnett, L.D.: Heuristic Optimization of Boolean Functions and Substitution Boxes for Cryptography. PhD thesis. Queensland University of Technology (2005)Google Scholar
  15. 15.
    Zhang, X., Zheng, Y.: GAC-the criterion of global avalanche characteristics of cryptographic functions. Journal of Universal Computer Science 1(5), 316–333 (1995)Google Scholar
  16. 16.
    Clark, J.A., Jacob, J.L., Stepney, S.: The design of S-boxes by simulated annealing. New Generation Computing 23(3), 219–231 (2005)CrossRefzbMATHGoogle Scholar
  17. 17.
    Preneel, B., Van Leekwijck, W., Van Linden, L., Govaerts, R., Vandewalle, J.: Propagation characteristics of Boolean functions. In: Damgård, I.B. (ed.) Advances in Cryptology - EUROCRYPT1990. LNCS, vol. 473, pp. 161–173. Springer, Heidelberg (1991)Google Scholar
  18. 18.
    Heys, H.M.: A Tutorial on Linear and Differential Cryptanalysis. Technical report (2001)Google Scholar
  19. 19.
    Nyberg, K.: Perfect Nonlinear S-Boxes. In: Davies, D.W. (ed.) Advances in Cryptology - EUROCRYPT 1991. LNCS, vol. 547, pp. 378–386. Springer, Heidelberg (1991)Google Scholar
  20. 20.
    Seberry, J., Zhang, X.M., Zheng, Y.: Systematic Generation of Cryptographically Robust S-boxes (Extended Abstract). In: Proceedings of the First ACM Conference on Computer and Communications Security, pp. 172–182 (1993)Google Scholar
  21. 21.
    Daemen, J., Rijmen, V.: The Design of Rijndael. Springer-Verlag New York, Inc., Secaucus (2002)Google Scholar
  22. 22.
    Saarinen, M.-J.O.: Cryptographic Analysis of All 4 x 4-Bit S-Boxes. In: Miri, A., Vaudenay, S. (eds.) SAC 2011. LNCS, vol. 7118, pp. 118–133. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  23. 23.
    Fan, L., Zhou, Y., Feng, D.: A Fast Implementation of Computing the Transparency Order of S-Boxes. In: The 9th International Conference for Young Computer Scientists, ICYCS 2008, pp. 206–211 (2008)Google Scholar
  24. 24.
    Bogdanov, A., Knudsen, L.R., Leander, G., Paar, C., Poschmann, A., Robshaw, M.J., Seurin, Y., Vikkelsoe, C.: PRESENT: An Ultra-Lightweight Block Cipher. In: Paillier, P., Verbauwhede, I. (eds.) CHES 2007. LNCS, vol. 4727, pp. 450–466. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  25. 25.
    Cid, C., Kiyomoto, S., Kurihara, J.: The RAKAPOSHI Stream Cipher. In: Qing, S., Mitchell, C.J., Wang, G. (eds.) ICICS 2009. LNCS, vol. 5927, pp. 32–46. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  26. 26.
    Kusnierczyk, W.: Rbenchmark: Benchmarking routine for R (2012)Google Scholar

Copyright information

© IFIP International Federation for Information Processing 2014

Authors and Affiliations

  • Stjepan Picek
    • 1
    • 2
  • Lejla Batina
    • 1
  • Domagoj Jakobović
    • 2
  • Barış Ege
    • 1
  • Marin Golub
    • 2
  1. 1.Institute for Computing and Information Sciences (ICIS)Radboud University NijmegenNijmegenThe Netherlands
  2. 2.Faculty of Electrical Engineering and ComputingUniversity of ZagrebZagrebCroatia

Personalised recommendations