On Cryptographically Secure Vectorial Boolean Functions

  • Takashi Satoh
  • Tetsu Iwata
  • Kaoru Kurosawa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1716)


In this paper, we show the first method to construct vectorial bent functions which satisfy both the largest degree and the largest number of output bits simultaneously. We next apply this method to construct balanced vectorial Boolean functions which have larger nonlinearities than previously known constructions.


Boolean Function Normal Basis Block Cipher Stream Cipher Primitive Element 
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.


  1. 1.
    Dillon, J.F.: Elementary Hadamard difference sets. In: The Sixth Southeastern Conference on Combinatorics, Graph Theory and Computing, pp. 237–249 (1975)Google Scholar
  2. 2.
    Ding, C., Xiao, G., Shan, W.: The stability theory of stream ciphers. In: Ding, C., Shan, W., Xiao, G. (eds.) The Stability Theory of Stream Ciphers. LNCS, vol. 561, Springer, Heidelberg (1991)Google Scholar
  3. 3.
    Dobbertin, H.: Construction of bent functions and balanced Boolean functions with high nonlinearity. In: Preneel, B. (ed.) FSE 1994. LNCS, vol. 1008, pp. 61–74. Springer, Heidelberg (1995)Google Scholar
  4. 4.
    Jakobsen, T., Knudsen, L.R.: The interpolation attack on block ciphers. In: Biham, E. (ed.) FSE 1997. LNCS, vol. 1267, pp. 28–40. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  5. 5.
    MacWilliams, F.J., Sloane, N.J.A.: The theory of error-correcting codes. North-Holland Publishing Company, Amsterdam (1977)zbMATHGoogle Scholar
  6. 6.
    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
  7. 7.
    Nyberg, K.: Perfect nonlinear S-boxes. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 378–386. Springer, Heidelberg (1991)Google Scholar
  8. 8.
    Nyberg, K.: On the construction of highly nonlinear permutations. In: Rueppel, R.A. (ed.) EUROCRYPT 1992. LNCS, vol. 658, pp. 92–98. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  9. 9.
    Rothaus, O.S.: On bent functions. Journal of Combinatorial Theory (A) 20, 300–305 (1976)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Seberry, J., Zhang, X.M., Zheng, Y.: Nonlinearity and propagation characteristics of balanced Boolean functions. Information and Computation 119(1), 1–13 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Zhang, X.M., Zheng, Y.: Cryptographically resilient functions. IEEE Transactions on Information Theory 43(5), 1740–1747 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Siegenthaler, T.: Correlation-immunity of nonlinear combining functions for cryptographic applications. IEEE Transactions on Information Theory 30(5), 776–780 (1984)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Takashi Satoh
    • 1
  • Tetsu Iwata
    • 2
  • Kaoru Kurosawa
    • 2
  1. 1.Faculty of International Environmental Engineering, Promotion and Development OfficeKitakyushu UniversityKitakyushuJapan
  2. 2.Department of Electrical and Electronic EngineeringFaculty of Engineering, Tokyo Institute of TechnologyTokyoJapan

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