Semi-bent functions

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 917)


Highly nonlinear balanced Boolean functions both satisfying the propagation criterion and having almost uniform correlation values with all linear functions are very important in the design of hash functions, stream and block ciphers. In particular, the output uncorrelated properties between two Boolean functions are required to design permutations. We present, so called, semi-bent functions which satisfy all of these properties.


Boolean Function Hash Function Propagation Criterion Block Cipher Stream Cipher 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C. Adams and S. Tavares, “The structured design of cryptographically good S-boxes”, Journal of Cryptology 3, no. 1, pp. 27–43, 1990.Google Scholar
  2. 2.
    E. Biham and A. Shamir, “Differential cryptanalysis of DES-like cryptosystems”, Journal of Cryptology 4, no. 1, pp. 3–72, 1991.Google Scholar
  3. 3.
    P. Camion, C. Carlet, P. Charpin and N. Sendrier, “On correlation-immune functions”, Advances in Cryptology — CRYPTO'91, Springer-Verlag, pp. 87–100, 1992.Google Scholar
  4. 4.
    S. Hirose and K. Ikeda, “A note on the propagation characteristics and the strict avalanche criteria”, The 1994 Symposium on Cryptography and Information Security, 1994.Google Scholar
  5. 5.
    M. Matsui, “Linear cryptanalysis method for DES cipher”, Advances in Cryptology — EUROCRYPT'93, Springer-Verlag, pp. 386–397, 1994.Google Scholar
  6. 6.
    W. Meier and O.Staffelbach, “Nonlinearity criteria for cryptographic functions”, Advances in Cryptology — EUROCRYPT'89, Springer-Verlag, pp. 549–562, 1990.Google Scholar
  7. 7.
    K. Nyberg, “On the construction of highly nonlinear permutations”, Advances in Cryptology — EUROCRYPT'92, Springer-Verlag, pp. 92–98, 1993.Google Scholar
  8. 8.
    K. Nyberg, “Differentially uniform mappings for cryptography”, Advances in Cryptology — EUROCRYPT'93, Springer-Verlag, pp. 55–64, 1994.Google Scholar
  9. 9.
    K. Nyberg and L.R. Knudsen, “Provable Security against Differential Cryptanalysis”, Advances in Cryptology — CRYPTO'92, Springer-Verlag, pp. 566–574, 1993.Google Scholar
  10. 10.
    J. Pieprzyk and G. Finkelstein, “Towards effective nonlinear cryptosystem design”, IEE Proceedings, Part E: Computers and Digital Techniques, Vol. 135, pp. 325–335, 1988.Google Scholar
  11. 11.
    B. Preneel, “Analysis and design of cryptographic hash functions”, Ph.D. Dissertation, Katholieke Universiteit Leuven, 1993.Google Scholar
  12. 12.
    B. Preneel, W. Van Leekwijck and L. Van Linden, “Propagation characteristics of Boolean functions”, Advances in Cryptology — EUROCRYPT'90, Springer-Verlag, pp. 161–173, 1991.Google Scholar
  13. 13.
    O.S. Rothaus, “On “bent” functions”, Journal of Combinatorial Theory (A), Vol. 20, pp. 300–305, 1976.Google Scholar
  14. 14.
    R.A. Rueppel, Stream Ciphers, in “Contemporary Cryptology: The Science of Information Integrity”, G.J. Simmons, Ed., IEEE Press, pp. 65–134, 1992.Google Scholar
  15. 15.
    J. Seberry, X. M. Zhang and Y. Zheng, “Systematic generation of cryptographically robust S-boxes”, In Proceedings of the first ACM Conference on Computer and Communications Security, pp. 172–182, 1993.Google Scholar
  16. 16.
    J. Seberry, X. M. Zhang and Y. Zheng, “On constructions and nonlinearity of correlation immune functions”, Advances in Cryptology — EUROCRYPT'93, Springer-Verlag, pp. 181–199, 1994.Google Scholar
  17. 17.
    J. Seberry, X. M. Zhang and Y. Zheng, “Nonlinearly balanced Boolean functions and their propagation characteristics”, Advances in Cryptology — CRYPTO'93, Springer-Verlag, pp. 49–60, 1994.Google Scholar
  18. 18.
    T. Siegenthaler, “Correlation immunity of non-linear combining functions for cryptographic applications”, IEEE Trans. Inform. Theory IT-30, pp. 776–780, 1984.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  1. 1.Electronics and Telecommunications Research InstituteTaejonKorea

Personalised recommendations