Skip to main content
Log in

Description of k-bent functions in four variables

  • Published:
Journal of Applied and Industrial Mathematics Aims and scope Submit manuscript

Abstract

A simple description is given of the class of 2-bent functions in four variables. This class consists of 384 quadratic functions with 12 distinct types of the quadratic part, which classifies all k-bent functions with at most four variables.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S. V. Agievich, “On the Representation of Bent-Functions by Bent-Rectangles,” in Fifth International Petrozavodsk Conference on Probabilistic Methods in Discrete Mathematics (Petrozavodsk, Russia, 2000), Proceedings (VSP, Boston, 2000), pp. 121–135 (also http://arxiv.org/abs/math/0502087v1).

    Google Scholar 

  2. C. Carlet, “Boolean Functions for Cryptography and Error Correcting Codes,” in Boolean Methods and Models, Ed. by P. Hammer and Y. Crama (Cambridge Univ., Cambridge, to appear).

  3. D. S. Krotov, “ℤ4-Linear Perfect Codes,” Diskret. Analiz i Issled. Operatsii 7(4), 78–90 (2000) [English translation is available at http://arxiv.org/abs/0710.0198].

    MATH  MathSciNet  Google Scholar 

  4. D. S. Krotov, “ℤ4-Linear Hadamard and Extended Perfect Codes,” in Proceedings of the International Workshop on Coding and Cryptography (Paris, 2001), pp. 329–334.

  5. O. A. Logachev, A. A. Sal’nikov, and V. V. Yashenko, Boolean Functions in Coding Theory and Cryptology (Center for the Uninterrupted Mathematical Education, Moscow, 2004) [in Russian].

    MATH  Google Scholar 

  6. F. J. MacWilliams and N. J. A. Sloane, Theory of Error Correcting Codes (Amsterdam, North-Holland, 1977).

    MATH  Google Scholar 

  7. Q. Meng, M. C. Yang, and H. Zhang, “A Novel Algorithm Enumerating Bent Functions,” http://eprint.iacr.org, 2004/274.

  8. B. Preneel, Analysis and Design of Cryptographic Hash Functions PhD Thesis (Katholieke Univ. Leuven, Leuven, Belgium, 1993).

    Google Scholar 

  9. O. Rothaus, “On Bent Functions,” J. Combin. Theory. Ser. A 20(3), 300–305 (1976).

    Article  MATH  MathSciNet  Google Scholar 

  10. N. N. Tokareva, “Bent Functions with Stronger Nonlinear Properties: k-Bent Functions,” Diskret. Analiz i Issled. Operatsii 14(4), 76–102 (2007) [J. Appl. Indust. Math. 2 (4), 566–584 (2008)].

    MathSciNet  Google Scholar 

  11. N. N. Tokareva, “On Quadratic Approximations in Block Ciphers,” Problemy Peredachi Informatsii 44(3), 105–127 (2008) [Problems Inform. Transmission 44 (3), 266–286 (2008)].

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. N. Tokareva.

Additional information

Original Russian Text © N.N. Tokareva, 2008, published in Diskretnyi Analiz i Issledovanie Operatsii, 2008, Vol. 15, No. 4, pp. 74–83.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tokareva, N.N. Description of k-bent functions in four variables. J. Appl. Ind. Math. 3, 284–289 (2009). https://doi.org/10.1134/S1990478909020148

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1990478909020148

Keywords

Navigation