Advertisement

A proof for the nonexistence of some homogeneous bent functions

  • Meng Qing-shu
  • Zhang Huan-guo
  • Qin Zhong-ping
  • Wang Zhang-yi
Article

Abstract

By the relationship between the first linear spectra of a function at partial points and the Hamming weights of the sub-functions, and by the Hamming weight of homogenous Boolean function, it is proved that there exist no homogeneous bent functions of degreem inn=2m variables form>3.

Key words

homogeneous bent functions Walsh transformation Hamming weight 

CLC number

TN 918.1 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Rothaus O S. On “Bent” Functions.Journal of Combinatorial Theory, 1976,A(20): 300–305.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Dillon J F. Elementary Hadmard Difference Sets. Ph. D. Dissertation, Maryland: University Maryland, 1974.Google Scholar
  3. [3]
    Carlet C. Two New Classes of Bent Functions.Advances in Cryptology-Eurocrypt' 93, LNCS 765. Berlin: Springer-Verlag, 1994. 77–101.Google Scholar
  4. [4]
    Hou Xiang-dong. Cubic Bent Functions.Discrete Mathematics, 1998,189: 149–161.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Carlet C. Generalized Partial Spread.IEEE Transaction on Information Theory, 1995,41(5): 1482–1487.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Qu Cheng-xin, Seberry J, Pieprzyk J. Homogeneous Bent Functions.Discrete Applied Mathematics, 2000,102: 133–139.CrossRefMathSciNetGoogle Scholar
  7. [7]
    Qu Cheng-xin, Seberry J, Pieprzyk J. On the Symmetric Property of Homogeneous Boolean Functions.Proceedings of the Australian Conference on Information Security and Privacy, LNCS 1587. Heidelberg: Springer-Verlag, 1999. 26–35.Google Scholar
  8. [8]
    Charnes C, Rotteler M, Beth T. Homogeneous Bent Functions, Invariants, and Designs.Codes and Cryptography, 2002,26: 139–154.MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    Xia Tian-bing, Seberry J, Pieprzyk J,et al. Homogeneous Bent Functions of Degreen in 2n Variables Do Not Exist forn>3.Discrete Applied Mathematics, 2004,142: 127–132.CrossRefMathSciNetGoogle Scholar
  10. [10]
    Carlet C, Sarkar P. Spectral Domain Analysis of Correlation Immune and Resilient Boolean Functions.Journal of Finite Fields and Applications, 2002,8: 120–130.MATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    Zhang Huan-guo, Feng Xiu-tao, Qin Zhong-ping,et al. Research on Evolutionary Cryptosystems and Evolutionary DES.Chinese Journal of Computers, 2003,26 (12): 1678–1684 (Ch).MathSciNetGoogle Scholar
  12. [12]
    Clark J A, Jacob J L, Stepney S,et al. Evolving Boolean Function Satisfying Mutiple Criteria.Indocrypt 2002, LNCS 2552. Heidelberg: Springer-Verlag, 2002. 246–259.Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • Meng Qing-shu
    • 1
  • Zhang Huan-guo
    • 1
  • Qin Zhong-ping
    • 2
  • Wang Zhang-yi
    • 1
  1. 1.School of ComputerWuhan UniversityWuhan HubeiChina
  2. 2.School of SoftwareHuazhong University of Science and TechnologyWuhan HubeiChina

Personalised recommendations