Several classes of negabent functions over finite fields

Highlight
  • 43 Downloads

Notes

Acknowledgements

This work was supported by Fundamental Research Funds for the Central Universities (Grant No. JB161504), China Postdoctoral Science Foundation (Grant No. 2016M602776), National Natural Science Foundation of China (Grant Nos. 61671013, 61602361, 61572460, 61402352), National Key R&D Program of China (Grant No. 2016YFB0800703), Open Project Program of the State Key Laboratory of Information Security (Grant No. 2017-ZD-01), National Development and Reform Commission (Grant No. (2012)1424), China 111 Project (Grant No. B16037), and Norwegian Research Council.

Supplementary material

11432_2017_9096_MOESM1_ESM.pdf (242 kb)
Supplementary material, approximately 243 KB.

References

  1. 1.
    Rothaus O S. On ‘bent’ functions. J Combin Theory A, 1976, 20: 300–305CrossRefMATHGoogle Scholar
  2. 2.
    Parker M G. The constabent properties of Golay-Davis-Jedwab sequences. In: Proceedings of IEEE International Symposium on Information Theory, Sorrento, 2000. 302Google Scholar
  3. 3.
    Parker M G, Pott A. On boolean functions which are bent and negabent. In: Proceedings of International Workshop on Sequences, Subsequences, and Consequences, Los Angeles, 2007. 9–23MATHGoogle Scholar
  4. 4.
    Stănică P, Gangopadhyay S, Chaturvedi A, et al. Investigations on bent and negabent functions via the nega-Hadamard transform. IEEE Trans Inf Theory, 2012, 58: 4064–4072MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Su W, Pott A, Tang X. Characterization of negabent functions and construction of bent-negabent functions with maximum algebraic degree. IEEE Trans Inf Theory, 2013, 59: 3387–3395MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Zhang F, Wei Y, Pasalic E. Constructions of bentnegabent functions and their relation to the completed Maiorana-McFarland class. IEEE Trans Inf Theory, 2015, 61: 1496–1506CrossRefMATHGoogle Scholar
  7. 7.
    Sarkar S. Characterizing negabent boolean functions over finite fields. In: Proceedings of the 7th International Conference on Sequences and Their Applications, Waterloo, 2012. 77–88MATHGoogle Scholar
  8. 8.
    Zhou Y, Qu L. Constructions of negabent functions over finite fields. Cryptogr Commun, 2017, 9: 165–180MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Lidl R, Niederreiter H. Finite fields. In: Encyclopedia of Mathematics and Its Applications. 2nd ed. Cambridge: Cambridge University Press, 1997Google Scholar
  10. 10.
    Mesnager S. Several new infinite families of bent functions and their duals. IEEE Trans Inf Theory, 2014, 60: 4397–4407MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Gaofei Wu
    • 1
  • Nian Li
    • 2
    • 3
  • Yuqing Zhang
    • 1
    • 4
  • Xuefeng Liu
    • 1
  1. 1.State Key Laboratory of Integrated Service NetworksXidian UniversityXi’anChina
  2. 2.Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied MathematicsHubei UniversityWuhanChina
  3. 3.Department of InformaticsUniversity of BergenBergenNorway
  4. 4.National Computer Network Intrusion Protection CenterUniversity of Chinese Academy of SciencesBeijingChina

Personalised recommendations