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New Classes of Bent Functions via the Switching Method

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Arithmetic of Finite Fields (WAIFI 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13638))

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Abstract

The switching method is a powerful method to construct bent functions. In this paper, using this method, we present two generic constructions of piecewise bent functions from known ones, which generalize some earlier works. Further, based on these two generic constructions, we obtain several infinite families of bent functions from quadratic bent functions and the Maiorana-MacFarland class of bent functions by calculating their duals. It is worth noting that our constructions can produce bent functions with the optimal algebraic degree.

This work was supported by the Knowledge Innovation Program of Wuhan-Basic Research under Grant 2022010801010319, the Natural Science Foundation of Hubei Province of China under Grant 2021CFA079 and the National Natural Science Foundation of China under Grant 62072162.

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References

  1. Carlet, C.: Boolean Functions for Cryptography and Coding Theory, Cambridge University Press, Cambridge (2021)

    Google Scholar 

  2. Cohen, G., Honkala, I., Litsyn, S., Lobstein, A.: Covering Codes. The North Holland, Amsterdam (1997)

    MATH  Google Scholar 

  3. Ding, C., Fan, C., Zhou, Z.: The dimension and minimum distance of two classes of primitive BCH codes. Finite Fields Appl. 45, 237–263 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  4. Kumar, P.V., Scholtz, R.A., Welch, L.R.: Generalized bent functions and their properties. J. Combin. Theory Ser. A 40(1), 90–107 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hou, X.: \(p\)-ary and \(p\)-ary versions of certain results about bent functions and resilient functions. Finite Fields Appl. 10(4), 566–582 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Helleseth, T., Kholosha, A.: Monomial and quadratic bent functions over the finite fields of odd characteristic. IEEE Trans. Inf. Theory 52(5), 2018–2032 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Mesnager, S.: Several new infinite families of bent functions and their duals. IEEE Trans. Inf. Theory 60(7), 4397–4407 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  8. Olsen, J., Scholtz, R., Welch, L.: Bent-function sequences. IEEE Trans. Inf. Theory 28(6), 858–864 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  9. Qi, Y., Tang, C., Zhou, Z., Fan, C.: Several infinite families of \(p\)-ary weakly regular bent functions. Adv. Math. Commun. 12(2), 303–315 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  10. Rothaus, O.S.: On bent functions. J. Combin. Theory Ser. A 20(3), 300–305 (1976)

    Article  MATH  Google Scholar 

  11. Tang, C., Zhou, Z., Qi, Y., Zhang, X., Fan, C., Helleseth, T.: Generic construction of bent functions and bent idempotents with any possible algebraic degrees. IEEE Trans. Inf. Theory 63(10), 6149–6157 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  12. Wang, L., Wu, B., Liu, Z., Lin, D.: Three new infinite families of bent functions. Sci. China Inf. Sci. 61(3), 1–14 (2018)

    Article  MathSciNet  Google Scholar 

  13. Xie X., Li N., Zeng X., Tang X., Yao Y.: Several classes of bent functions over finite fields. arXiv: 2108.00612 (2021)

  14. Xu, G., Cao, X., Xu, S.: Several new classes of Boolean functions with few Walsh transform values. Appl. Algebra Eng. Commun. Comput. 28(2), 155–176 (2017)

    Article  MATH  Google Scholar 

  15. Xu, G., Cao, X., Xu, S.: Constructing new APN functions and bent functions over finite fields of odd characteristic via the switching method. Cryptogr. Commun. 8(1), 155–171 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  16. Xu, G., Cao, X., Xu, S.: Several classes of quadratic ternary bent, near-bent and 2-plateaued functions. Int. J. Found. Comput. Sci. 28(1), 1–18 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  17. Xu, G., Cao, X., Xu, S.: Two classes of \(p\)-ary bent functions and linear codes with three or four weights. Cryptogr. Commun. 9(1), 117–131 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  18. Zheng, L., Peng, J., Kan, H., Li, Y.: Several new infinite families of bent functions via second order derivatives. Cryptogr. Commun. 12(6), 1143–1160 (2020). https://doi.org/10.1007/s12095-020-00436-0

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, 430062, China

    Xi Xie, Bing Chen, Nian Li & Xiangyong Zeng

Authors
  1. Xi Xie
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  2. Bing Chen
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  3. Nian Li
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  4. Xiangyong Zeng
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Corresponding author

Correspondence to Nian Li .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Paris VIII, Paris, France

    Sihem Mesnager

  2. School of Mathematics, Southwest Jiaotong University, Chengdu, China

    Zhengchun Zhou

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Xie, X., Chen, B., Li, N., Zeng, X. (2023). New Classes of Bent Functions via the Switching Method. In: Mesnager, S., Zhou, Z. (eds) Arithmetic of Finite Fields. WAIFI 2022. Lecture Notes in Computer Science, vol 13638. Springer, Cham. https://doi.org/10.1007/978-3-031-22944-2_19

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  • DOI: https://doi.org/10.1007/978-3-031-22944-2_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-22943-5

  • Online ISBN: 978-3-031-22944-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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