Volume 30 Issue 6
Nov.  2021
Turn off MathJax
Article Contents
YANG Zhiyao, KE Pinhui, CHEN Zhixiong, “New Secondary Constructions of Generalized Bent Functions,” Chinese Journal of Electronics, vol. 30, no. 6, pp. 1022-1029, 2021, doi: 10.1049/cje.2021.08.003
Citation: YANG Zhiyao, KE Pinhui, CHEN Zhixiong, “New Secondary Constructions of Generalized Bent Functions,” Chinese Journal of Electronics, vol. 30, no. 6, pp. 1022-1029, 2021, doi: 10.1049/cje.2021.08.003

New Secondary Constructions of Generalized Bent Functions

doi: 10.1049/cje.2021.08.003
Funds:

This work is supported by the National Natural Science Foundation of China (No.61772292, No.61772476), the Provincial Natural Science Foundation of Fujian (No.2019J01273) and Fujian Normal University Innovative Research Team (No.IRTL1207).

  • Received Date: 2021-01-08
  • Rev Recd Date: 2021-04-30
  • Available Online: 2021-09-23
  • Publish Date: 2021-11-05
  • Three new secondary constructions of generalized bent functions are presented. We provide a secondary construction of generalized bent functions from indirect sum methods proposed by Carlet et al. A new secondary construction of generalized bent functions from four initial functions is also investigated. We demonstrate that many known constructions can be derived from our proposed construction as special cases by choosing proper initial functions and parameters. By modifying the new construction, a novel secondary construction of generalized bent functions from two initial generalized bent functions is obtained. For the binary case, the dual functions of the bent functions by our method are presented, which share the same formula as the indirect sum.
  • loading
  • C. Carlet, Boolean Functions for Cryptography and Coding Theory, Cambridge University Press, New York, USA, pp.76-142, 2020.
    O.S. Rothaus, "On "bent" functions", Journal of Combinatorial Theory, Series A, Vol.20, pp.300-305, 1976.
    C. Carlet and S. Mesnager, "Four decades of research on bent functions", Designs, Codes and Cryptography, Vol.78, No.1, pp.5-50, 2016.
    S. Mesnager, Bent Functions:Fundamentals and Results, Springer-Verlag, Berlin, Germany, pp.69-108, 2016.
    C. Carlet, F.R. Zhang and Y.P. Hu, "Secondary constructions of bent functions and their enforcement", Advances in Mathematics of Communications, Vol.6, No.3, pp.305-314, 2012.
    S. Mesnager, F.R. Zhang and Y. Zhou, "On construction of bent functions involving symmetric functions and their duals", Advances in Mathematics of Communications, Vol.11, No.2, pp.347-352, 2017.
    C. Carlet, "On the secondary constructions of resilient and bent functions", Proc. of the Workshop on Coding, Cryptography and Combinatorics, Birkhauser-Verlag, Basel, Switzerland, pp.3-28, 2004.
    S. Hodžić, E. Pasalic and Y.Z. Wei, "A general framework for secondary constructions of bent and plateaued functions", Designs, Codes and Cryptography, Vol.88, No.10, pp.2007-2035, 2020.
    T.T. Pang, X.Y. Zeng, N. Li, et al., "A class of new quadratic vectorial bent functions", Chinese Journal of Electronics, Vol.29, No.5, pp.873-879, 2020.
    P. Stănică, S. Gangopadhyay, A. Chaturvedi, et al., "Investigations on bent and negabent functions via the negaHadamard transform", IEEE Transactions on Information Theory, Vol.58, No.6, pp.4064-4072, 2012.
    P. Stănică, "On weak and strong 2k-bent Boolean functions", IEEE Transactions on Information Theory, Vol.62, No.5, pp.2827-2835, 2016.
    F.R. Zhang, C. Carlet, Y.P. Hu, et al., "New secondary constructions of bent functions", Applicable Algebra in Engineering, Communication and Computing, Vol.27, No.5, pp.413-434, 2016.
    F.R. Zhang, C. Carlet, Y.P. Hu, et al., "Secondary constructions of highly nonlinear Boolean functions and disjoint spectra plateaued functions", Information Science, Vol.283, pp.94-106, 2014.
    Q.L. Zhao, G. Han, D. Dong, et al., "Constructing oddvariable rotation symmetric Boolean functions with optimal algebraic immunity and high nonlinearity", Chinese Journal of Electronics, Vol.28, No.1, pp.45-51, 2019.
    P.V. Kumar, R.A. Scholtz and L.R. Welch, "Generalized bent functions and their properties", Journal of Combinatorial Theory, Series A, Vol.40, No.1, pp.90-107, 1985.
    T. Martinsen, W. Meidl, S. Mesnager, et al., "Decomposing generalized bent and hyperbent functions", IEEE Transactions on Information Theory, Vol.63, No.12, pp.7804-7812, 2017.
    S. Mesnager, C.M. Tang and Y.F. Qi, "Generalized plateaued functions and admissible (plateaued) functions", IEEE Transactions on Information Theory, Vol.63, No.10, pp.6139-6148, 2017.
    S. Mesnager, C. Riera and P. Stănică, "Multiple characters transforms and generalized Boolean functions", Cryptography and Communications, Vol.11, No.6, pp.1247-1260, 2019.
    K.U. Schmidt, "Quaternary constant-amplitude codes for multi-code CDMA", IEEE Transactions on Information Theory, Vol.55, No.4, pp.1824-1832, 2009.
    K.U. Schmidt, "Z4-Valued quadratic forms and quaternary sequence families", IEEE Transactions on Information Theory, Vol.55, No.12, pp.5803-5810, 2009.
    P. Stănică, T. Martinsen, S. Gangopadhyay, et al., "Bent and generalized bent Boolean functions", Designs, Codes and Cryptography, Vol.69, No.1, pp.77-94, 2013.
    W. Meidl, "A secondary construction of bent functions, octal gbent functions and their duals", Mathematics and Computers in Simulation, Vol.143, pp.57-64, 2018.
    F.R. Zhang, S.X. Xia, P. Stănică, et al., "Further results on constructions of generalized bent Boolean functions", Science China:Information Sciences, Vol.59. No.5, pp.1-3, 2016.
    S. Hodžić and E. Pasalic, "Generalized bent functions-Some general construction methods and related necessary and sufficient conditions", Cryptography and Communications, Vol.7, No.4, pp.469-483, 2015.
    T. Martinsen, W. Meidl and P. Stănică, "Generalized bent functions and their Gray images", Arithmetic of Finite Fields, Vol.17, No.6, pp.160-173, 2016.
    S. Mesnager, C.M. Tang, Y.F. Qi, et al., "Further results on generalized bent functions and their complete characterization", IEEE Transactions on Information Theory, Vol.64, No.7, pp.5441-5452, 2018.
    B.K. Singh, "On cross-correlation spectrum of generalized bent functions in generalized Maiorana-McFarland class", Information Science Letter, Vol.2, No.3, pp.139-145, 2013.
    S. Hodžić, W. Meidl and E. Pasalic, "Full characterization of generalized bent functions as (semi)-bent spaces, their dual, and the Gray image", IEEE Transactions on Information Theory, Vol.64, No.7, pp.5432-5440, 2018.
    C.M. Tang, C. Xiang, Y.F. Qi, et al., "Complete characterization of generalized bent and 2k-bent Boolean functions", IEEE Transactions on Information Theory, Vol.63, No.7, pp.4668-4674, 2017.
    Z.P. Zhuo, J.F. Chong and S.M. Wei, "Some properties correlation functions on generalized Boolean functions", Chinese Journal of Electronics, Vol.24, No.1, pp.166-169, 2015.
    S. Hodžić, E. Pasalic, "Construction methods for generalized bent functions", Discrete Applied Mathematics, Vol.238, pp.14-23, 2018.
    T. Martinsen, W. Meidl and P. Stănică, "Partial spread and vectorial generalized bent functions", Designs, Codes and Cryptography, Vol.85, No.1, pp.1-13, 2017.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (517) PDF downloads(51) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return