ZHOU Junchao, XU Yunge, ZHANG Wanshan. On Quadratic Vectorial Bent Functions in Trace Forms[J]. Chinese Journal of Electronics, 2020, 29(5): 865-872. doi: 10.1049/cje.2020.08.001
Citation: ZHOU Junchao, XU Yunge, ZHANG Wanshan. On Quadratic Vectorial Bent Functions in Trace Forms[J]. Chinese Journal of Electronics, 2020, 29(5): 865-872. doi: 10.1049/cje.2020.08.001

On Quadratic Vectorial Bent Functions in Trace Forms

doi: 10.1049/cje.2020.08.001
Funds:  This work is supported by the National Natural Science Foundation of China (No.61761166010), the Major Technological Innovation Special Project of Hubei Province (No.2019ACA144), and the Technology Creative Project of Excellent Middle and Young Team of Hubei Province (No.T201920).
More Information
  • Corresponding author: ZHANG Wanshan (corresponding author) was born in Hubei Province, China, in 1973. He received the B.S. degree from the Department of Computer Science, Hubei University in 1996, and received the M.S. degree from Hubei University in 2002. He is currently the teacher of the Compter Sicence Department, School of Computer and Information Engineering, Hubei University, and the researcher of the Hubei Engineering Research Center of Educational Informationalization. (Email:zwshubu@hubu.edu.cn)
  • Received Date: 2019-01-29
  • Rev Recd Date: 2020-04-12
  • Publish Date: 2020-09-10
  • By permutation behavior of certain linearized polynomials, the bentness of quadratic vectorial bent functions of the form F (x)=+Trmkt(ckx1+2kt) is investigated, where n=2kt and m|kt with k, t being positive integers. The numerical results show that there exist new quadratic vectorial bent functions obtained up to extended affine equivalence
  • loading
  • O. Rothaus, "On ‘bent’ functions", J. Combin. Theory Ser. A, Vo1.20, No.3, pp.300-305, 1976.
    F. J. MacWilliams and N. J. A. Sloane, The Theory of ErrorCorrecting Codes, North-Holland, Amsterdam, Netherlands, 1977.
    T. Helleseth and P.V. Kumar, "Sequences with low correlation", In Handbook of Coding Theory, V. S. Pless and W. C. Huffman, Eds, New York, USA, 1998.
    C. Carlet, Boolean Functions for Cryptography and Error Correcting Codes, Cambridge Univ. Press, Cambridge, U.K., pp.257-397, 2010.
    X.Y. Zeng, L. Hu, W.F. Jiang, et al., "The weight distribution of a class of p-ary cyclic codes", Finite Fields Appl., Vol.16, No.1, pp.56-73, 2010.
    X.Y. Zeng, J.Y. Shan and L. Hu,"A triple-error-correcting cyclic code from the Gold and Kasami-Welch APN power functions", Finite Fields Appl., Vol. 18, No.1, pp.70-92, 2012.
    W.J. Jia, X.Y. Zeng, T. Helleseth, et al., "A class of binomial bent functions over the finite fields of odd characteristic", IEEE Trans.Inf. Theory, Vol.58, No.9, pp.6054-6063, 2012.
    H. Cai, X.Y. Zeng, T. Helleseth, et al., "A new construction of zero-difference balanced functions and its applications", IEEE Trans.Inf. Theory, Vol.59, No.8, pp.5008-5015, 2013.
    C. Carlet and S. Mesnager, "Four decades of research on bent functions", Des. Codes Cryptogr., Vo1.78, No.1, pp.5-50, 2016.
    K. Nyberg, "Perfect nonlinear S-boxes", Advances in Cryptology EUROCRYPT'91, LNCS, Vo1.547, pp.378-386, 1992.
    L. Budaghyan and C. Carlet, "CCZ-equivalence of bent vectorial functions and related constructions", Des. Codes Cryptogr., Vo1.59, No.13, pp.69-87, 2011.
    E. Pasalic and W. Zhang, "On multiple output bent functions", Inf. Process. Lett., Vo1.112, No.21, pp.811-815, 2012.
    D.S. Dong, X. Zhang, L.J. Qu, et al., "A note on vectorial bent functions", Information Processing Letters, Vo1.113, No.22, pp.866-870, 2013.
    A. Muratovi?-Ribi?, E. Pasalic and S. Bajri?, "Vectorial bent functions from multiple terms trace functions", IEEE Trans. Inf. Theory, Vo1.60, No.2, pp.1337-1347, 2014.
    A. Muratovi?-Ribi?, E. Pasalic and S. Bajri?, "Vectorial hyperbent trace functions from the PSap class-Their exact number and specification", IEEE Trans. Inf. Theory, Vo1.60, No.7, pp.4408-4413, 2014.
    Y.W. Xu, C. Carlet, S. Mesnager, et al., "Classification of bent monomials, constructions of bent multinomials and upper bounds on the nonlinearity of vectorial functions", IEEE Trans. Inf. Theory, Vo1.64, No.1, pp.367-383, 2017.
    A. Pott, E. Pasalic, A. Muratovi?-Ribi?, et al., "On the maximum number of bent components of vectorial functions", IEEE Trans. Inf. Theory, Vo1.64, No.1, pp.403-411, 2018.
    S. Mesnager, F.R. Zhang, C.M. Tang, et al., "Further study on the maximum number of bent components of vectorial functions", Des. Codes Cryptogr., Vo1.87, No.11, pp.2597-2610, 2019.
    P. Charpin, E. Pasalic, and C. Tavernier, "On bent and semi-bent quadratic Boolean functions", IEEE Trans. Inf. Theory, Vo1.51, No.12, pp.4286-4298, 2005.
    W.P. Ma, M. Lee and F.T. Zhang, "A new class of bent functions", IEICE Trans. Fund., Vo1.E88-A, No.7, pp.2039-2040, 2005.
    N. Yu and G. Gong, "Constructions of quadratic bent functions in polynomial forms", IEEE Trans. Inf. Theory, Vo1.52, No.7, pp.3291-3299, 2006.
    H.G. Hu and D.G. Feng, "On quadratic bent functions in polynomial forms", IEEE Trans. Inf. Theory, Vo1.53, No.7, pp.2610-2615, 2007.
    F.R. Zhang, Y.P. Hu, M. Xie, et al., "Constructions of quadratic bent functions over finite field", Journal of Beijing University of Posts and Telecommunications, Vo1.33, No.3, pp.52-56, 2010. (in Chinese)
    Y.F. He and W.P. Ma, "On quadratic bent functions represented by trace", IEEE International Conference on Intelligent Computing and Intelligent Systems, Vo1.2, pp.75-77, 2010.
    N. Li, X.H. Tang and T. Helleseth, "New constructions of quadratic bent functions in polynomial forms", IEEE Trans. Inf. Theory, Vo1.60, No.9, pp.5760-5767, 2014.
    D.M. Huang, C.M. Tang, Y.F. Qi, et al., "New quadratic bent functions in polynomial forms with coefficients in extension fields", AAECC, Vo1.30, No.4, pp.333-347, 2019.
    C. Carlet, P. Charpin and V. Zinoviev, "Codes, bent functions and permutations suitable for DES-like cryptosystem", Des. Codes Cryptogr., Vol.15, No.2, pp.125-156, 1998.
    K. Nyberg, "Differentially uniform mappings for cryptography", Advances in Cryptology EUROCRYPT'93, LNCS, Springer-Verlag, Vo1.765, pp.55-64, 1994.
    R. Lidl and H. Niederreiter, Finite Fields, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, England, 1997.
    S.M. Dodunekov and J.E.M. Nilsson, "Algebraic decoding of the Zetterberg codes", IEEE Trans. Inf. Theory, Vo1.38, No.5, pp.1570-1573, 1992.
    A. Alahmadi, H. Akhazmi, T. Helleseth, et al., "On the lifted Zetterberg code", Des. Codes Cryptogr., Vo1.80, No.3, pp.561-576, 2016.
    Z.R. Tu, X.Y. Zeng, C.L. Li, et al., "A class of new permutation trinomials", Finite Fields Appl., Vo1.50, pp.178-195, 2018.
  • 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 (147) PDF downloads(67) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return