摘要
创新点
对文献 [Stanica P, Martinsen T, Gangopadhyay S, Singh B J. Bent and generalized bent Boolean functions. Des. Codes Cryptogr., 2013, 69: 77–94.]中的三个重要结果做了进一步的研究。 第一, 通过对关于 2 个变元对称的 n+2 元广义 bent 函数的研究, 刻画了一类关于 m 个变元对称的 n+m 元广义 bent 函数, 其中 m 为偶数。 第二, 基于广义 bent 函数已知抽象结果, 给出了构造该类广义 bent 函数几种具体的新方法, 提高了过去的结果。
References
Rothaus O S. On ‘bent’ functions. J Combin Theory A, 1976, 20: 300–305
Carlet C. Two new classes of bent functions. In: Proceedings of Workshop on the Theory and Application of Cryptographic Techniques, Lofthus, 1994. 77–101
Zhang F, Wei Y, Pasalic E. Constructions of bentnegabent functions and their relation to the completedMaiorana-McFarland class. IEEE Trans Inf Theory, 2015, 61: 1496–1506
Zhang W G, Xiao G Z. Constructions of almost optimal resilient Boolean functions on large even number of variables. IEEE Trans Inf Theory, 2009, 55: 5822–5831
Zhang W G, Jiang F Q, Tang D. Construction of highly nonlinear resilient Boolean functions satisfying strict avalanche criterion. Sci China Inf Sci, 2014, 57: 049101
Schmidt K U. Quaternary constant-amplitude codes for multicode CDMA. IEEE Trans Inf Theory, 2009, 55: 1824–1832
Solé P, Tokareva N. Connections between quaternary and binary bent functions. http://eprint.iacr.org /2009/544.pdf
Stănică P, Gangopadhyay S, Chaturvedi A, et al. Nega-Hadamard transform, bent and negabent functions. In: Proceedings of 6th International Conference on Sequences and Their Applications, Paris, 2010. 359–372
Stănică P, Martinsen T, Gangopadhyay S, et al. Bent and generalized bent Boolean functions. Des Codes Cryptogr, 2013, 69: 77–94
Zhao Y, Li H L. On bent functions with some symmetric properties. Discret Appl Math, 2006, 154: 2537–2543
Author information
Authors and Affiliations
Corresponding author
Electronic supplementary material
Rights and permissions
About this article
Cite this article
Zhang, F., Xia, S., Stănică, P. et al. Further results on constructions of generalized bent Boolean functions. Sci. China Inf. Sci. 59, 059102 (2016). https://doi.org/10.1007/s11432-016-5543-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11432-016-5543-7