XU Yuwei, LIU Feng, WU Chuankun, “Preimage Distributions of Perfect Nonlinear Functions and Vectorial Plateaued Functions,” Chinese Journal of Electronics, vol. 28, no. 5, pp. 933-937, 2019, doi: 10.1049/cje.2019.06.013
Citation: XU Yuwei, LIU Feng, WU Chuankun, “Preimage Distributions of Perfect Nonlinear Functions and Vectorial Plateaued Functions,” Chinese Journal of Electronics, vol. 28, no. 5, pp. 933-937, 2019, doi: 10.1049/cje.2019.06.013

Preimage Distributions of Perfect Nonlinear Functions and Vectorial Plateaued Functions

doi: 10.1049/cje.2019.06.013
Funds:  This work is supported by the National Natural Science Foundation of China (No.61671448), the Strategic Priority Research Program of the Chinese Academy of Sciences (No.XDA06010701), and the National Key R&D Program of China (No.2016YFB0800100).
  • Received Date: 2017-03-17
  • Rev Recd Date: 2017-04-19
  • Publish Date: 2019-09-10
  • By converting the problem of preimage distribution of a perfect nonlinear function with three binary outputs to that with two binary outputs, this paper presents the preimage distributions of perfect nonlinear functions with three binary outputs. This paper also characterizes the fundamental characterization of the preimage distribution of vectorial plateaued functions with single amplitude and its component functions being all unbalanced, and gives the preimage distributions of such functions with two or three binary outputs.
  • loading
  • C. Blondeau and K. Nyberg, "Perfect nonlinear functions and cryptography", Finite Fields and Their Applications, Vol.32, pp.120-147, 2015.
    A. Çeşmelioğlu and W. Meidl, "A construction of bent functions from plateaued functions", Designs, codes and cryptography, Vol.66, No.1-3, pp.231-242, 2013.
    S. Mesnager and J.-P. Flori, "Hyperbent functions via Dillonlike exponents", IEEE Transactions on Information Theory, Vol.59, No.5, pp.3215-3232, 2013.
    C. Carlet, C. Ding, and J. Yuan, "Linear codes from perfect nonlinear mappings and their secret sharing schemes", IEEE Transactions on Information Theory, Vol.51, No.6, pp.2089-2102, 2005.
    C. Ding, "Algebraic constructions of constant composition codes", IEEE transactions on information theory, Vol.51, No.4, pp.1585-1589, 2005.
    C. Xiang, K. Feng, and C. Tang, "A construction of linear codes over F2t from boolean functions", IEEE Transactions on Information Theory, Vol.63, No.1, pp.169-176, 2017.
    C. Carlet and C. Ding, "Highly nonlinear mappings", Journal of complexity, Vol.20, No.2, pp.205-244, 2004.
    C. Carlet, "Boolean and vectorial plateaued functions and APN functions", IEEE Transactions on Information Theory, Vol.61, No.11, pp.6272-6289, 2015.
    C. Li, Q. Li, and S. Ling, "Properties and applications of preimage distributions of perfect nonlinear functions", IEEE Transactions on Information Theory, Vol.55, No.1, pp.64-69, 2009.
    Y. Zheng and X.-M. Zhang, "Plateaued functions", Proc. of Information and Communication Security, Sydney, Australia, pp.284-300. Springer, 1999.
    Y. Zheng and X.-M. Zhang, "On plateaued functions", IEEE Transactions on Information Theory, Vol.47, No.3, pp.1215-1223, 2001.
  • 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 (450) PDF downloads(127) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return