GE Hui, SUN Yujuan, XIE Chunlei, “The GAC Property of a Class of 1-Resilient Functions with High Nonlinearity,” Chinese Journal of Electronics, vol. 29, no. 2, pp. 220-227, 2020, doi: 10.1049/cje.2019.12.008
Citation: GE Hui, SUN Yujuan, XIE Chunlei, “The GAC Property of a Class of 1-Resilient Functions with High Nonlinearity,” Chinese Journal of Electronics, vol. 29, no. 2, pp. 220-227, 2020, doi: 10.1049/cje.2019.12.008

The GAC Property of a Class of 1-Resilient Functions with High Nonlinearity

doi: 10.1049/cje.2019.12.008
Funds:  This work is supported by the National Natural Science Foundation of China (No.61672414) and National Cryptography Development Fund (No.MMJJ20170113).
  • Received Date: 2019-01-15
  • Rev Recd Date: 2019-04-29
  • Publish Date: 2020-03-10
  • The absolute and sum-of-squares indicators are used to evaluate the Global avalanche characteristics (GAC) of Boolean functions in a global manner. The GAC properties of a class of highly nonlinear 1-resilient Boolean functions are given. We derive new upper bounds of the absolute and sumof-squares indicators for a class of 1-resilient Boolean functions with high nonlinearity. Compared to the known 1-resilient Boolean functions, the constructed functions possess higher nonlinearity and better GAC properties.
  • loading
  • C.E. Shannon, “Communication theory of secrecy systems”, Bell System Technical Journal, Vol.28, No.4, pp.656-715, 1949.
    W. Zhang and G. Xiao, “Constructions of almost optimal resilient Boolean functions on large even number of variables”, IEEE Transactions on Information Theory, Vol.55, No.12, pp.5822-5831, 2009.
    W. Zhang and E. Pasalic, “Constructions of resilient s-boxes with strictly almost optimal nonlinearity through disjoint linear codes”, IEEE Transactions on Information Theory, Vol.60, No.3, pp.1638-1651, 2014.
    W. Zhang and E. Pasalic, “Generalized maiorana-mcfarland construction of resilient Boolean functions with high nonlinearity and good algebraic properties”, IEEE Transactions on Information Theory, Vol.60, No.10, pp.6681-6695, 2014.
    W. Zhang and E. Pasalic, “Highly nonlinear balanced s-boxes with good differential properties”, IEEE Transactions on Information Theory, Vol.60, No.12, pp.7970-7979, 2014.
    W. Zhang, “High-meets-low: Construction of strictly almost optimal resilient Boolean functions via fragmentary walsh spectra”, IEEE Transactions on Information Theory, Vol.65, No.9, pp.5856-5864, 2019.
    Q. Zhao, G. Han, D. Zheng, 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.
    D. Tang, C. Carlet, X. Tang, et al., “Construction of highly nonlinear 1-resilient Boolean functions with optimal algebraic immunity and provably high fast algebraic immunity”, IEEE Transactions on Information Theory, Vol.63, No.9, pp.6113-6125, 2017.
    D. Tang, W. Zhang and X. Tang, “Construction of balanced Boolean functions with high nonlinearity and good autocorrelation properties”, Designs, Codes and Cryptography, Vol.67, No.1, pp.77-91, 2013.
    D. Tang and S. Maitra, “Construction of n-variable (n ≡ 2 mod 4) balanced Boolean functions with maximum absolute value in autocorrelation spectra < 2n/2”, IEEE Transactions on Information Theory, Vol.64, No.1, pp.393-402, 2018.
    J. Du, S. Pang, Q. Wen, et al., “Construction and count of 1-resilient rotation symmetric Boolean functions on pr variables”, Chinese Journal of Electronics, Vol.23, No.4, pp.816-820, 2014.
    S. Pang, W. Xu, J. Du, et al., “Construction and count of 1-resilient rotation symmetric Boolean functions on 4p variables”, Chinese Journal of Electronics, Vol.26, No.6, pp.1276-1283, 2017.
    W. Zhang and E. Pasalic, “Improving the lower bound on the maximum nonlinearity of 1-resilient Boolean functions and designing functions satisfying all cryptographic criteria”, Information Science, Vol.376, No.2, pp.21-30, 2017.
    O.S. Rothaus, “On ‘bent' functions”, Journal of Combinatorial Theory, Vol.20, No.3, pp.300-305, 1976.
    A. Canteaut and C. Carlet, “Propagation characteristics and correlation immunity of highly nonlineaar Boolean functions”, Advances in Cryptology-EUROCRYPT'00, Lecture Notes in Computer Science, Springer-Verlag, Berlin, Germany, Vol.1807, pp.507-522, 2000.
    S. Maitra, “Highly nonlinear balanced Boolean functions with good local and global avalanche characteristics”, Information Processing Letters, Vol.83, No.4, pp.281-286, 2002.
    P. Stanica and S.H. Sung, “Improving the nonlinearity of certain balanced Boolean functions with good local and global avalanche characteristics”, Information Processing Letters, Vol.79, No.4, pp.167-172, 2001.
    P. Stanica, “Nonlinearity, local and global avalanche characteristics of balanced Boolean functions”, Discrete Mathematics, Vol.248, No.1, pp.181-193, 2002.
    S. Maitra and E. Pasalic, “A maiorana-mcfarland type construction for resilient functions on variables (n even) with nonlinearity > 2n-1-2n/2+2n/2-2”, Discrete Applied Mathematics, Vol.154, No.2, pp.357-369, 2006.
    W. Meier and O. Staffelbach, “Nonlinearity criteria for cryptographic functions”, Advances in Cryptology-EUROCRYPT'89, Lecture Notes in Computer Science, Springer-Verlag, Berlin, Germany, Vol.434, pp.549-562, 1990.
    F.J. Macwilliams and N.J.A. Sloane, The Theory of ErrorCorrecting Codes, North-Holland, Amsterdam, Netherlands, 1977.
    G. Xiao and J.L. Massey, “A spectral characterization of correlation-immune combining functions”, IEEE Transactions on Information Theory, Vol.34, No.3, pp.569-571, 1988.
    X. Zhang and Y. Zheng, “GAC-the criterion for global avalanche characteristics of cryptographic functions”, Journal of Universal Computer Science, Vol.1, No.5, pp.320-337, 1995.
    C. Carlet, “Partially-bent functions”, Designs, Codes and Cryptography, Vol.3, No.2, pp.135-145, 1993.
  • 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 (491) PDF downloads(298) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return