DU Jiao, FU Shaojing, QU Longjiang, et al., “The Existence of a Class of Balanced Multi-output Rotation Symmetric Boolean Functions,” Chinese Journal of Electronics, vol. 27, no. 5, pp. 995-1001, 2018, doi: 10.1049/cje.2018.04.005
Citation: DU Jiao, FU Shaojing, QU Longjiang, et al., “The Existence of a Class of Balanced Multi-output Rotation Symmetric Boolean Functions,” Chinese Journal of Electronics, vol. 27, no. 5, pp. 995-1001, 2018, doi: 10.1049/cje.2018.04.005

The Existence of a Class of Balanced Multi-output Rotation Symmetric Boolean Functions

doi: 10.1049/cje.2018.04.005
Funds:  This work is supported by National Key R&D Program of China (No.2017YFB0802000), National Natural Science Foundation of China (No.61672530, No.61722213, No.61572026, No.U1404601, No.11501181), and Ph.D research startup foundation of Henan Normal University (No.5101019170133).
More Information
  • Corresponding author: LI Chao (corresponding author) received the B.S. degree in mathematics in 1987 from the University of Information Engineering of China, the M.S. degree in mathematics in 1990 from the University of Science and Technology of China, and the Ph.D. degree in engineering in 2002 from the National University of Defense Technology of China. Since December 2001, he has been a professor with the Department of Mathematics and System Science, National University of Defense Technology. His research fields include coding theory, cryptography and sequences. (Email:lichao nudt@sina.com)
  • Received Date: 2016-06-08
  • Rev Recd Date: 2017-06-30
  • Publish Date: 2018-09-10
  • A new characterization of balanced rotation symmetric (n,m)-functions is presented. Based on the characterization, the nonexistence of balanced rotation symmetric (pr, m)-functions is determined, where p is an odd prime and m ≥ 2. And there exist balanced rotation symmetric (2r, m)-functions for 2 ≤ m ≤ 2r-r. With the help of these results, we also prove that there exist rotation symmetric resilient (2r, m)-functions for 2 ≤ m ≤ 2r-r-1.
  • loading
  • E. Filiol and C. Fontaine, “Highly nonlinear balanced Boolean functions with good correlation immunity”, Advances in Cryptology-EUROCRYPT’98, Lecture Notes in Computer Science, Springer-Verlag, Espoo, Finland, Vol.1403, pp.475-488, 1998.
    Y. Yuan and Y.Q. Zhao, “Cryptological properties of multioutput rotation symmetric functions”, Journal on Communications, Vol.30, No.11A, pp.1-7, 2009. (in Chinese)
    P. Stanica, S. Maitra and J. Clark, “Results on rotation symmetric bent and correlation immune Boolean functions”, Fast Software Encryption Workshop (FSE 2004), Lecture Notes in Computer Science, Springer Verlag, New Delhi, India, Vol.3017, pp.161-177, 2004.
    P. Stanica and S. Maitra, “Rotation symmetric Boolean functions count and cryptographic properties”, Discrete Applied Mathematics, Vol.156, No.10, pp.1567-1580, 2008.
    P. Ke, L. Huang and S. Zhang, “Improved lower bound on the number of balanced symmetric functions over GF (p)”, Information Science, Vol.179, pp.682-687, 2009.
    S. Fu, L. Qu, C. Li, et al., “Balanced rotation symmetric Boolean functions with maximum algebraic immunity”, IET Information Security, Vol.5, Iss.2, pp.93-99, 2011.
    C. Carlet, D.K. Dalai, K.C. Gupta, et al., “Algebraic immunity for cryptographically significant Boolean functions: Analysis and construction”, IEEE Trans. Inform. Theory, Vol.52, No.7, pp.3105-3121, 2006.
    S. Fu, C. Li and L. Qu, “On the number of rotation symmetric Boolean functions”, Science China Information Science, Vol.53, No.3, pp.537-545, 2010.
    J. Du, Q. Wen, J. Zhang, 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.
    J. Du, Q. Wen, J. Zhang, et al., “Construction and counting of 1-resilient RSBFs on pq variables”, IEICE Trans. Fundamentals., Vol.E96-A, No.7, pp.1653-1656, 2013.
    J. Du, Q. Wen, J. Zhang, et al., “Constructions of resilient RSBFs on given number of variables”, IET Information Security, Vol.8, Iss.5, pp.265-272, 2014.
    S. Kavut, “Results on rotation symmetric S-boxes”, Information Science, Vol.201, pp.93-113, 2012.
    V. Rijmen, P. Barreto, D. Gazzoni, et al., “Rotation symmetry in algebraically generated cryptographic substitution tables”, Inf. Process. Lett., Vol.106, pp.246-250, 2008.
    B. Mazumdar, D. Mukhopadhyay and I. Sengupta, “Design and implementation of rotation symmetric S-boxes with high nonlinearity and high DPA resiliency”, IEEE International Symposium on Hardware-Oriented Security and Trust (HOST), pp.87-92, 2013.
    G. Gao, T.W. Cusick and W. Liu. “Families of rotation symmetric functions with useful cryptographic properties”, IET Information Security, Vol.8, No.6, pp.297-302, 2014.
    W. Zhang and E. Pasalic, “Generalized Maiorana-McFarland construction of resilient Boolean functions with high nonlinearity and good algebraic properties”, IEEE Trans. Inform. Theory, Vol.60, No.10, pp.6681-6695, 2014.
    P. Camion, C. Carlet, P. Charpin, et al., “On correlationimmune functions”, Advance in Cryptology-CRYPTO’91, Lecture Notes in Computer Science, Springer-verlag, Berlin, Germany, Vol.576, pp.86-100, 1992.
    D.R. Stinson., “Resilient functions and large sets of orthogonal arrays”, Congr. Numer., Vol.92, pp.105-110,1993.
    J. Zhang, Z. You and Z. Li, “Enumeration of binary orthogonal arrays of strength 1”, Discrete Mathematics, Vol.239, No.1-3, pp.191-198, 2001.
    P. Camion and A. Canteaut, “Correlation-immune and resilient functions over a finite alphabet and their applications in cryptography”, Designs, Codes and Cryptography, Vol.16, pp.121-149, 1999.
  • 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 (352) PDF downloads(210) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return