DU Jiao, PANG Shanqi, WEN Qiaoyan, LIAO Xin. Construction and Count of 1-Resilient Rotation Symmetric Boolean Functions on pr Variables[J]. Chinese Journal of Electronics, 2014, 23(4): 816-820.
Citation: DU Jiao, PANG Shanqi, WEN Qiaoyan, LIAO Xin. Construction and Count of 1-Resilient Rotation Symmetric Boolean Functions on pr Variables[J]. Chinese Journal of Electronics, 2014, 23(4): 816-820.

Construction and Count of 1-Resilient Rotation Symmetric Boolean Functions on pr Variables

Funds: This work is supported by National Natural Science Foundation of China (No.11171093, No.11471104, No.61402154, No.61402162, No.61300181, No.61272057, No.61202434, No.61170270, No.61100203, No.61121061), the Fundamental Research Funds for the Central Universities (No.BUPT2011YB01, No.2012RC0612), the Natural Science Research Program of the Education Department of Henan Province (No.2011B110010), Innovative Research Team (in Science and Technology) in University of Henan Province (No.14IRTSTHN023), Specialized Research Fund for the Doctoral Program of Higher Education (No.20130161120004) and Hunan Provincial Natural Science Foundation of China (No.14JJ7024).
More Information
  • Received Date: June 30, 2013
  • Revised Date: November 30, 2013
  • Published Date: October 04, 2014
  • Construction and count of 1-resilient Rotation symmetric Boolean functions (RSBFs) on pr variables are demonstrated. It is proved that constructions of 1-resilient RSBFs on pr variables are equivalent to solving an equation system. An accurate enumeration formula of all 1-resilient RSBFs on pr variables is also proposed. Some examples are given, and the exact numbers of 1-resilient RSBFs on 8 and 9 variables are obtained respectively.
  • E. Filiol, et al., 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.
    J. Pieprzyk and C.X. Qu, Fast hashing and rotation symmetric functions, Journal Universal Computer Science, Vol.5, No.1, pp.20-31,1999.
    W. Cusick, P. Stanica and S. Maitra, Fast evaluation, weight and nonlinearity of rotation symmetric functions, Discrete mathematics, Vol.258, No.1-3, pp.289-301, 2002.
    P. Stanica, et al, 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.
    S. Sarkar and S. Maitra, Construction of rotation symmetric Boolean functions with maximum algebraic immunity on odd number of variables, Boztas, S. Lu, H-F.(eds.)AAECC 2007, Lecture Notes in Computer Science, Springer, Heidelberg, Vol.4851, pp.271-280, 2007.
    P. Stanica and S. Maitra, Rotation symmetric Boolean functions count and cryptographic properties, Discrete Applied Mathematics, Vol.156, No.10, pp.1567-1580, 2008.
    S. Fu, C. Li, K. Matsuura and L. Qu, Construction of rotation symmetric Boolean functions with maximum algebraic immunity, Cryptology and Network Security, Proc. of the 8th International Conference, Kanazawa, Japan, pp.402-412, 2009.
    S. Fu, L. Qu, C. Li and B. Sun, Balanced rotation symmetric Boolean functions with maximum algebraic immunity, IET Information Security, Vol.5, No.2, pp.93-99, 2011.
    P. Stanica and S. Maitra, A constructive count of rotation symmetric functions, Information Processing Letters, Vol.88, No.6, pp.299-304, 2003.
    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 Sciences, Vol.53, No.3, pp.537-545, 2010.
    T. Siegenthaler, Correlation-immune of nonlinear combining functions for cryptographic applications, IEEE Trans. Inform. Theory, Vol.30, No.5, pp.776-780, 1984.
    B. Chor, O. Goldreich, J. Hasted, et al., The bit extraction problem or t-resilient functions, Proc. of the 26th IEEE Symposium on Foundations of Computer Science, pp.396-407, 1985.
    C.H. Bennett, et al, Privacy amplification by public discussion, SIAM J. Comput., Vol.17, pp.210-229, 1988.
    W. Zhang and G. Xiao, Constructions of almost optimal resilient Boolean functions on large even number of variables, IEEE Trans. Inform. Theory, Vol.55, No.12, pp.5822-5831, 2009.
    J. Le and A. Viola, Equivalence class of Boolean functions for first-order correlation, IEEE Trans. Inform. Theory, Vol.56, No.3, pp.1247-1261, 2010.
    S. Maitra and E. Pasalic, Further constructions of resilient Boolean functions with very High nonlinearity, IEEE Trans. Inform. Theory, Vol.48, No.7, pp.1825-1834, 2002.
    P. Camion, C. Carlet, P. Charpin, et al., On correlation-immune 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. Sarkar and S. Maitra, Balancedness and correlation immunity of symmetric Boolean functions, Discrete Mathematics, Vol.307, No.19-20, pp.2351-2358, 2007.
    J. Peng and H. Kan, Constructing correlation immune symmetric Boolean functions, IEICE Trans. Fundamentals., Vol.E94-A, No.7, pp.1591-1596, 2011.
    K. Gopalakrisnan, D.G. Hoffman and D.R. Stinson, A note on a conjecture concerning symmetric resilient functions, Information processing letter, Vol.47, No.3, pp.139-143, 1993.
    C. Wu and E. Dawson, Correlation immunity and resiliency of symmetric Boolean functions, Theoretical Computer Science, Vol.312, No.2-3, pp.321-335, 2004.
    J. Du, Q. Wen, et al., Construction and count of resilient rotation symmetric Boolean functions with prime number variables, Journal on Communications, Vol.34, No.3, pp.6-13, 2013. (in Chinese)
    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 rotation symmetric Boolean functions on given number of variables, IET Information Security, Vol.8, No.5, pp.265-272, 2014.
    Q. Wen, X. Niu and Y. Yang, The Boolean Functions in Modern Cryptology, Science Press, Beijing, China, 2000. (in Chinese)
    H. Zheng and C. Jin, Construction and enumeration of mth-order correlation immune functions, Acta Electronica Sinica, Vol.36, No.4, pp.804-808, 2008. (in Chinese)
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