YE Zhifan, KE Pinhui, CHEN Zhixiong, “Linear Complexity of d-Ary Sequence Derived from Euler Quotients over GF(q),” Chinese Journal of Electronics, vol. 28, no. 3, pp. 529-534, 2019, doi: 10.1049/cje.2019.02.004
Citation: YE Zhifan, KE Pinhui, CHEN Zhixiong, “Linear Complexity of d-Ary Sequence Derived from Euler Quotients over GF(q),” Chinese Journal of Electronics, vol. 28, no. 3, pp. 529-534, 2019, doi: 10.1049/cje.2019.02.004

Linear Complexity of d-Ary Sequence Derived from Euler Quotients over GF(q)

doi: 10.1049/cje.2019.02.004
Funds:  This work is supported by the National Natural Science Foundation of China (No.61772292, No.61772476), the Provincial Natural Science Foundation of Fujian (No.2019J01273) and the Foundation of Fujian Educational Committee (No.JAT170627).
More Information
  • Corresponding author: KE Pinhui (corresponding author) received the Ph.D. degree in Cryptography from Beijing University of Posts and Telecommunications in 2006. He is now a professor of Fujian Normal University. His research interests include sequence design and algebraic coding. (Email:keph@fjnu.edu.cn)
  • Received Date: 2017-04-18
  • Publish Date: 2019-05-10
  • For an odd prime p and positive integers r, d such that 0 < dpr, a generic construction of dary sequence based on Euler quotients is presented in this paper. Compared with the known construction, in which the support set of the sequence is fixed and d is usually required to be a prime, the support set of the proposed sequence is flexible and d could be any positive integer less then pr in our construction. Furthermore, the linear complexity of the proposed sequence over prime field GF(q) with the assumption of qp-1 ≢ 1 mod p2 is determined. An algorithm of computing the linear complexity of the sequence is also given. Our results indicate that, with some constrains on the support set, the new sequences possess large linear complexities.
  • loading
  • Z. X. Chen, X. N. Du and R. Marzouk, "Trace representation of pseudorandom binary sequences derived from Euler quotients", Appl. Algebra Eng. Commun. Comput, Vol.26, No.6, pp.555-570, 2015.
    V. Tomasevic, S. Bojanic and O. Niteo-Taladriz, "Fiding an internal state of RC4 stream cipher", Information Sciences. Vol.177, pp.1715-1727, 2007.
    G. Golomb and G. Gong, "Signal designs with good correlations", For Wireless Communications, Cryptography and Radar Applications, Cambridge, U.K.:Cambridge University Press, 2005.
    W. W. Liang, X. Y. Zeng, Y. E. Xu, "The periods of a class of nonlinear feedback shift register sequences", Chinese Journal of Electronics, Vol.25, No.2, pp.296-303, 2016.
    P. H. Ke, Z. F. Ye, S. Y. Zhang, Z. L. Chang, "On the cross-correlation distribution of d-ary generalized LegendreSidelnikov sequences", Chinese Journal of Electronics, Vol.27, No.2, pp.287-291, 2018.
    Z. X. Chen, Z. H. Niu and C. H. Wu, "On the k-error linear complexity of binary sequences derived from polynomial quotients", Science China-Inform. Sci. Vol.58, No.9, pp.1-15, 2015.
    Z. F. Ye, P. H. Ke, S. Y. Zhang, et al., "Some notes on pseudorandom binary sequences derived from Fermat-Euler quotients", IEICE Trans. on Fundamentals, Vol.98, No.10, pp.2199-2202, 2015.
    X. N. Du, Z. X. Chen and L. Hu, "Linear complexity of binary sequences derived from Euler quotients with primepower modulus", Inform. Process. Lett. Vol.112, pp.604-609, 2012.
    Gómez-Pérez and A. Winterhof, "Multiplicative character sums of Fermat quotients and pseudorandom sequences", Period. Math. Hungar. Vol.64, pp.161-168, 2012.
    Z. X. Chen and X. N. Du, "On the linear complexity of binary threshold sequences derived from Fermat quotients", Des. Codes and Cryptogr., Vol.67, pp.317-323, 2013.
    Z. X. Chen, A. Ostafe and A. Winterhof, "Structure of pseudorandom numbers derived from Fermat quotients", Arithmetic of Finite Fields-WAIFI 2010, Lecture Notes in Comput. Sci., pp.73-85, 2010.
    Z. X. Chen, "Trace representation and linear complexity of binary sequences derived from Fermat quotients", Science China-Information Sciences, Vol.57, No.11, pp.1-10, 2014.
    X. N. Du, C. H. Wu, and W. Y. Wei, "An extension of binary threshold sequence from Fermat quotient", Advances in Mathematics of Communications., Vol.10, No.4, pp.743-752, 2016.
    Massey J.L, "Shift register synthesis and BCH decoding", IEEE Trans. Inf. Theory, Vol.15, No.1, pp.122-127, 1969.
    C. Ding, "Cyclic codes from cyclotomic sequences of order four", Finite Fields and Their Applications, Vol.23, pp.8-34, 2013.
    Z. F. Ye, P. H. Ke and Z. X. Chen, "Further results on pseudorandom binary sequences derived from Fermat-Euler quotients", 10th International Conference on Information, Communications and Signal Processing (ICICS 2015), pp.1-4, 2015.
    Agoh, Takashi, Karl Dilcher, and Ladislav Skula, "Fermat quotients for composite moduli, Journal of Number Theory", Vol.66, No.1, pp.29-50, 1997.
  • 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 (624) PDF downloads(160) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return