WU Chenhuang and CHEN Zhixiong, “Elliptic Curve Quaternary Sequences Constructed Using the Reverse Gray Mapping,” Chinese Journal of Electronics, vol. 23, no. 3, pp. 448-453, 2014,
Citation: WU Chenhuang and CHEN Zhixiong, “Elliptic Curve Quaternary Sequences Constructed Using the Reverse Gray Mapping,” Chinese Journal of Electronics, vol. 23, no. 3, pp. 448-453, 2014,

Elliptic Curve Quaternary Sequences Constructed Using the Reverse Gray Mapping

Funds:  This work is partially supported by the National Natural Science Foundation of China (No.61373140, No.61170246) and the Special Scientific Research Program in Fujian Province Universities of China (No.JK2013044).
  • Received Date: 2011-09-01
  • Rev Recd Date: 2014-01-01
  • Publish Date: 2014-07-05
  • Quaternary sequences are the most important sequences in view of many practical applications. Using the reverse Gray mapping, we propose a new construction of elliptic curve quaternary sequences with strong pseudorandom properties. We apply a result of Marzouk and Winterhof on the relation between the pseudorandom measures for binary sequences and the measures for quaternary sequences to analyze the well-distribution measure and correlation measure of order l, which were introduced by Mauduit and Sárközy, for the proposed sequences.
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  • S. Krone, D. Sarwate, "Quadriphase sequences for spread spectrum multiple-access communication", IEEE Transactions on Information Theory, Vol.30, No.3, pp.520-529, 1984.
    H. Lüke, H. Schotten, H. Hadinejad-Mahram, "Binary and quadriphase sequences with optimal autocorrelation properties: A survey", IEEE Transactions on Information Theory, Vol.49, No.12, pp.3271-3282, 2003.
    J. Jang, Y. Kim, S. Kim, et al., "New quaternary sequences with ideal autocorrelation constructed from binary sequences with ideal autocorrelation", IEEE International Symposium on Information Theory, Seoul, Korea, pp.278-281, 2009.
    Y. Kim, J. Jang, S. Kim, et al., "New quaternary sequences with optimal autocorrelation", IEEE International Symposium on Information Theory, Seoul, Korea, pp.286-289, 2009.
    Y. Kim, J. Jang, S. Kim, et al., "New construction of quaternary sequences with ideal autocorrelation from Legendre sequences", IEEE International Symposium on Information Theory, Seoul, Korea, pp.282-285, 2009.
    I. Shparlinski, "Pseudorandom number generators from elliptic curves", Recent Trends in Cryptography-American Mathematical Society, Vol.477, pp.121-141, 2009.
    C. Mauduit, A. Sárközy, "On finite pseudorandom binary sequences I: Measures of pseudorandomness, the Legendre symbol", Acta Arithmetica, Vol.82, pp.365-377, 1997.
    J. Cassaigne, C. Mauduit, A. Sárközy, "On finite pseudorandom binary sequences, VII: The measures of pseudorandomness", Acta Arithmetica, Vol.103, pp.97-118, 2002.
    L. Goubin, C. Mauduit, A. Sárközy, "Construction of large families of pseudorandom binary sequences", Journal of Number Theory, Vol.106, No.1, pp.56-69, 2004.
    K. Gyarmati, "On a family of pseudorandom binary sequences", Periodica Mathematica Hungarica, Vol.49, No.2, pp.45-63, 2004.
    C. Mauduit, J. Rivat, A. Sárközy, "Construction of pseudorandom binary sequences using additive characters", Monatshefte für Mathematik, Vol.141, No.3, pp.197-208, 2004.
    Z. Chen, "Elliptic curve analogue of Legendre sequences", Monatshefte für Mathematik, Vol.154, No.1, pp.1-10, 2008.
    Z. Chen, S. Li, G. Xiao, "Construction of pseudo-random binary sequences from elliptic curves by using discrete logarithm", Proceeding of International Conference on Sequences and Their Applications-SETA'06, LNCS.4086(G. Gong, et al. eds), Berlin, Springer-Verlag, pp.285-294, 2006.
    Z. Chen, G. Xiao, "‘Good' pseudo-random binary sequences from elliptic curves", available at http://eprint.iacr.org/2007/275.pdf, 2007.
    C. Mauduit, A. Sárközy, "On finite pseudorandom sequences of k symbols", Indag. Math. (N.S.), Vol.13, No.1, 89-101, 2002.
    R. Ahlswede, C. Mauduit, A. Sárközy, "Large families of pseudorandom sequences of k symbols and their complexity-Part I", General Theory of Information Transfer and Combinatorics, LNCS.4123(R. Ahlswede et al. eds), Berlin, Springer-Verlag, pp.293-307, 2006.
    R. Ahlswede, C. Mauduit, A. Sárközy, "Large families of pseudorandom sequences of k symbols and their complexity-Part II", General Theory of Information Transfer and Combinatorics, LNCS.4123(R. Ahlswede et al. eds), Berlin, Springer-Verlag, pp.308-325, 2006.
    G. Bérczi, "On finite pseudorandom sequences of k symbols", Periodica Mathematica Hungarica, Vol.47, No.1-2, pp.29-44, 2003.
    A. Enge, "Elliptic curves and their applications to cryptography: An introduction", Kluwer Academic Publishers, Dordrecht, MA, USA, 1999.
    D. Kohel, I. Shparlinski, "On exponential sums and group generators for elliptic curves over finite fields", Proceedings of Algorithmic Number Theory Symposium 2000, LNCS.1838(W. Bosma et al. eds), Berlin, Springer-Verlag, pp.395-404, 2000.
    G. Gong, T. Berson, D. Stinson, "Elliptic curve pseudorandom sequence generator", Proceedings of 6th Annual Workshop on Selected Areas of Cryptography, LNCS.1758(H. Heys et al. eds), Berlin, Springer-Verlag, pp.34-48, 1999.
    G. Gong, C. Lam, "Linear recursive sequences over elliptic curves", Proceedings of Sequences and Their Applications-SETA'01, (T. Helleseth, et al. eds), Berlin, Spring-Verlag, pp.182-196, 2002.
    R. Lidl, H. Niederreiter, Finite Fields, Cambridge Univ. Press, Cambridge, 1997.
    R. Marouk, A. Winterhof, "On the pseudorandomness of binary and quaternary sequences linked by the Gray mapping", Periodica Mathematica Hungarica, Vol.60, No.1, pp.13-23, 2010.
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