大族长度为pq的伪随机k元序列

刘华宁, 高波

数学学报 ›› 2017, Vol. 60 ›› Issue (3) : 401-414.

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数学学报 ›› 2017, Vol. 60 ›› Issue (3) : 401-414. DOI: 10.12386/A2017sxxb0033
论文

大族长度为pq的伪随机k元序列

    刘华宁, 高波
作者信息 +

Large Family of Pseudorandom Sequence of k Symbols with Length pq

    Hua Ning, LIU Bo GAO
Author information +
文章历史 +

摘要

Mauduit 与 Sárközy 在一系列论文中研究了k元序列的伪随机性. 本文通过对模 pq 剩余类环 Zpq进行分割,进而结合离散对数的方法,构造了一大族长度为 pq 的伪随机k元序列,并证明其具有很好的伪随机性.

Abstract

In a series of papers Mauduit and Sárközy introduced and studied the measures of finite sequences of k symbols. In this paper we construct large family of pseudorandom sequences of k symbols with length pq using the residue class ring modulo pq and the methods of discrete logarithm, and study the pseudorandom properties.

关键词

伪随机 k元序列 / 离散对数 / 指数和 / 特征和

Key words

pseudorandom sequence ofksymbol / discrete logarithm / exponential sum / character sum

引用本文

导出引用
刘华宁, 高波. 大族长度为pq的伪随机k元序列. 数学学报, 2017, 60(3): 401-414 https://doi.org/10.12386/A2017sxxb0033
Hua Ning, LIU Bo GAO. Large Family of Pseudorandom Sequence of k Symbols with Length pq. Acta Mathematica Sinica, Chinese Series, 2017, 60(3): 401-414 https://doi.org/10.12386/A2017sxxb0033

参考文献

[1] Ahlswede R., Mauduit C., Sárközy A., Large Families of Pseudorandom Sequences ofkSymbols and Their Complexity-Part I, General Theory of Information Transfer and Combinatorics, LNCS 4123, Springer-Verlag, Berlin, 2006:293-307.
[2] Ahlswede R., Mauduit C., Sárközy A., Large Families of Pseudorandom Sequences ofkSymbols and Their Complexity-Part II, General Theory of Information Transfer and Combinatorics, LNCS 4123, SpringerVerlag, Berlin, 2006:308-325.
[3] Chen Z., Du X., Wu C., Pseudorandomness of certain sequences ofksymbols with length pq, J. Comput. Sci. Tech., 2011, 26(2):276-282.
[4] Dartyge C., Sárközy A., Large families of pseudorandom subsets formed by power residues, Unif. Distrib. Theory, 2007, 2(2):73-88.
[5] Gomez D., Winterhof A., Multiplicative character sums of Fermat quotients and pseudorandom sequences, Period. Math. Hung., 2012, 64(2):161-168.
[6] Mak K., More constructions of pseudorandom sequences ofksymbols, Finite Fields Appl., 2014, 25(1):222-233.
[7] Mauduit C., Sárközy A., On finite pseudorandom binary sequences I:measure of pseudorandomness, the Legendre symbol, Acta Arith., 1997, 82(82):365-377.
[8] Mauduit C., Sárközy A., On finite pseudorandom sequences ofksymbols, Indag. Math., 2002, 13(1):89-101.
[9] Menezes A. J., van Oorschot P. C., Vanstone S. A., Handbook of Applied Cryptography, CRC Press, Boca Raton, 1996.
[10] Tóth V., Extension of the notion of collision and avalanche effect to sequences ofksymbols, Period. Math. Hung., 2012, 65(2):229-238.

基金

国家自然科学基金资助项目(11571277);陕西省自然科学基金资助项目(2014JM1007);陕西省青年科技新星资助项目(2014KJXX-61)及省工业科技攻关项目(2016GY-080,2016GY-077)

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