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The 4-Adic Complexity of A Class of Quaternary Cyclotomic Sequences with Period 2p
arXiv - CS - Information Theory Pub Date : 2020-11-24 , DOI: arxiv-2011.11875
Shiyuan Qiang, Yan Li, Minghui Yang, Keqin Feng

In cryptography, we hope a sequence over $\mathbb{Z}_m$ with period $N$ having larger $m$-adic complexity. Compared with the binary case, the computation of 4-adic complexity of knowing quaternary sequences has not been well developed. In this paper, we determine the 4-adic complexity of the quaternary cyclotomic sequences with period 2$p$ defined in [6]. The main method we utilized is a quadratic Gauss sum $G_{p}$ valued in $\mathbb{Z}_{4^N-1}$ which can be seen as a version of classical quadratic Gauss sum. Our results show that the 4-adic complexity of this class of quaternary cyclotomic sequences reaches the maximum if $5\nmid p-2$ and close to the maximum otherwise.

中文翻译:

一类周期为2p的四级环原子序列的4-Adic复杂度

在密码学中,我们希望$ \ mathbb {Z} _m $上的序列的期间$ N $具有更大的$ m $ -adic复杂度。与二元情况相比,已知四元序列的4-adic复杂度的计算尚未得到很好的发展。在本文中,我们确定在[6]中定义的周期为2 $ p $的四级环原子序列的4-adic复杂度。我们使用的主要方法是以$ \ mathbb {Z} _ {4 ^ N-1} $表示的二次高斯和$ G_ {p} $,可以看作是经典二次高斯和的一种形式。我们的结果表明,如果$ 5 \ nmid p-2 $,此类四级环原子序列的4-adic复杂度达到最大值,否则接近最大值。
更新日期:2020-11-25
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