一类周期为2 p的四元分圆序列的4-Adic复杂度
The 4-Adic Complexity of A Class of Quaternary Cyclotomic Sequences with Period 2p
摘要：
在密码学中，希望周期为$N$的$\mathbb{Z}_m$上的序列具有较大的$m$ -adic复杂度.与二元情况相比，已知四元序列的4-adic复杂度的计算还没有得到很好的发展。本文确定了[6]中定义的周期为2的四元分圆序列$p$的4-adic复杂度。我们使用的主要方法是二次高斯和$G_{p}$值在$\mathbb{Z}_{4^N-1}$，它可以被看作是一个版本的经典二次高斯和。我们的结果表明，这类四元分圆序列的4-adic复杂度在$5\nmid p-2$时达到最大值，否则接近最大值。
英文摘要：
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.
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