论文标题
与周期2p的一类Quaternary循环序列的4-辅助复杂性
The 4-Adic Complexity of A Class of Quaternary Cyclotomic Sequences with Period 2p
论文作者
论文摘要
在密码学中，我们希望$ \ mathbb {z} _m $具有较大$ m $ - adic复杂性的序列。与二进制案例相比，了解第四纪序列的4-辅助复杂性的计算尚未得到很好的发展。在本文中，我们确定了[6]中定义的2 $ p $的第四纪环流序列的4个辅助复杂性。我们利用的主要方法是二次高斯总和$ g_ {p} $，价值在$ \ mathbb {z} _ {4^n-1} $中，它可以看作是经典的二次高斯总和。我们的结果表明，如果$ 5 \ nmid p-2 $，则这类四级环体序列的4-辅助复杂性达到最大值，否则接近最大值。
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.
