SNOW-V is a stream cipher recently designed for the 5G communication systems. This paper proposes two efficient algorithms to evaluate precise correlations of SNOW-V’s two main nonlinear components, fully considering the linear hull effects. Based on these algorithms, we can efficiently find more high-correlation linear approximations than before. The ideas of these algorithms can be generalized to other similar nonlinear components in symmetric cipher. We apply our algorithms to the full SNOW-V stream cipher to search for different types of high-correlation linear approximations. Our results depict more linear approximations with higher correlations than those recently proposed for full SNOW-V and SNOW-\(\text {V}_{\boxplus _{32},\boxplus _8}\). The best linear approximation we found has an absolute correlation \(2^{-47.567}\). There are at least 8, 135 and 1092 linear approximations, whose absolute correlations are greater than \(2^{-47.851}\), \(2^{-49}\) and \(2^{-50}\), respectively. These linear approximations can derive a fast correlation attack with time/memory/data complexities \(2^{240.86}\), \(2^{240.37}\) and \(2^{236.87}\), which is better than previously known fast correlation attacks on full SNOW-V. Moreover, we propose some properties for linear trails with three active S-boxes, which give a theoretical explanation of what the automatic search method lacks of. Our work provides more detailed linear approximation properties for the full SNOW-V.

SNOW-V 是最近为 5G 通信系统设计的流密码。本文提出了两种有效的算法来评估 SNOW-V 的两个主要非线性分量的精确相关性，充分考虑了线性船体效应。基于这些算法，我们可以有效地找到比以前更多的高相关线性近似。这些算法的思想可以推广到对称密码中其他类似的非线性分量。我们将我们的算法应用于完整的 SNOW-V 流密码，以搜索不同类型的高相关线性近似。我们的结果描述了比最近针对完整 SNOW-V 和 SNOW- \(\text {V}_{\boxplus _{32},\boxplus _8}\)提出的具有更高相关性的更多线性近似. 我们发现的最佳线性近似具有绝对相关性\(2^{-47.567}\)。至少有 8、135 和 1092 个线性近似，其绝对相关性大于\(2^{-47.851}\)、\(2^{-49}\)和\(2^{-50}\)， 分别。这些线性近似可以推导出具有时间/内存/数据复杂性\(2^{240.86}\)、\(2^{240.37}\)和\(2^{236.87}\)的快速相关攻击，这比以前已知的对完整 SNOW-V 的快速相关攻击要好。此外，我们提出了具有三个活动 S 盒的线性轨迹的一些属性，这对自动搜索方法缺乏什么给出了理论解释。我们的工作为完整的 SNOW-V 提供了更详细的线性近似属性。