In this paper, we present a generic framework for decomposing block cipher structure with secret components. The generic framework is based on the zero-correlation linear cryptanalysis and exploits clusters of zero-correlation linear hulls to establish a system of equations to recover the secret components. In order to solve such a system, we convert the operations into the field of real numbers. By utilizing the coordinate partition technique, both the time and data complexity will be mitigated to make the framework more competitive. We apply the framework to the Feistel structure with SP-type round functions and both the attack rounds and complexity perform better than previous results. Finally, we apply the proposed framework to the Type-1 Feistel structure to demonstrate its generality and improve the previous results against such structure. Our work provides further insights into the security of block cipher structure with secret components.

在本文中，我们提出了一种用于分解具有秘密组件的分组密码结构的通用框架。通用框架基于零相关线性密码分析，并利用零相关线性船体的簇建立方程组以恢复秘密分量。为了解决这样的系统，我们将运算转换为实数字段。通过使用坐标分区技术，可以减少时间和数据复杂度，从而使框架更具竞争力。我们将该框架应用于具有SP类型回合功能的Feistel结构，并且攻击回合和复杂性均比以前的结果更好。最后，我们将提出的框架应用于Type-1 Feistel结构，以证明其通用性并针对该结构改进先前的结果。