The rectangle attack has shown to be a very powerful form of cryptanalysis against block ciphers. Given a rectangle distinguisher, one expects to mount key recovery attacks as efficiently as possible. In the literature, there have been four algorithms for rectangle key recovery attacks. However, their performance varies from case to case. Besides, numerous are the applications where the attacks lack optimality. In this paper, we delve into the rectangle key recovery and propose a unified and generic key recovery algorithm, which supports any possible attacking parameters. Not only does it encompass the four existing rectangle key recovery algorithms, but it also reveals five new types of attacks that were previously overlooked. Further, we put forward a counterpart for boomerang key recovery attacks, which supports any possible attacking parameters as well. Along with these new key recovery algorithms, we propose a framework to automatically determine the best parameters for the attack. To demonstrate the efficiency of the new key recovery algorithms, we apply them to Serpent, AES-192, CRAFT, SKINNY, and Deoxys-BC-256 based on existing distinguishers, yielding a series of improved attacks.

矩形攻击已被证明是针对分组密码的一种非常强大的密码分析形式。给定一个矩形区分符，人们期望尽可能有效地发起密钥恢复攻击。在文献中，存在四种用于矩形密钥恢复攻击的算法。然而，它们的性能因情况而异。此外，许多应用程序的攻击缺乏优化性。在本文中，我们深入研究了矩形密钥恢复，并提出了一种统一且通用的密钥恢复算法，该算法支持任何可能的攻击参数。它不仅涵盖了四种现有的矩形密钥恢复算法，而且还揭示了以前被忽视的五种新型攻击。此外，我们提出了回旋镖密钥恢复攻击的对应方案，它也支持任何可能的攻击参数。除了这些新的密钥恢复算法之外，我们还提出了一个框架来自动确定攻击的最佳参数。为了证明新密钥恢复算法的效率，我们基于现有区分器将其应用于Serpent、AES -192、CRAFT、SKINNY和Deoxys-BC -256 ，产生了一系列改进的攻击。