Breaking symmetric cryptosystems using the offline distributed Grover-meets-Simon algorithm

The model of superposition queries in symmetric cryptanalysis has yielded remarkable results, such as Simon's period-finding algorithm, which can break many constructions in polynomial time. However, due to limitations of current physical devices, quantum circuits with long depths are often noisy and difficult to realize in practice. The novel computing architecture of distributed quantum computing is expected to reduce the noise and depth of quantum circuits. In this paper, we propose an offline algorithm model that combines distributed Simon's and Grover's algorithms. This model enables us to perform key recovery attacks on different rounds Feistel structures, Even Mansour construction, and the FX construction, while minimizing the quantum query complexity. Despite being limited to classical queries and offline quantum computations, we leverage the algebraic structure of cryptosystems to achieve successful key recovery attacks.