Quantum cryptanalysis on Feistel variants in related-key settings

Simon’s algorithm is a well-known quantum algorithm that can achieve exponential acceleration. This paper studies the applications of Simon’s algorithmin analyzing the security of Feistel variants, namely, several well-known cryptographic structures derived from the Feistel structure. Specifically, we study quantum related-key attacks on Feistel variants in the setting that adversaries can only control part of the key difference in quantum superposition. We delve into observing the quantum related-key attacks on the balanced Feistel structure given by Cid et al. and slightly improve the existing method to design periodic functions, ultimately providing a new approach to building periodic functions in single-key settings. Based on these results, we propose a general technique to construct quantum related-key distinguishers exploiting the quantum single-key distinguishers construction technique. As applications of our proposed technique, we demonstrate how to construct new polynomial-time quantum related-key chosen-plaintext distinguishers on several Feistel variants: Feistel-KF, SM4-like, MARS-like, and Type-1/2/3 generalized Feistel-KF structures.