Quantum Automated Tools for Finding Impossible Differentials

Abstract

Due to the superiority of quantum computing, traditional cryptography is facing a severe threat. This makes the security evaluation of cryptographic systems in quantum attack models both significant and urgent. For symmetric ciphers, the security analysis heavily relies on cryptanalysis tools. Thus, exploring the use of quantum algorithms in traditional cryptanalysis tools has garnered considerable attention. In this study, we utilize quantum algorithms to improve impossible differential attacks and design two quantum automated tools to search for impossible differentials. The proposed quantum algorithms exploit the idea of miss-in-the-middle and the properties of truncated differentials. We rigorously prove their validity and calculate the quantum resources required for their implementation. Compared to the existing classical automated cryptanalysis, the proposed quantum tools have the advantage of accurately characterizing S-boxes while only requiring polynomial complexity, and can take into consideration the impact of the key schedules in a single-key model.