A Quantum Automatic Tool for Finding Impossible Differentials

TL;DR

This paper introduces quantum algorithms and automatic tools that enhance the search for impossible differentials in cryptanalysis, leveraging quantum computing to improve efficiency and accuracy over classical methods.

Contribution

It presents novel quantum algorithms and tools for impossible differential cryptanalysis, exploiting quantum properties to achieve polynomial complexity and consider key schedule impacts.

Findings

Quantum tools accurately characterize S-boxes.

Polynomial complexity of the quantum algorithms.

Effective consideration of key schedules in analysis.

Abstract

Due to the superiority of quantum computing, traditional cryptography is facing severe threat. This makes the security evaluation of cryptographic systems in quantum attack models significant and urgent. For symmetric ciphers, the security analysis heavily relies on cyptanalytic tools. Thus exploring the use of quantum algorithms to traditional cyptanalytic tools has drawn a lot of attention. In this study, we utilize quantum algorithms to improve impossible differential attack, and design two quantum automatic tools for searching 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 to implement them. Compared to existing classical automatic cryptanalysis, the quantum tools proposed 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 single-key model.