Quantum Demiric-Selçuk Meet-in-the-Middle Attacks: Applications to 6-Round Generic Feistel Constructions

This paper shows that quantum computers can significantly speed-up a type of meet-in-the-middle attacks initiated by Demiric and Selcuk (DS-MITM attacks), which is currently one of the most powerful cryptanalytic approaches in the classical setting against symmetric-key schemes. The quantum DS-MITM attacks are demonstrated against 6 rounds of the generic Feistel construction supporting an n-bit key and an n-bit block, which was attacked by Guo et al. in the classical setting with data, time, and memory complexities of \(O(2^{3n/4})\). The complexities of our quantum attacks depend on the adversary’s model. When the adversary has an access to quantum computers for offline computations but online queries are made in a classical manner, the attack complexities become \(\tilde{O}(2^{n/2})\), which significantly improves the classical attack. The attack is then extended to the case that the adversary can make superposition queries. The attack is based on 3-round distinguishers with Simon’s algorithm and then appends 3 rounds for key recovery. This can be solved by applying the combination of Simon’s and Grover’s algorithms recently proposed by Leander and May.