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

• Published in: Security and Cryptography for Networks Vol. 11035; pp. 386 - 403
• Main Authors: Hosoyamada, Akinori, Sasaki, Yu
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2018; Springer International Publishing
• Series: Lecture Notes in Computer Science
• Subjects: Claw finding algorithm; Demiric-Selçuk meet-in-the-middle attack; Feistel construction; Grover’s algorithm; Post-quantum cryptography; Q1 model
• ISBN: 9783319981123; 3319981129
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-319-98113-0_21

This paper shows that quantum computers can significantly speed-up a type of meet-in-the-middle attacks initiated by Demiric and Selçuk (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(23n/4)$$O(2^{3n/4})$$. 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 O~(2n/2)$$\tilde{O}(2^{n/2})$$, 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.