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International Conference on Security and Cryptography for Networks

SCN 2018: Security and Cryptography for Networks pp 386–403Cite as

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

Part of the Lecture Notes in Computer Science book series (LNSC,volume 11035)

Abstract

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 \(O(2^{3n/4})\). 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.

Keywords

  • Post-quantum cryptography
  • Demiric-Selçuk meet-in-the-middle attack
  • Feistel construction
  • Grover’s algorithm
  • Claw finding algorithm
  • Q1 model

Due to space limitations, some details and proofs are left to the full paper [HS17].

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Fig. 1.

Notes

  1. 1.

    Dong and Wang [DW17] independently pointed out the combination of the 3-round distinguisher [KM10] and key recovery attack [LM17].

  2. 2.

    Since any Q1 attack can be trivially converted to a Q2 attack by regarding quantum oracles as classical oracles, we can construct a Q2 attack with \(\max (T, D, M, N)\,=\,N^{1/2} \ll N^{3/4}\) from the best Q1 attack. However, such a Q2 attack requires time \(T=N\) in the case that only \(O(\log N)\) qubits are available.

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Authors and Affiliations

  1. NTT Secure Platform Laboratories, 3-9-11, Midori-cho Musashino-shi, Tokyo, 180-8585, Japan

    Akinori Hosoyamada & Yu Sasaki

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  1. Akinori Hosoyamada
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  2. Yu Sasaki
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Correspondence to Akinori Hosoyamada .

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Editors and Affiliations

  1. University of Catania, Catania, Italy

    Dario Catalano

  2. University of Salerno, Fisciano, Italy

    Roberto De Prisco

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Hosoyamada, A., Sasaki, Y. (2018). Quantum Demiric-Selçuk Meet-in-the-Middle Attacks: Applications to 6-Round Generic Feistel Constructions. In: Catalano, D., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2018. Lecture Notes in Computer Science(), vol 11035. Springer, Cham. https://doi.org/10.1007/978-3-319-98113-0_21

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