Abstract
The Feistel-2 (a.k.a, Feistel-KF) structure is a variant of the Feistel structure such that the i-th round function is given by \(\mathsf {F}_i(k_i \oplus x)\), where \(\mathsf {F}_i\) is a public random function and its input/output length is n/2 bits. Isobe and Shibutani showed a meet-in-the-middle attack in the classical setting with \((D,T)=(O(1),O(2^{n/2}))\) on the 3-round Feistel-2 structure where D and T are the numbers of online/offline queries, respectively. In their attack, since two round keys are recovered simultaneously, a naive application of Grover’s algorithm for two keys needs \(T = O(2^{n/2})\) in the quantum setting. In this paper, we introduce a new known plaintext attack and chosen plaintext attack on the 3-round Feistel-2 structure in the quantum setting using Grover’s algorithm by recovering the round key one by one in \((D,T)=(O(1),O(2^{n/4}))\). Our attack does not need any quantum query to the encryption oracle (i.e., working in the Q1 model).
T. Daiza—Presently, he is with Toppan Inc.
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Notes
- 1.
For example, how to efficiently dissect the MPMCT gate to atomic gates is shown in [21].
References
Luby, M., Rackoff, C.: How to construct pseudorandom permutations from pseudorandom functions. SIAM J. Comput. 17(2), 373–386 (1988)
Even, S., Mansour, Y.: A construction of a cipher from a single pseudorandom permutation. In: ASIACRYPT, pp 210–224 (1991)
Lampe, R., Seurin, Y.: Security analysis of key-alternating Feistel Ciphers. In: FSE, pp. 243–264 (2014)
Isobe, T., Shibutani, K.: All subkeys recovery attack on block ciphers: extending meet-in-the-middle approach. In: Knudsen, L.R., Wu, H. (eds.) SAC 2012. LNCS, vol. 7707, pp. 202–221. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-35999-6_14
Isobe, T., Shibutani, K.: Generic key recovery attack on Feistel scheme. In: ASIACRYPT, vol. 1, pp. 464–485 (2013)
Demirci, H., Aydin Selçuk, A.: A meet-in-the-middle attack on 8-round AES. In: FSE, pp.116–126 (2008)
Guo, J., Jean, J., Nikolic, I., Sasaki, Y.: Meet-in-the-middle attacks on generic Feistel constructions. In: ASIACRYPT, pp. 458–477 (2014)
Dinur, I., Dunkelman, O., Keller, N., Shamir, A.: New attacks on Feistel structures with improved memory complexities. In: CRYPTO, vol. 1, pp. 433–454 (2014)
Dinur, I., Dunkelman, O., Keller, N., Shamir, A.: Efficient dissection of Bicomposite problems with cryptanalytic applications. J. Cryptol. 32(4), 1448–1490 (2018). https://doi.org/10.1007/s00145-018-9303-2
Daiza, T., Kurosawa, K.: Optimum attack on 3-round feistel-2 structure. In: IWSEC, pp. 175–192 (2021)
Grover, L.K.: A fast quantum mechanical algorithm for database search. In: STOC, pp. 212–219 (1996)
Brassard, G., Høyer, P., Tapp, A.: Quantum cryptanalysis of hash and claw-free functions. In: LATIN, pp. 163–169 (1998)
Hosoyamada, A., Sasaki, Yu.: Quantum demiric-Selçuk meet-in-the-middle attacks: applications to 6-round generic Feistel constructions. In: SCN, pp. 12–14 (2014)
Bonnetain, X., Naya-Plasencia, M., Schrottenloher, A.: On quantum slide attacks. In: SAC, pp. 492–519 (2019)
Bonnetain, X., Hosoyamada, A., Naya-Plasencia, M., Sasaki, YU., Schrottenloher, A.: Quantum attacks without superposition queries: the offline Simon’s algorithm. In: ASIACRYPT, pp. 552–583 (2019)
Simon, D.R.: On the power of quantum computation. SIAM J. Comput. 26(5), 1474–1483 (1997)
Kuwakado, H., Morii, M.: Quantum distinguisher between the 3-round Feistel cipher and the random permutation. In: ISIT, pp. 2682–2685 (2019)
Kaplan, M., Leurent, G., Leverrier, A., Naya-Plasencia, M.: Breaking symmetric cryptosystems using quantum period finding. In: CRYPTO, vol. 2, pp. 207–237 (2016)
Leander, G., May, A.: Grover meets Simon - Quantumly attacking the FX-construction. In: ASIACRYPT, vol. 2, pp. 161–178 (2017)
Cid, C., Hosoyamada, A., Liu, Y., Sim, S.M.: Quantum cryptanalysis on contracting Feistel structures and observation on related-key settings. In: INDOCRYPT, pp. 373–394 (2020)
Sasanian, Z., Miller, D.M.: Reversible and quantum circuit optimization: a functional approach. In: RC, pp. 112–124 (2012)
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Daiza, T., Yoneyama, K. (2022). Quantum Key Recovery Attacks on 3-Round Feistel-2 Structure Without Quantum Encryption Oracles. In: Cheng, CM., Akiyama, M. (eds) Advances in Information and Computer Security. IWSEC 2022. Lecture Notes in Computer Science, vol 13504. Springer, Cham. https://doi.org/10.1007/978-3-031-15255-9_7
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