Applications of Simon’s algorithm in quantum attacks on Feistel variants

Cui, Jingyi; Guo, Jin‐Liang; Ding, Shuzhen

doi:10.1007/s11128-021-03027-x

Cited by 12 publications

(6 citation statements)

References 34 publications

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“…On the one hand, Simon's algorithm can also assist classical cryptanalysis techniques, such as linear cryptanalysis [6,7], slide attacks [8], just as Grover's algorithm is used to quantize classical cryptanalysis techniques, such as differential attacks [9], linear attacks [7,9,10], Demirci and Selçuk meet-in-the-middle attacks [11], integral attacks [12]. On the other hand, with the distinguishing property of periodicity of functions, some quantum attacks [13][14][15][16][17][18] based on Simon's algorithm are proposed. In 2012, Kuwakado and Morii proposed a key-recovery attack on the Even-Mansour cipher [19].…”

Section: Introductionmentioning

confidence: 99%

Quantum Cryptanalysis on Feistel Variants in Related-Key Settings

Wang,

Chen,

Xiang

et al. 2024

Preprint

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Simon’s algorithm is a well-known quantum algorithm that can achieve exponential acceleration. This paper studies the applications of Simon’s algorithm in analyzing the security of Feistel variants, several well-known cryptographic structures derived from the Feistel structure. Specifically, we study quantum related-key attacks on Feistel variants in the setting that adversaries can only control part of the key difference in quantum superposition. We delve into observing the quantum related-key attacks on the balanced Feistel structure given by Cid \textit{et al.} and slightly improve the existing method to design periodic functions, ultimately providing a new approach to building periodic functions in single-key settings. Based on these results, we propose a general technique to construct quantum related-key distinguishers exploiting the quantum single-key distinguishers construction technique. As applications of our proposed technique, we demonstrate how to construct new polynomial-time quantum related-key chosen-plaintext distinguishers on several Feistel variants: Feistel-KF, SM4-like, MARS-like, Type-1/2/3 generalized Feistel-KF structures.

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Section: Introductionmentioning

confidence: 99%

Quantum Cryptanalysis on Feistel Variants in Related-Key Settings

Wang,

Chen,

Xiang

et al. 2024

Preprint

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“…For example, in 2021, Bathe et al presented key-recovery attacks against ChaCha by Grover's search algorithm [10]. Simon's algorithm is a period finding algorithm in polynomial time and has been widely used in cryptanalysis of symmetric ciphers [6,[11][12][13][14][15][16][17][18][19][20][21][22][23]. For example, Kuwakado and Morii used Simon's algorithm to distinguish a three-round Feistel structure with a random permutation in 2010 [19], and then recovered the key of the Even-Mansour cipher in 2012 [24].…”

Section: Introductionmentioning

confidence: 99%

“…In 2020, Dong et al presented quantum analyses on Feistel structure and generalized Feistel structure based on Simon's algorithm [14,25]. In 2021, Cui et al used Simon's algorithm to launch quantum attacks on Feistel variant schemes [13]. In 2022, Mao et al used Simon's algorithm to launch quantum attacks on Lai-Massey structure [26].…”

Section: Introductionmentioning

confidence: 99%

Quantum Related-Key Attack Based on Simon’s Algorithm and Its Applications

Zhang

2023

Symmetry

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With the development of quantum technology, quantum computing has an increasingly significant impact on cryptanalysis. Several quantum algorithms, such as Simon’s algorithm, Grover’s algorithm, the Bernstein–Vazirani algorithm, Shor’s algorithm, and the Grover-meets-Simon algorithm, have been proposed successively. However, almost all cryptanalysis is based on the quantum chosen-plaintext attack (qCPA) model. This paper focuses on a powerful cryptanalytic model, quantum related-key attack (qRKA), and proposes a strategy of qRKAs against symmetric ciphers using Simon’s algorithm. We construct a periodic function to efficiently recover the secret key of symmetric ciphers if the attacked symmetric ciphers satisfy Simon’s promise, and present the complexity analysis on specific symmetric ciphers. Then, we apply qRKA to the Even–Mansour cipher and SoEM construction, recover their secret keys, and show their complexity comparison in the distinct attack models. This work is of great significance for the qRKA cryptanalysis of existing provably secure cryptographic schemes and the design of future quantum secure cryptographic schemes.

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“…These include attacks on Types I and II GFS [4], Even-Mansour scheme, authentication codes [5], FX-constructions [6], five-round Feistel scheme [7], 2/4K-Feistel scheme, 2/4K-DES [8]. Moreover, cryptographic primitives such as MISTY L/R, CAST-256, CLEFIA, MARS, SMS4, and Skipjack-A/B have also been subjected to quantum cryptanalysis [9].…”

Section: Introductionmentioning

confidence: 99%

Quantum Distinguishing Attacks on Generalized Feistel Schemes

Fesenko,

Zvychaina

2023

TACS

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It turned out that in addition to problems with classical asymmetric cryptography in the post-quantum period, there are certain doubts about the strength of symmetric cryptographic schemes. This paper demonstrates that on Type III Generalized Feistel Scheme (GFS), by selectively fixing specific parts of the plaintext at the input to the GFS, it is possible to reduce the problem of distinguishing between random text and encrypted output of the same GFS to the Simon problem through different approaches.Our method enables the cracking of the cipher up to 𝑑 rounds in polynomial time, while a more sophisticated approach based on different formulas from other paths of the cipher can crack 𝑑 + 1 rounds with the same time complexity in quantum adversary model. These distinct approaches yield varying results in terms of scheme security, indicating the potential to break more rounds in the GFS using the same methodology.

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Applications of Simon’s algorithm in quantum attacks on Feistel variants

Cited by 12 publications

References 34 publications

Quantum Cryptanalysis on Feistel Variants in Related-Key Settings

Quantum Cryptanalysis on Feistel Variants in Related-Key Settings

Quantum Related-Key Attack Based on Simon’s Algorithm and Its Applications

Quantum Distinguishing Attacks on Generalized Feistel Schemes

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