Quantum Attacks on Lai-Massey Structure

Generalized Feistel schemes (GFSs) are extremely important and extensively researched cryptographic schemes. In this paper, the security of Type‐1 GFS in quantum circumstances is investigated. On the one hand, in the qCCA setting, a new quantum polynomial‐time distinguisher on ‐round Type‐1 GFS with branches is given, which extends the previous results by rounds. This leads to a more efficient analysis of type‐1 GFS, that is, the complexity of some previous key‐recovery attacks is reduced by a factor of , where k is the key length of the internal round function. On the other hand, for CAST‐256, which is a certain block cipher based on Type‐1 GFS, a 17‐round quantum distinguisher in the qCPA setting is given. Based on this, an ‐round quantum key‐recovery attack with complexity is constructed.

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“…Definition 2 [35,45] . (PRP-qCCA) Let E k : K × X → X be a family of permutations indexed by the elements in K, g : X → X.…”

Section: Pseudo-random Permutationmentioning

confidence: 99%

Quantum Attacks on Type‐1 Generalized Feistel Schemes

et al. 2023

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“…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]. The Bernstein-Vazirani algorithm can be used to find the linear structures of a Boolean function, which enables quantum attacks against block ciphers.…”

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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