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.
Abstract 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.
This paper investigates generalizations of the Lai-Massey scheme, including unified constructionscombining it with the Feistel scheme (MD GLM, UFLM, L-Feistel, and quasi-Feistel). New reductionsto the quasi-Feistel scheme are provided. Known efficient quantum attacks are analyzed, includingchosen-plaintext attacks on 3 rounds and chosen-ciphertext attacks on 4 rounds for a special case of thequasi-Feistel cipher using Simon’s algorithm. It is demonstrated that restrictions in that work led to thedegeneration of the quasi-Feistel scheme into the standard Feistel scheme, replicating known quantumattacks on the Feistel scheme. New two-round distinguishing attacks are presented for the L-Feistel andMD-1 GLM schemes, enabling round key recovery.
Feistel schemes are important components of symmetric ciphers, which have been extensively studied in the classical setting. We examine the extension methods of differential distinguishers of Feistel key-function and Feistel function-key schemes. The schemes are subjected to quantum differential collision distinguishing attacks based on the methods. The results show that the complexity is lower than that of differential attacks using only Grover algorithm, and the complexity of differential collision attack based on the Brassard-Høyer-Tapp and Grover algorithms is lower than that of quantization when using only the Grover algorithm. The results also show that different algorithms and methods can be combined to produce a more effective cryptanalysis approach. This provides a research direction for post-quantum cryptographic analysis and design.
With the rapid advancement of quantum computing, the security of traditional cryptographic systems is facing significant challenges. As a fundamental component of symmetric cryptography, block ciphers have attracted increasing attention regarding their quantum security in recent years.
In this paper, we propose new quantum attacks on two Feistel-type constructions, i.e., New Structure IV and the lightweight block cipher LBlock, under the quantum chosen-plaintext attack (qCPA) model. First, we construct an 8-round quantum distinguisher for New Structure IV and perform an
r(r>12)-round quantum key-recovery attack. Compared with Li et al.'s qCPA-based result presented at INSCRYPT 2024, our attack reduces the time complexity by a factor of
2n/2, where
n denotes the subkey length. Second, we design a 9-round quantum distinguisher for LBlock and extend it to an
r(r>15)-round quantum key-recovery attack. The proposed quantum distinguisher covers one more round than Liu et al.'s automated-search distinguisher at ASIACRYPT 2025, which results in a
216 reduction in the time complexity of our
r-round quantum key-recovery attack on LBlock. Furthermore, by analyzing the structure of the round function and the key scheduling of LBlock, we reduce the subkey guess space for the 15-round attack from 76 bits to 52 bits, lowering the time complexity from
O(238) to
O(226) by a factor of
212.
With the application of quantum algorithms in cryptanalysis keeping increasing. Currently, there are many works based on Simon’s algorithm for generalized Feistel scheme (GFS), mostly using manual derivation to construct periodic functions. We present the functional form of the output component’s algebraic expression. Then we propose the transformation rules of functional form of algebraic expression through round function. Afterwards, we present an algorithm to find GFS’s longest round distinguishers based on Simon’s algorithm. Based on this, we get quantum distinguishers of Type-1 GFS, Type-2 GFS and Type-3 GFS under quantum chosen plaintext attack (qCPA) setting and quantum chosen ciphertext attack (qCCA) setting. For Type-1 GFS, the longest round quantum distinguisher based on Simon’s algorithm is unique under qCPA/qCCA setting, which is [Formula: see text]-round/[Formula: see text]-round. For [Formula: see text]-branch Type-2 GFS, [Formula: see text] kinds of [Formula: see text]-round distinguishers have been found under qCPA/qCCA setting. For Type-3 GFS, the longest round distinguisher based on Simon’s algorithm is unique under qCPA/qCCA setting, which is [Formula: see text]-round/3-round.