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International Conference on Networks, Communications and Information Technology (CNCIT)

Improved quantum attack on several generalized unbalanced Feistel structures

Kun Zou, Xinfeng Dong, Zhang Fuzhong

Published Jun 1, 2022• 7 citations
Publisher

Abstract

By studying the attack technology based on Simon, Grover and other quantum algorithms for the security of block cipher structure, this paper proposes new quantum attack on 6 generalized unbalanced Feistel structures. We improve the attack results of n-cell structure, New Structure I/III/IV structure and FBC-like structure, and give a quantum attack on Skipjack structure for the first time. Based on Simon algorithm, this paper constructs a n2-round, a 12/12/6-round and a 4-round quantum distinguisher about n-cell structure, New structure I/III/IV and FBC-like structure, improving n2-n-1 rounds, 6 rounds/3 rounds/1 round and 1 round separately, comparing to the previous results. In addition, this paper also constructs a 9-round quantum distinguisher about Skipjack structure. Moreover, this paper proposes a quantum key recovery attack on the above six structures in combination with Grover algorithm, and the time complexities of attacks are analyzed.

DOI
10.1109/cncit56797.2022.00026

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By studying the attack technology based on Simon, Grover and other quantum algorithms for the security of block cipher structure, this paper proposes new quantum attack on 6 generalized unbalanced Feistel structures. We improve the attack results of n-cell structure, New Structure I/III/IV structure and FBC-like structure, and give a quantum attack on Skipjack structure for the first time. Based on Simon algorithm, this paper constructs a n2-round, a 12/12/6-round and a 4-round quantum distinguisher about n-cell structure, New structure I/III/IV and FBC-like structure, improving n2-n-1 rounds, 6 rounds/3 rounds/1 round and 1 round separately, comparing to the previous results. In addition, this paper also constructs a 9-round quantum distinguisher about Skipjack structure. Moreover, this paper proposes a quantum key recovery attack on the above six structures in combination with Grover algorithm, and the time complexities of attacks are analyzed.
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)r(r>12)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/22^{n/2}2n/2, where nnn denotes the subkey length. Second, we design a 9-round quantum distinguisher for LBlock and extend it to an r(r>15)r(r>15)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 2162^{16}216 reduction in the time complexity of our rrr-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)O(2^{38})O(238) to O(226)O(2^{26})O(226) by a factor of 2122^{12}212.
Abstract Symmetric cryptography is expected to be quantum safe when long‐term security is needed. Kuwakado and Morii gave a 3‐round quantum distinguisher of the Feistel cipher based on Simon's algorithm. However, the quantum distinguisher without considering the specific structure of the round function is not accurate enough. A new quantum cryptanalysis method for Feistel structure is studied here. It can make full use of the specific structure of the round function. The properties of Camellia round function and its linear transformation P are taken into account, and a 5‐round quantum distinguisher is proposed. Then, the authors follow a key‐recovery attack framework by Leander and May, that is, Grover‐meet‐Simon algorithm, and give a quantum key‐recovery attack on 7‐round Camellia in Q2 model with the time complexity of 2 24 . It is the very first time that the specific structure of the round function is used to improve quantum attack on Camellia.
The Feistel structure represents a fundamental architectural component within the domain of symmetric cryptographic algorithms, with a substantial body of research conducted within the context of classical computing environments. Nevertheless, research into specific symmetric cryptographic algorithms utilizing the Feistel structure is relatively scarce in quantum computing environments. This paper, for the first time, proposes a five-round distinguisher for Camellia under the quantum chosen-ciphertext attack (qCCA) setting, with its effectiveness empirically validated. Additionally, by combining Grover’s algorithm and Simon’s algorithm, we construct a nine-round key-recovery attack model against Camellia. Through an in-depth analysis of Camellia’s key expansion algorithm, we significantly reduce the complexity of the key-recovery attack. The proposed attack achieves a time complexity of 261.5 for recovering the correct key bits and requires 531 quantum bits.
Abstract Quantum attacks employing superposition queries (Q2 model) have been demonstrated to compromise numerous classically secure block-cipher constructions. These attacks embed the target encryption structure into a period-finding problem, which dedicated quantum algorithms, including the Simon and BV algorithms, can solve. After restoring the secret state, attackers can launch an attack by recovering the key (the secret state contains key information) or distinguishing it from random permutations. In this paper, we investigate the quantum security of Feistel-like ciphers in a related-key setting. For several constructions, we demonstrate how to define a periodic function that can be evaluated using the Simon algorithm with only O(n)O(n)O(n) O ( n ) quantum queries to the encryption oracle, where n represents the block size. This enables secret-state recovery attacks on Type-1/2 generalized Feistel schemes, as well as key-recovery attacks on the Feistel-FK and Misty L-KF constructions. All these attacks achieve an exponential reduction in query complexity compared to the best known classical or quantum methods.
The development of post-quantum cryptography requires cryptographic primitives that remain secure against quantum adversaries. Quantum key-recovery attacks constitute a fundamental class of quantum cryptanalytic techniques, and the resistance of a cryptosystem to such attacks serves as an important indicator of its overall security. Since the Feistel structure is a core component in the design of many block ciphers, efficient quantum key-recovery attacks on Feistel ciphers provide valuable insights into evaluating and strengthening their security. In this paper, we propose an efficient generic quantum key-recovery attack on Feistel ciphers. Our attack integrates universal hash families with Simon's and Grover's algorithms to perform key-recovery. We rigorously analyze the correctness of the proposed attack and derive its time and quantum resource complexities. A comprehensive comparison with existing keyrecovery attacks shows that the proposed approach improves both quantum resource usage and dominant query complexity, and therefore yields a more efficient quantum key-recovery attack. Our work enhances the understanding of Feistel ciphers under quantum threats and informs the design of robust cryptosystems for the post-quantum era.
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.