https://doi.org/10.1140/epjqt/s40507-026-00481-3
Research
Quantum related-key attacks on Feistel-like ciphers
1
School of Computer and Big Data (School of Cybersecurity), Heilongjiang University, 150080, Harbin, China
2
School of Mathematical Science, Heilongjiang University, 150080, Harbin, China
3
School of Computer Science (National Pilot Software Engineering School), Beijing University of Posts and Telecommunications, 100876, Beijing, China
4
State Key Laboratory of Cryptology, 100878, Beijing, China
a
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b
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c
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Received:
8
September
2025
Accepted:
11
February
2026
Published online:
17
February
2026
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 
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.
Key words: Block cipher / Related-key attack / Quantum cryptanalysis / Simon algorithm / Circuit implementation
© The Author(s) 2026
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