CryptoDB
Quantum Periodic Distinguisher Construction: Symbolization Method and Automated Tool
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| Conference: | ASIACRYPT 2025 |
| Abstract: | As one of the famous quantum algorithms, Simon's algorithm enables the efficient derivation of the period of periodic functions in polynomial time. However, the complexity of constructing periodic functions has hindered the widespread application of Simon's algorithm in symmetric-key cryptanalysis. Currently, aside from the exhaustive search-based testing method introduced by Canale et al. at CRYPTO 2022, there is no unified model for effectively searching for periodic distinguishers. Although Xiang et al. established a link between periodic functions and truncated differential theory at ToSC 2024, their approach lacks the ability to construct periods using unknown differentials and does not provide automated tools. This limitation underscores the inadequacy of existing methods in identifying periodic distinguishers for complex structures. In this paper, we address the challenge of advancing periodic distinguishers for symmetric-key ciphers. First, we propose a more generalized method for constructing periodic distinguishers, addressing the limitations of Xiang et al.'s theory in handling unknown differences. We further extend it to probabilistic periodic distinguishers. As a result, our method can cover a wider range of periodic distinguishers. Second, we introduce a novel symbolic representation to simplify the search for periodic distinguishers, and propose the first fully automated SMT-based search model, which efficiently addresses the challenges of manual searching in complex structures. Based on our method, we have achieved new quantum distinguishers with the following round configurations: 10 rounds for GFS-4F, 10 rounds for LBlock, 10 rounds for TWINE, and 16 rounds for Skipjack-B, improving the previous best results by 1, 2, 2, and 3 rounds, respectively. Our model also identifies the first 7/8/9-round periodic distinguishers for SKINNY. Compared with existing distinguishers (Hadipour et al., CRYPTO 2024) with the same round in the classical setting, our distinguishers achieve lower data complexity. |
BibTeX
@inproceedings{asiacrypt-2025-35953,
title={Quantum Periodic Distinguisher Construction: Symbolization Method and Automated Tool},
publisher={Springer-Verlag},
author={Qun Liu and Haoyang Wang and Jinliang Wang and Boyun Li and Meiqin Wang},
year=2025
}