International Association for Cryptologic Research

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Persistence of Hourglass(-like) Structure: Improved Differential-Linear Distinguishers for Several ARX Ciphers

Authors:
Xinxin Gong , State Key Laboratory of Cryptology, Beijing
Qingju Wang , Telecom Paris, Institut Polytechnique de Paris
Yonglin Hao , State Key Laboratory of Cryptology, Beijing
Lin Jiao , State Key Laboratory of Cryptology, Beijing
Xichao Hu , State Key Laboratory of Cryptology, Beijing
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Conference: ASIACRYPT 2025
Abstract: The ARX structure plays a crucial role in symmetric-key primitives, with differential-linear (DL) attacks being among the most effective cryptanalysis techniques against ARX ciphers. In this paper, we present a systematic re-decomposition technique for DL distinguishers of ARX ciphers and identify for the first time the hourglass(-like) structural commonalities among optimal DL distinguishers searched out by various deduction techniques, also supported through comprehensive experiments, which motivate us to develop an efficient and generalized approach to construct optimal hourglass(-like) structural DL distinguishers. Our method yields significant advances when applied to \speck, \alzette, and the underlying permutations of \siphash{} and \chaskey: (1) the first 11- to 14-round DL distinguishers of \alzette; (2) the first (valid) DL distinguishers for 11-round \speck32, 12-round \speck48, and 16-round \speck96; (3) \emph{deterministic} (correlation $\pm1$) 3-round DL distinguishers for \siphash-2-4 and significantly improved 4-round ones. All these distinguishers are equipped with both theoretical and experimental verifications. We further analyze ARX-based Latin dance stream ciphers, achieving improved DL distinguishers for 7/7.25-round \chacha, 8-round \salsa, and 5.5-round \forro. Though some of the improvements are not significant, we have verified the effectiveness of our method across a broader range of instances. This work provides new insights for DL distinguisher construction and enhances understanding of the security of ARX ciphers.
BibTeX
@inproceedings{asiacrypt-2025-36038,
  title={Persistence of Hourglass(-like) Structure: Improved Differential-Linear Distinguishers for Several ARX Ciphers},
  publisher={Springer-Verlag},
  author={Xinxin Gong and Qingju Wang and Yonglin Hao and Lin Jiao and Xichao Hu},
  year=2025
}