Abstract
The most crucial but time-consuming task for differential cryptanalysis is to find a differential with a high probability. To tackle this task, we propose a new SAT-based automatic search framework to efficiently figure out a differential with the highest probability under a specified condition. As the previous SAT methods (e.g., the Sun et al.’s method proposed at ToSC 2021(1)) focused on accelerating the search of an optimal single differential characteristic, these are not optimized for evaluating a clustering effect to obtain a tighter differential probability of differentials. In contrast, our framework takes advantage of a method to solve incremental SAT problems in parallel using a multi-threading technique, and consequently, it offers the following advantages compared with the previous methods: (1) speedy identification of a differential with the highest probability under the specified conditions; (2) efficient construction of the truncated differential with the highest probability from the obtained multiple differentials; and (3) applicability to a wide class of the symmetric-key primitives. To demonstrate the effectiveness of our framework, we apply it to the block cipher PRINCE and the tweakable block cipher QARMA. We successfully figure out the tight differential bounds for all variants of PRINCE and QARMA within the practical time, thereby identifying the longest distinguisher for all the variants, which improves existing ones by one to four more rounds. Besides, we uncover notable differences between PRINCE and QARMA in the behavior of differential, especially for the clustering effect. We believe that our findings shed light on new structural properties of these important primitives.
Due to the page limitation, we leave the part of (1) descriptions of several basic algorithms and SAT models, (2) a detailed explanation of our investigation about the impact of multi-threading techniques, (3) key-recovery attacks, and (4) discussion of good parameters in our algorithms to the full version of this paper (https://eprint.iacr.org/2023/1227).
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Notes
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CryptoMiniSat5 is the winner of the incremental library track at SAT competition 2020.
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Acknowledgments
Takanori Isobe is supported by JST, PRESTO Grant Number JPMJPR2031. These research results were also obtained from the commissioned research (No. 05801) by National Institute of Information and Communications Technology (NICT), Japan.
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Sakamoto, K., Ito, R., Isobe, T. (2024). Parallel SAT Framework to Find Clustering of Differential Characteristics and Its Applications. In: Carlet, C., Mandal, K., Rijmen, V. (eds) Selected Areas in Cryptography – SAC 2023. SAC 2023. Lecture Notes in Computer Science, vol 14201. Springer, Cham. https://doi.org/10.1007/978-3-031-53368-6_20
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