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A New Method for Searching Cubes and Its Application to 815-Round Trivium

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Abstract

The cube attack proposed by Dinur and Shamir is one of the most important key-recovery attacks against Trivium. Recently division property based cube attacks have been extensively studied and significantly improved. In particular, the MILP modeling technique for the three-subset division property without unknown subset proposed by Hao, et al. at EUROCRYPT 2020 and the new technique with nested monomial predictions proposed by Hu, et al. at ASIACRYPT 2021 are best techniques to recover exact superpolies in division property based cube attacks. Consequently, at this state of the art, whether a superpoly can be recovered in division property based cube attacks is mainly decided by the scale of the superpoly, that is, the number of terms. Hence the choice for proper cubes corresponding to low-complexity superpolies is more critical now. Some effective cube construction methods were proposed for experimental cube attacks, but not applicable to division property based cube attacks. In this paper, the authors propose a heuristic cube criterion and a cube sieve algorithm, which can be combined with the three-subset division property to recover a number of superpolies. Applied to 815-round Trivium, the authors recovered 417 superpolies from 441 cubes obtained by our algorithm of sizes between 41 and 48. The success rate is 94.56%. There are 165 non-constant superpolies with degree less than 14. In order to demonstrate the significance of the new algorithm, the authors tested the best superpoly recovery technique at EUROCRYPT 2020 using random cubes of similar sizes on 815-round Trivium. The experimental result shows that no cube could be completely recovered within a given period of time because the superpolies for random cubes are too complex.

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Authors and Affiliations

  1. PLA Strategic Support Force Information Engineering University, Zhengzhou, 450001, China

    Chen Liu, Tian Tian & Wenfeng Qi

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  1. Chen Liu
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  2. Tian Tian
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  3. Wenfeng Qi
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Correspondence to Tian Tian.

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The authors declare no conflict of interest.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant No. 61672533.

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Liu, C., Tian, T. & Qi, W. A New Method for Searching Cubes and Its Application to 815-Round Trivium. J Syst Sci Complex 36, 2234–2254 (2023). https://doi.org/10.1007/s11424-023-1497-1

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  • DOI: https://doi.org/10.1007/s11424-023-1497-1

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