Abstract
Correlation cube attacks were proposed by Liu et al. at EUROCRYPT 2018, which targeted a modern symmetric-key cryptosystem based on nonlinear feedback shift registers. The main idea of correlation cube attacks lies in recovering the secret key by exploiting conditional correlation properties between the superpoly of a cube and a specific set of low-degree polynomials called a basis. In this paper, we propose a new correlation cube attack based on the division property. The new attack expresses a given superpoly p as \( fg\oplus h \) and calculates correlation probabilities for all possible f, where f only involves key variables. This novel idea breaks the restriction on the basis used in the original attack and provides more choices to find good correlation probabilities, thus making the correlation cube attack much more powerful. Besides, the first application of the division property to correlation cube attacks is given, which aided by MILP modeling techniques facilitates the search for desirable cubes. As illustrations, we apply the new correlation cube attack to Trivium. For 844-round Trivium, we can recover about 4-bit key information on average with the time complexity \(2^{45}\), which could be fully verified by experiments. This is so far the best key recovery attack for 844-round Trivium.
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Appendix: The Cubes, Equations and Probabilities
Appendix: The Cubes, Equations and Probabilities
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Che, C., Tian, T. (2023). A New Correlation Cube Attack Based on Division Property. In: Simpson, L., Rezazadeh Baee, M.A. (eds) Information Security and Privacy. ACISP 2023. Lecture Notes in Computer Science, vol 13915. Springer, Cham. https://doi.org/10.1007/978-3-031-35486-1_3
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