Abstract
The cube attack is one of the most important cryptanalytic techniques against Trivium. As the method of recovering superpolies becomes more and more effective, another problem of cube attacks, i.e., how to select cubes that can effectively attack, is attracting more and more attention. In this paper, we present a novel framework to search for valuable cubes whose superpolies have an independent secret variable each, i.e., a linear variable not appearing in any nonlinear term. To control online complexity, valuable cubes are selected from very few large cubes. New ideas are given on the large cube construction and the subcube sieve. As illustrations, we apply the new algorithm to the stream cipher Trivium. For 815-round Trivium, the complexity of full key-recovery attack is \(2^{47.32}\). For 820-round Trivium, the complexity of full key-recovery attack is \(2^{53.17}\). Strong experimental evidence shows that the full key-recovery attacks on 815- and 820-round Trivium could be completed within six hours and two weeks on a PC with two RTX3090 GPUs, respectively.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
All the related codes and results could be found on https://github.com/LLuckyRabbit/search-for-valuables-cubes.
References
Dinur, I., Shamir, A.: Cube attacks on tweakable black box polynomials. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 278–299. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-01001-9_16
Fouque, P.-A., Vannet, T.: Improving key recovery to 784 and 799 rounds of Trivium using optimized cube attacks. In: Moriai, S. (ed.) FSE 2013. LNCS, vol. 8424, pp. 502–517. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-43933-3_26
Todo, Y., Isobe, T., Hao, Y., Meier, W.: Cube attacks on non-blackbox polynomials based on division property. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10403, pp. 250–279. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63697-9_9
Wang, Q., Hao, Y., Todo, Y., Li, C., Isobe, T., Meier, W.: Improved division property based cube attacks exploiting algebraic properties of superpoly. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10991, pp. 275–305. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96884-1_10
Wang, S., Hu, B., Guan, J., Zhang, K., Shi, T.: MILP-aided method of searching division property using three subsets and applications. In: Galbraith, S.D., Moriai, S. (eds.) ASIACRYPT 2019. LNCS, vol. 11923, pp. 398–427. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-34618-8_14
Fu, X., Wang, X., Dong, X., Meier, W.: A key-recovery attack on 855-round Trivium. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10992, pp. 160–184. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96881-0_6
Ye, C., Tian, T.: Revisit division property based cube attacks: key-recovery or distinguishing attacks? IACR Trans. Symmetric Cryptol. 2019(3), 81–102 (2019)
Hao, Y., Leander, G., Meier, W., Todo, Y., Wang, Q.: Modeling for three-subset division property without unknown subset. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12105, pp. 466–495. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45721-1_17
Cannière, C.D., Preneel, B.: Trivium specifications. eSTREAM portfolio, Profile 2 (HW) (2006)
Ye, C.-D., Tian, T.: A practical key-recovery attack on 805-round Trivium. In: Tibouchi, M., Wang, H. (eds.) ASIACRYPT 2021. LNCS, vol. 13090, pp. 187–213. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-92062-3_7
Hu, K., Sun, S., Wang, M., Wang, Q.: An algebraic formulation of the division property: revisiting degree evaluations, cube attacks, and key-independent sums. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12491, pp. 446–476. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64837-4_15
Hu, K., Sun, S., Todo, Y., Wang, M., Wang, Q.: Massive superpoly recovery with nested monomial predictions. In: Tibouchi, M., Wang, H. (eds.) ASIACRYPT 2021. LNCS, vol. 13090, pp. 392–421. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-92062-3_14
Sun, Y.: Automatic search of cubes for attacking stream ciphers. IACR Trans. Symmetric Cryptol. 2021(4), 100–123 (2021)
Ye, C., Tian, T.: A new framework for finding nonlinear superpolies in cube attacks against trivium-like ciphers. In: Susilo, W., Yang, G. (eds.) ACISP 2018. LNCS, vol. 10946, pp. 172–187. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-93638-3_11
Liu, M., Yang, J., Wang, W., Lin, D.: Correlation cube attacks: from weak-key distinguisher to key recovery. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10821, pp. 715–744. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78375-8_23
Che, C., Tian, T.: An experimentally verified attack on 820-round Trivium (full version). IACR Cryptol. ePrint Arch. 2022, 1518 (2022)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Che, C., Tian, T. (2023). An Experimentally Verified Attack on 820-Round Trivium. In: Deng, Y., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2022. Lecture Notes in Computer Science, vol 13837. Springer, Cham. https://doi.org/10.1007/978-3-031-26553-2_19
Download citation
DOI: https://doi.org/10.1007/978-3-031-26553-2_19
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-26552-5
Online ISBN: 978-3-031-26553-2
eBook Packages: Computer ScienceComputer Science (R0)