A Practical Key-Recovery Attack on 805-Round Trivium | SpringerLink
Skip to main content
Springer Nature Link
Log in

A Practical Key-Recovery Attack on 805-Round Trivium

  • Conference paper
  • First Online:
Advances in Cryptology – ASIACRYPT 2021 (ASIACRYPT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13090))

Abstract

The cube attack is one of the most important cryptanalytic techniques against Trivium. Many key-recovery attacks based on cube attacks have been established. However, few attacks can recover the 80-bit full key information practically. In particular, the previous best practical key-recovery attack was on 784-round Trivium proposed by Fouque and Vannet at FSE 2013. To mount practical key-recovery attacks, it requires a sufficient number of low-degree superpolies. It is difficult both for experimental cube attacks and division property based cube attacks with randomly selected cubes due to lack of efficiency. In this paper, we give a new algorithm to construct candidate cubes targeting linear superpolies. Our experiments show that the success probability is \( 100\% \) for finding linear superpolies using the constructed cubes. We obtain over 1000 linear superpolies for 805-round Trivium. With 42 independent linear superpolies, we mount a practical key-recovery attack on 805-round Trivium, which increases the number of attacked rounds by 21. The complexity of our attack is \( 2^{41.40} \), which could be carried out on a PC with a GTX-1080 GPU in several hours.

Supported by the National Natural Science Foundations of China under grant nos. 61672533.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 11439
Price includes VAT (Japan)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 14299
Price includes VAT (Japan)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    Constant polynomials are also linear. However, key bits could not be recovered from constant superpolies directly. Hence, in this paper, when talking about linear superploies, we do not take the constant linear into consideration.

  2. 2.

    Here, we only consider the VK-terms formed in the first two ways and do not take the terms which are eliminated by the XOR operation into consideration.

References

  1. Aumasson, J.-P., Dinur, I., Meier, W., Shamir, A.: Cube testers and key recovery attacks on reduced-round MD6 and Trivium. In: Dunkelman, O. (ed.) FSE 2009. LNCS, vol. 5665, pp. 1–22. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03317-9_1

    Chapter  Google Scholar 

  2. De Cannière, C., Preneel, B.: Trivium. In: Robshaw, M., Billet, O. (eds.) New Stream Cipher Designs. LNCS, vol. 4986, pp. 244–266. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-68351-3_18

  3. Dinur, I., Güneysu, T., Paar, C., Shamir, A., Zimmermann, R.: An experimentally verified attack on full Grain-128 using dedicated reconfigurable hardware. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 327–343. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25385-0_18

    Chapter  Google Scholar 

  4. 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

    Chapter  Google Scholar 

  5. Dinur, I., Shamir, A.: Breaking Grain-128 with dynamic cube attacks. In: Joux, A. (ed.) FSE 2011. LNCS, vol. 6733, pp. 167–187. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21702-9_10

    Chapter  Google Scholar 

  6. 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

    Chapter  Google Scholar 

  7. Hao, Y., Leander, G., Meier, W., Todo, Y., Wang, Q.: Modeling for three-subset division property without unknown subset. IACR Cryptol. ePrint Arch. 2020, 441 (2020)

    MATH  Google Scholar 

  8. 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

    Chapter  Google Scholar 

  9. 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

    Chapter  Google Scholar 

  10. Huang, S., Wang, X., Xu, G., Wang, M., Zhao, J.: Conditional cube attack on reduced-round Keccak sponge function. In: Coron, J.-S., Nielsen, J.B. (eds.) EUROCRYPT 2017. LNCS, vol. 10211, pp. 259–288. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-56614-6_9

    Chapter  Google Scholar 

  11. Joux, A.: Algorithmic Cryptanalysis, 1st edn. Chapman & Hall/CRC Cryptography and Network Security Series. Chapman and Hall/CRC (2009)

    Google Scholar 

  12. Kesarwani, A., Roy, D., Sarkar, S., Meier, W.: New cube distinguishers on NFSR-based stream ciphers. Des. Codes Cryptogr. 88(1), 173–199 (2020)

    Article  MathSciNet  Google Scholar 

  13. Li, Z., Bi, W., Dong, X., Wang, X.: Improved conditional cube attacks on Keccak keyed modes with MILP method. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10624, pp. 99–127. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70694-8_4

    Chapter  Google Scholar 

  14. Liu, M.: Degree evaluation of NFSR-based cryptosystems. In: Katz, J., Shacham, H. (eds.) CRYPTO 2017. LNCS, vol. 10403, pp. 227–249. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63697-9_8

    Chapter  Google Scholar 

  15. 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

    Chapter  Google Scholar 

  16. Mroczkowski, P., Szmidt, J.: Corrigendum to: the cube attack on stream cipher Trivium and quadraticity tests. IACR Cryptol. ePrint Arch. 2011, 32 (2011)

    MATH  Google Scholar 

  17. Rahimi, M., Barmshory, M., Mansouri, M.H., Aref, M.R.: Dynamic cube attack on Grain-v1. IET Inf. Secur. 10(4), 165–172 (2016)

    Article  Google Scholar 

  18. Sarkar, S., Maitra, S., Baksi, A.: Observing biases in the state: case studies with Trivium and Trivia-SC. Des. Codes Crypt. 82(1), 351–375 (2016). https://doi.org/10.1007/s10623-016-0211-x

    Article  MathSciNet  MATH  Google Scholar 

  19. Stankovski, P.: Greedy distinguishers and nonrandomness detectors. In: Gong, G., Gupta, K.C. (eds.) INDOCRYPT 2010. LNCS, vol. 6498, pp. 210–226. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17401-8_16

    Chapter  Google Scholar 

  20. Sun, L., Wang, W., Wang, M.: MILP-aided bit-based division property for primitives with non-bit-permutation linear layers. Cryptology ePrint Archive, Report 2016/811 (2016)

    Google Scholar 

  21. 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

    Chapter  Google Scholar 

  22. Todo, Y., Isobe, T., Hao, Y., Meier, W.: Cube attacks on non-blackbox polynomials based on division property. IEEE Trans. Comput. 67(12), 1720–1736 (2018)

    Article  MathSciNet  Google Scholar 

  23. Todo, Y., Morii, M.: Bit-based division property and application to Simon family. In: Peyrin, T. (ed.) FSE 2016. LNCS, vol. 9783, pp. 357–377. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-52993-5_18

    Chapter  Google Scholar 

  24. 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

    Chapter  Google Scholar 

  25. 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

    Chapter  Google Scholar 

  26. Xiang, Z., Zhang, W., Bao, Z., Lin, D.: Applying MILP method to searching integral distinguishers based on division property for 6 lightweight block ciphers. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 648–678. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53887-6_24

    Chapter  Google Scholar 

  27. 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

    Chapter  Google Scholar 

  28. Ye, C.-D., Tian, T.: Revisit division property based cube attacks: key-recovery or distinguishing attacks? IACR Trans. Symmetric Cryptol. 2019(3), 81–102 (2019)

    Article  Google Scholar 

  29. Ye, C.-D., Tian, T.: Algebraic method to recover superpolies in cube attacks. IET Inf. Secur. 14(4), 430–441 (2020)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Chen-Dong Ye & Tian Tian

Authors
  1. Chen-Dong Ye
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tian Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. NTT Corporation, Tokyo, Japan

    Mehdi Tibouchi

  2. Nanyang Technological University, Singapore, Singapore

    Huaxiong Wang

Rights and permissions

Reprints and permissions

Copyright information

© 2021 International Association for Cryptologic Research

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Ye, CD., Tian, T. (2021). A Practical Key-Recovery Attack on 805-Round Trivium. In: Tibouchi, M., Wang, H. (eds) Advances in Cryptology – ASIACRYPT 2021. ASIACRYPT 2021. Lecture Notes in Computer Science(), vol 13090. Springer, Cham. https://doi.org/10.1007/978-3-030-92062-3_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-92062-3_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-92061-6

  • Online ISBN: 978-3-030-92062-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Societies and partnerships

Search

Navigation