Skip to main content
SpringerLink
Log in

Differential-Linear Cryptanalysis of Round-Reduced SPARX-64/128

  • Conference paper
  • First Online:
Information Security and Cryptology (Inscrypt 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14527))

Included in the following conference series:

  • 138 Accesses

Abstract

SPARX is a family of ARX-based block ciphers introduced at ASIACRYPT 2016, which is designed according to the long-trail strategy (LTS). For SPARX-64/128 with block size 64 and key size 128, the best known attack is a differential cryptanalysis of 16-round SPARX-64/128. In this paper, we further present a differential-linear cryptanalysis of SPARX-64/128. Due to the special structure of the round function, we first present some 6-round differential-linear characteristics of SPARX-64/128, then obtain two 14-round differential-linear characteristics of SPARX-64/128 by adding a 7-round differential characteristic before and a one-round linear approximation after the characteristics. By extending backwards three rounds before the 14-round differential-linear characteristics, we present a differential-linear cryptanalysis of 17-round SPARX-64/128, which covers one more round than previous work.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 74.99
Price excludes VAT (USA)
  • 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

References

  1. Abdelkhalek, A., Tolba, M., Youssef, A.M.: Impossible differential attack on reduced round SPARX-64/128. In: Joye, M., Nitaj, A. (eds.) AFRICACRYPT 2017. LNCS, vol. 10239, pp. 135–146. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-57339-7_8

    Chapter  Google Scholar 

  2. Ankele, R., List, E.: Differential cryptanalysis of round-reduced Sparx-64/128. In: Preneel, B., Vercauteren, F. (eds.) ACNS 2018. LNCS, vol. 10892, pp. 459–475. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-93387-0_24

    Chapter  Google Scholar 

  3. Bar-On, A., Dunkelman, O., Keller, N., Weizman, A.: DLCT: a new tool for differential-linear cryptanalysis. In: Ishai, Y., Rijmen, V. (eds.) EUROCRYPT 2019. LNCS, vol. 11476, pp. 313–342. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17653-2_11

    Chapter  Google Scholar 

  4. Beaulieu, R., Shors, D., Smith, J., Treatman-Clark, S., Weeks, B., Wingers, L.: The SIMON and SPECK lightweight block ciphers. In: Proceedings of the 52nd Annual Design Automation Conference, San Francisco, CA, USA, June 7–11, 2015. pp. 175:1–175:6. ACM (2015). https://doi.org/10.1145/2744769.2747946

  5. Beierle, C.: Improved differential-linear attacks with applications to ARX ciphers. J. Cryptol. 35(4), 29 (2022). https://doi.org/10.1007/s00145-022-09437-z

    Article  MathSciNet  Google Scholar 

  6. Beierle, C., Leander, G., Todo, Y.: Improved differential-linear attacks with applications to ARX ciphers. In: Micciancio, D., Ristenpart, T. (eds.) CRYPTO 2020. LNCS, vol. 12172, pp. 329–358. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-56877-1_12

    Chapter  Google Scholar 

  7. Bernstein, D.J.: Chacha, a variant of salsa20 (2008). https://cr.yp.to/chacha.html

  8. Biham, E., Carmeli, Y.: An improvement of linear cryptanalysis with addition operations with applications to FEAL-8X. In: Joux, A., Youssef, A. (eds.) SAC 2014. LNCS, vol. 8781, pp. 59–76. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-13051-4_4

    Chapter  Google Scholar 

  9. Biham, E., Dunkelman, O., Keller, N.: Enhancing differential-linear cryptanalysis. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 254–266. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-36178-2_16

    Chapter  Google Scholar 

  10. Dey, S., Garai, H.K., Sarkar, S., Sharma, N.K.: Revamped differential-linear cryptanalysis on reduced round ChaCha. In: Dunkelman, O., Dziembowski, S. (eds.) Advances in Cryptology - EUROCRYPT 2022–41st Annual International Conference on the Theory and Applications of Cryptographic Techniques, Trondheim, Norway, May 30 - June 3, 2022, Proceedings, Part III. LNCS, vol. 13277, pp. 86–114. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-07082-2_4

  11. Dinu, D., Perrin, L., Udovenko, A., Velichkov, V., Großschädl, J., Biryukov, A.: Design strategies for ARX with provable bounds: Sparx and LAX. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 484–513. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53887-6_18

    Chapter  Google Scholar 

  12. Fu, K., Wang, M., Guo, Y., Sun, S., Hu, L.: MILP-based automatic search algorithms for differential and linear trails for speck. In: Peyrin, T. (ed.) FSE 2016. LNCS, vol. 9783, pp. 268–288. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-52993-5_14

    Chapter  Google Scholar 

  13. Huang, T., Tjuawinata, I., Wu, H.: Differential-linear cryptanalysis of ICEPOLE. In: Leander, G. (ed.) FSE 2015. LNCS, vol. 9054, pp. 243–263. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48116-5_12

    Chapter  Google Scholar 

  14. Langford, S.K., Hellman, M.E.: Differential-linear cryptanalysis. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 17–25. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48658-5_3

    Chapter  Google Scholar 

  15. Leurent, G.: Improved differential-linear cryptanalysis of 7-round Chaskey with partitioning. In: Fischlin, M., Coron, J.-S. (eds.) EUROCRYPT 2016. LNCS, vol. 9665, pp. 344–371. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49890-3_14

    Chapter  Google Scholar 

  16. Lipmaa, H., Moriai, S.: Efficient algorithms for computing differential properties of addition. In: Matsui, M. (ed.) FSE 2001. LNCS, vol. 2355, pp. 336–350. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45473-X_28

    Chapter  Google Scholar 

  17. Liu, M., Lu, X., Lin, D.: Differential-linear cryptanalysis from an Algebraic perspective. In: Malkin, T., Peikert, C. (eds.) CRYPTO 2021. LNCS, vol. 12827, pp. 247–277. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-84252-9_9

    Chapter  Google Scholar 

  18. Liu, Y., Sun, S., Li, C.: Rotational cryptanalysis from a differential-linear perspective. In: Canteaut, A., Standaert, F.-X. (eds.) EUROCRYPT 2021, Part 1. LNCS, vol. 12696, pp. 741–770. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-77870-5_26

    Chapter  Google Scholar 

  19. Lu, J.: A methodology for differential-linear cryptanalysis and its applications. In: Canteaut, A. (ed.) FSE 2012. LNCS, vol. 7549, pp. 69–89. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34047-5_5

    Chapter  Google Scholar 

  20. Mouha, N., Mennink, B., Van Herrewege, A., Watanabe, D., Preneel, B., Verbauwhede, I.: Chaskey: an efficient MAC algorithm for 32-bit microcontrollers. In: Joux, A., Youssef, A. (eds.) SAC 2014. LNCS, vol. 8781, pp. 306–323. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-13051-4_19

    Chapter  Google Scholar 

  21. Niu, Z., Sun, S., Liu, Y., Li, C.: Rotational differential-linear distinguishers of ARX ciphers with arbitrary output linear masks. In: Dodis, Y., Shrimpton, T. (eds.) Advances in Cryptology - CRYPTO 2022. CRYPTO 2022, LNCS, vol. 13507, pp 3–32. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-15802-5_1

  22. Schulte-Geers, E.: On CCZ-equivalence of addition mod 2\({}^{n}\). Des. Codes Cryptogr. 66(1–3), 111–127 (2013). https://doi.org/10.1007/s10623-012-9668-4

    Article  MathSciNet  Google Scholar 

  23. Selçuk, A.A.: On probability of success in linear and differential cryptanalysis. J. Cryptol. 21(1), 131–147 (2008). https://doi.org/10.1007/s00145-007-9013-7

    Article  MathSciNet  Google Scholar 

  24. Sun, L., Wang, W., Wang, M.: Accelerating the search of differential and linear characteristics with the SAT method. IACR Trans. Symmetric Cryptol. 2021(1), 269–315 (2021). https://doi.org/10.46586/tosc.v2021.i1.269-315

Download references

Acknowledgements

We thank the anonymous reviewers for their careful reading and helpful comments.

Author information

Authors and Affiliations

  1. Information Engineering University, Zhengzhou, China

    Zhichao Xu, Hong Xu, Lin Tan & Wenfeng Qi

Authors
  1. Zhichao Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hong Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lin Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wenfeng Qi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hong Xu .

Editor information

Editors and Affiliations

  1. Shandong University, Jinan, China

    Chunpeng Ge

  2. Columbia University, New York, NY, USA

    Moti Yung

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Xu, Z., Xu, H., Tan, L., Qi, W. (2024). Differential-Linear Cryptanalysis of Round-Reduced SPARX-64/128. In: Ge, C., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2023. Lecture Notes in Computer Science, vol 14527. Springer, Singapore. https://doi.org/10.1007/978-981-97-0945-8_11

Download citation

  • DOI: https://doi.org/10.1007/978-981-97-0945-8_11

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-97-0944-1

  • Online ISBN: 978-981-97-0945-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation