Rotational-XOR Differential Rectangle Cryptanalysis on Simon-Like Ciphers | SpringerLink
Skip to main content
Springer Nature Link
Log in

Rotational-XOR Differential Rectangle Cryptanalysis on Simon-Like Ciphers

  • Conference paper
  • First Online:
Topics in Cryptology – CT-RSA 2023 (CT-RSA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13871))

Included in the following conference series:

Abstract

In this paper, we propose a rectangle-like method called rotational-XOR differential rectangle attack to search for better distinguishers. It is a combination of the rotational-XOR cryptanalysis and differential cryptanalysis in the rectangle-based way. In particular, we put a rotational-XOR characteristic before a differential characteristic to construct a rectangle structure. By choosing some appropriate rotational-XOR and differential characteristics as well as considering multiple differentials, some longer distinguishers that have the probability greater than \(2^{-2n}\) can be constructed effectively where n is the block size of a block cipher. We apply this new method to some versions of Simon and Simeck block ciphers. As a result, we obtain rotational-XOR differential rectangle distinguishers up to 16, 16, 17, 16 and 21 rounds for Simon32/64, Simon48/72, Simon48/96, Simeck32 and Simeck48, respectively. Our distinguishers for Simon32/64 and Simon48/96 are both longer than the best differential and rotational-XOR distinguishers. Also, our distinguisher for Simeck32 is longer than the best differential distinguisher (14 rounds) and has the full weak key space (i.e., \(2^{64}\)) whereas the 16-round rotational-XOR distinguisher has a weak key class of \(2^{36}\). In addition, our distinguisher for Simeck48 has a better weak key class (\(2^{72}\) weak keys) than the 21-round rotational-XOR distinguisher (\(2^{60}\) weak keys). To the best of our knowledge, this is the first time to consider the combinational cryptanalysis based on rotational-XOR and differential cryptanalysis using the rectangle structure.

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

References

  1. Ashur, T., Liu, Y.: Rotational cryptanalysis in the presence of constants. IACR Trans. Symmetric Cryptol. 2016(1), 57–70 (2016). https://doi.org/10.13154/tosc.v2016.i1.57-70

    Article  Google Scholar 

  2. 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 

  3. Beaulieu, R., Shors, D., Smith, J., Treatman-Clark, S., Weeks, B., Wingers, L.: The SIMON and SPECK families of lightweight block ciphers. IACR Cryptol. ePrint Arch., p. 404 (2013). http://eprint.iacr.org/2013/404

  4. Biham, E., Anderson, R., Knudsen, L.: Serpent: a new block cipher proposal. In: Vaudenay, S. (ed.) FSE 1998. LNCS, vol. 1372, pp. 222–238. Springer, Heidelberg (1998). https://doi.org/10.1007/3-540-69710-1_15

    Chapter  Google Scholar 

  5. Biham, E., Dunkelman, O., Keller, N.: The rectangle attack—rectangling the Serpent. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 340–357. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44987-6_21

    Chapter  Google Scholar 

  6. Biham, E., Shamir, A.: Differential cryptanalysis of DES-like cryptosystems. In: Menezes, A.J., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 2–21. Springer, Heidelberg (1991). https://doi.org/10.1007/3-540-38424-3_1

    Chapter  Google Scholar 

  7. Biryukov, A., Roy, A., Velichkov, V.: Differential analysis of block ciphers SIMON and SPECK. In: Cid, C., Rechberger, C. (eds.) FSE 2014. LNCS, vol. 8540, pp. 546–570. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46706-0_28

    Chapter  Google Scholar 

  8. Cid, C., Huang, T., Peyrin, T., Sasaki, Yu., Song, L.: Boomerang connectivity table: a new cryptanalysis tool. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10821, pp. 683–714. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78375-8_22

    Chapter  Google Scholar 

  9. Huang, M., Wang, L., Zhang, Y.: Improved automatic search algorithm for differential and linear cryptanalysis on SIMECK and the applications. In: Naccache, D., et al. (eds.) ICICS 2018. LNCS, vol. 11149, pp. 664–681. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-01950-1_39

    Chapter  Google Scholar 

  10. Khovratovich, D., Nikolić, I.: Rotational cryptanalysis of ARX. In: Hong, S., Iwata, T. (eds.) FSE 2010. LNCS, vol. 6147, pp. 333–346. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13858-4_19

    Chapter  Google Scholar 

  11. Khovratovich, D., Nikolić, I., Pieprzyk, J., Sokołowski, P., Steinfeld, R.: Rotational cryptanalysis of ARX revisited. In: Leander, G. (ed.) FSE 2015. LNCS, vol. 9054, pp. 519–536. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48116-5_25

    Chapter  Google Scholar 

  12. Knudsen, L., Wagner, D.: Integral cryptanalysis. In: Daemen, J., Rijmen, V. (eds.) FSE 2002. LNCS, vol. 2365, pp. 112–127. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45661-9_9

    Chapter  Google Scholar 

  13. Kölbl, S., Leander, G., Tiessen, T.: Observations on the SIMON block cipher family. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9215, pp. 161–185. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47989-6_8

    Chapter  Google Scholar 

  14. Kölbl, S., Roy, A.: A brief comparison of Simon and Simeck. In: Bogdanov, A. (ed.) LightSec 2016. LNCS, vol. 10098, pp. 69–88. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-55714-4_6

    Chapter  MATH  Google Scholar 

  15. Koo, B., Jung, Y., Kim, W.: Rotational-XOR rectangle cryptanalysis on round-reduced SIMON. Secur. Commun. Netw. 2020, 1–12 (2020). https://doi.org/10.1155/2020/5968584

    Article  Google Scholar 

  16. 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 

  17. Leurent, G., Pernot, C., Schrottenloher, A.: Clustering effect in Simon and Simeck. In: Tibouchi, M., Wang, H. (eds.) ASIACRYPT 2021. LNCS, vol. 13090, pp. 272–302. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-92062-3_10

    Chapter  Google Scholar 

  18. 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 

  19. Liu, Z., Li, Y., Wang, M.: Optimal differential trails in Simon-like ciphers. IACR Trans. Symmetric Cryptol. 2017(1), 358–379 (2017). https://doi.org/10.13154/tosc.v2017.i1.358-379

    Article  Google Scholar 

  20. Lu, J., Liu, Y., Ashur, T., Sun, B., Li, C.: Rotational-XOR cryptanalysis of Simon-like block ciphers. In: Liu, J.K., Cui, H. (eds.) ACISP 2020. LNCS, vol. 12248, pp. 105–124. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-55304-3_6

    Chapter  Google Scholar 

  21. Lu, J., Liu, Y., Ashur, T., Sun, B., Li, C.: Improved rotational-XOR cryptanalysis of Simon-like block ciphers. IET Inf. Secur. 16(4), 282–300 (2022). https://doi.org/10.1049/ise2.12061

    Article  MATH  Google Scholar 

  22. Matsui, M.: Linear cryptanalysis method for DES cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48285-7_33

    Chapter  Google Scholar 

  23. Murphy, S.: The return of the cryptographic boomerang. IEEE Trans. Inf. Theory 57(4), 2517–2521 (2011). https://doi.org/10.1109/TIT.2011.2111091

    Article  MathSciNet  MATH  Google Scholar 

  24. Rohit, R., Gong, G.: Correlated sequence attack on reduced-round Simon-32/64 and Simeck-32/64. IACR Cryptol. ePrint Arch., p. 699 (2018). https://eprint.iacr.org/2018/699

  25. Wagner, D.: The boomerang attack. In: Knudsen, L. (ed.) FSE 1999. LNCS, vol. 1636, pp. 156–170. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48519-8_12

    Chapter  Google Scholar 

  26. Wang, X., Wu, B., Hou, L., Lin, D.: Automatic search for related-key differential trails in SIMON-like block ciphers based on MILP. In: Chen, L., Manulis, M., Schneider, S. (eds.) ISC 2018. LNCS, vol. 11060, pp. 116–131. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-99136-8_7

    Chapter  Google Scholar 

  27. 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 

  28. Yang, G., Zhu, B., Suder, V., Aagaard, M.D., Gong, G.: The Simeck family of lightweight block ciphers. In: Güneysu, T., Handschuh, H. (eds.) CHES 2015. LNCS, vol. 9293, pp. 307–329. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48324-4_16

    Chapter  Google Scholar 

Download references

Acknowledgement

We would like to thank Maria Eichlseder and all the anonymous reviewers for their valuable comments to improve the quality of this paper. This work was supported by the National Natural Science Foundation of China (No. 62272147), the Science and Technology on Communication Security Laboratory Foundation (No. 6142103012207), the Research Foundation of Department of Education of Hubei Province (No. D2020104) and the Wuhan Science and Technology Bureau (NO. 2022010801020328).

Author information

Authors and Affiliations

  1. School of Cyber Science and Technology, Hubei University, Wuhan, 430062, China

    Siwei Chen, Mingming Zhu, Zejun Xiang, Runqing Xu & Shasha Zhang

  2. Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan, 430062, China

    Xiangyong Zeng

Authors
  1. Siwei Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mingming Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zejun Xiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Runqing Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xiangyong Zeng
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Shasha Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zejun Xiang .

Editor information

Editors and Affiliations

  1. Oregon State University, Corvallis, OR, USA

    Mike Rosulek

Algorithm to Calculate \(\tilde{q}\) for Simon-Like Ciphers

Algorithm to Calculate \(\tilde{q}\) for Simon-Like Ciphers

figure b

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Chen, S., Zhu, M., Xiang, Z., Xu, R., Zeng, X., Zhang, S. (2023). Rotational-XOR Differential Rectangle Cryptanalysis on Simon-Like Ciphers. In: Rosulek, M. (eds) Topics in Cryptology – CT-RSA 2023. CT-RSA 2023. Lecture Notes in Computer Science, vol 13871. Springer, Cham. https://doi.org/10.1007/978-3-031-30872-7_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-30872-7_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-30871-0

  • Online ISBN: 978-3-031-30872-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation