Skip to main content
SpringerLink
Log in

Compact Representation for Division Property

  • Conference paper
  • First Online:
Book cover Cryptology and Network Security (CANS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10052))

Included in the following conference series:

Abstract

The division property, which is a new method to find integral characteristics, was proposed at Eurocrypt 2015. Thereafter, some applications and improvements have been proposed. The bit-based division property is also one of such improvements, and the accurate integral characteristic of Simon32 is theoretically proved. In this paper, we propose the compact representation for the bit-based division property. The disadvantage of the bit-based division property is that it cannot be applied to block ciphers whose block length is over 32 because of high time and memory complexity. The compact representation partially solves this problem, and we apply this technique to 64-bit block cipher PRESENT to illustrate our method. We can accurately evaluate the propagation characteristic of the bit-based division property thanks to the compact representation. As a result, we find 9-round integral characteristics, and the characteristic is improved by two rounds than previous best characteristic. Moreover, we attack 12-round PRESENT-80 and 13-round PRESENT-128 by using this new characteristic.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Notes

  1. 1.

    This method is often called the higher-order differential attack [5, 7].

  2. 2.

    In [14], they proposed two variants of the bit-based division property: the conventional bit-based division property and the bit-based division property using three subsets. In this paper, we focus on the conventional bit-based division property.

  3. 3.

    In [12], the division property was referred to as \(\mathcal{D}_{\mathbb {K}}^{n,m}\).

References

  1. Bogdanov, A., Knudsen, L.R., Leander, G., Paar, C., Poschmann, A., Robshaw, M.J.B., Seurin, Y., Vikkelsoe, C.: PRESENT: an ultra-lightweight block cipher. In: Paillier, P., Verbauwhede, I. (eds.) CHES 2007. LNCS, vol. 4727, pp. 450–466. Springer, Heidelberg (2007). doi:10.1007/978-3-540-74735-2_31

    Chapter  Google Scholar 

  2. Boura, C., Canteaut, A.: Another view of the division property (2016). (Accepted to CRYPTO2016). https://eprint.iacr.org/2016/554

    Google Scholar 

  3. Collard, B., Standaert, F.-X., Quisquater, J.-J.: Improving the time complexity of Matsui’s linear cryptanalysis. In: Nam, K.-H., Rhee, G. (eds.) ICISC 2007. LNCS, vol. 4817, pp. 77–88. Springer, Heidelberg (2007). doi:10.1007/978-3-540-76788-6_7

    Chapter  Google Scholar 

  4. Daemen, J., Knudsen, L., Rijmen, V.: The block cipher Square. In: Biham, E. (ed.) FSE 1997. LNCS, vol. 1267, pp. 149–165. Springer, Heidelberg (1997). doi:10.1007/BFb0052343

    Chapter  Google Scholar 

  5. Knudsen, L.R.: Truncated and higher order differentials. In: Preneel, B. (ed.) FSE 1994. LNCS, vol. 1008, pp. 196–211. Springer, Heidelberg (1995). doi:10.1007/3-540-60590-8_16

    Chapter  Google Scholar 

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

    Chapter  Google Scholar 

  7. Lai, X.: Higher order derivatives and differential cryptanalysis. In: Blahut, R.E., Costello, D.J., Maurer, U., Mittelholzer, T. (eds.) Communications and Cryptography. The Springer International Series in Engineering and Computer Science, vol. 276, pp. 227–233. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  8. Li, Y., Wu, W., Zhang, L.: Improved integral attacks on reduced-round CLEFIA block cipher. In: Jung, S., Yung, M. (eds.) WISA 2011. LNCS, vol. 7115, pp. 28–39. Springer, Heidelberg (2012). doi:10.1007/978-3-642-27890-7_3

    Chapter  Google Scholar 

  9. Sasaki, Y., Wang, L.: Meet-in-the-middle technique for integral attacks against feistel ciphers. In: Knudsen, L.R., Wu, H. (eds.) SAC 2012. LNCS, vol. 7707, pp. 234–251. Springer, Heidelberg (2013). doi:10.1007/978-3-642-35999-6_16

    Chapter  Google Scholar 

  10. Sun, B., Hai, X., Zhang, W., Cheng, L., Yang, Z.: New observation on division property. IACR Cryptology ePrint Archive 2015, 459 (2015). http://eprint.iacr.org/2015/459

  11. Todo, Y.: Integral cryptanalysis on full MISTY1. In: Gennaro, R., Robshaw, M. (eds.) CRYPTO 2015. LNCS, vol. 9215, pp. 413–432. Springer, Heidelberg (2015). doi:10.1007/978-3-662-47989-6_20

    Chapter  Google Scholar 

  12. Todo, Y.: Structural evaluation by generalized integral property. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 287–314. Springer, Heidelberg (2015). doi:10.1007/978-3-662-46800-5_12

    Google Scholar 

  13. Todo, Y., Aoki, K.: FFT key recovery for integral attack. In: Gritzalis, D., Kiayias, A., Askoxylakis, I. (eds.) CANS 2014. LNCS, vol. 8813, pp. 64–81. Springer, Heidelberg (2014). doi:10.1007/978-3-319-12280-9_5

    Google Scholar 

  14. Todo, Y., Morii, M.: Bit-based division property and application to Simon family. IACR Cryptology ePrint Archive 2016, 285 (2016). (Accepted to FSE2016). https://eprint.iacr.org/2016/285

  15. Wu, S., Wang, M.: Integral attacks on reduced-round PRESENT. In: Qing, S., Zhou, J., Liu, D. (eds.) ICICS 2013. LNCS, vol. 8233, pp. 331–345. Springer, Heidelberg (2013). doi:10.1007/978-3-319-02726-5_24

    Chapter  Google Scholar 

  16. Yeom, Y., Park, S., Kim, I.: On the security of CAMELLIA against the square attack. In: Daemen, J., Rijmen, V. (eds.) FSE 2002. LNCS, vol. 2365, pp. 89–99. Springer, Heidelberg (2002). doi:10.1007/3-540-45661-9_7

    Chapter  Google Scholar 

  17. Z’aba, M.R., Raddum, H., Henricksen, M., Dawson, E.: Bit-pattern based integral attack. In: Nyberg, K. (ed.) FSE 2008. LNCS, vol. 5086, pp. 363–381. Springer, Heidelberg (2008). doi:10.1007/978-3-540-71039-4_23

    Chapter  Google Scholar 

  18. Zhang, H., Wu, W.: Structural evaluation for generalized feistel structures and applications to LBlock and TWINE. In: Biryukov, A., Goyal, V. (eds.) INDOCRYPT 2015. LNCS, vol. 9462, pp. 218–237. Springer, Heidelberg (2015). doi:10.1007/978-3-319-26617-6_12

    Chapter  Google Scholar 

  19. Zhang, H., Wu, W., Wang, Y.: Integral attack against bit-oriented block ciphers. In: Kwon, S., Yun, A. (eds.) ICISC 2015. LNCS, vol. 9558, pp. 102–118. Springer, Heidelberg (2016). doi:10.1007/978-3-319-30840-1_7

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. NTT Secure Platform Laboratories, Tokyo, Japan

    Yosuke Todo

  2. Kobe University, Kobe, Japan

    Yosuke Todo & Masakatu Morii

Authors
  1. Yosuke Todo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Masakatu Morii
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yosuke Todo .

Editor information

Editors and Affiliations

  1. Università degli Studi di Milano, Crema, Italy

    Sara Foresti

  2. Università degli Studi di Salerno, Fisciano, Italy

    Giuseppe Persiano

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing AG

About this paper

Cite this paper

Todo, Y., Morii, M. (2016). Compact Representation for Division Property. In: Foresti, S., Persiano, G. (eds) Cryptology and Network Security. CANS 2016. Lecture Notes in Computer Science(), vol 10052. Springer, Cham. https://doi.org/10.1007/978-3-319-48965-0_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-48965-0_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-48964-3

  • Online ISBN: 978-3-319-48965-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation