Skip to main content
SpringerLink
Log in

Accurate Estimation of the Full Differential Distribution for General Feistel Structures

  • Conference paper
  • First Online:
Information Security and Cryptology (Inscrypt 2015)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9589))

Included in the following conference series:

Abstract

Statistical cryptanalysis is one of the most powerful tools to analyze symmetric key cryptographic primitives such as block ciphers. One of these attacks, the differential attack has been demonstrated to break a wide range of block ciphers. Block cipher proposals previously obtain a rough estimate of their security margin against differential attacks by counting the number of active S-Box along a differential path. However this method does not take into account the complex clustering effect of multiple differential paths. Analysis under full differential distributions have been studied for some extremely lightweight block ciphers such as KATAN and SIMON, but is still unknown for ciphers with relatively large block sizes. In this paper, we provide a framework to accurately estimate the full differential distribution of General Feistel Structure (GFS) block ciphers with relatively large block sizes. This framework acts as a convenient tool for block cipher designers to determine the security margin of their ciphers against differential attacks. We describe our theoretical model and demonstrate its correctness by performing experimental verification on a toy GFS cipher. We then apply our framework to two concrete GFS ciphers, LBlock and TWINE to derive their full differential distribution by using super computer. Based on the results, we are able to attack 25 rounds of TWINE-128 using a distinguishing attack, which is comparable to the best attack to date. Besides that, we are able to depict a correlation between the hamming weight of an input differential characteristic and the complexity of the attack. Based on the proposed framework, LBlock and TWINE have shown to have 178 and 208-bit security respectively.

J. Chen is partly supported by the National Natural Science Foundation of China under Grant 61302161.

A. Miyaji is partly supported by Grant-in-Aid for Scientific Research (C)(15K00183) and (15K00189).

C. Su is partly supported by JSPS KAKENHI 15K16005.

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

References

  1. Albrecht, M.R., Leander, G.: An all-in-one approach to differential cryptanalysis for small block ciphers. In: Knudsen, L.R., Wu, H. (eds.) SAC 2012. LNCS, vol. 7707, pp. 1–15. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  2. Alex Biryukov, P.D., Perrin, L.: Differential analysis and meet-in-the-middle attack against round-reduced twine. Cryptology ePrint Archive, Report 2015/240 (2015)

    Google Scholar 

  3. Selçuk, A.A., Biçak, A.: On probability of success in linear and differential cryptanalysis. In: Cimato, S., Galdi, C., Persiano, G. (eds.) SCN 2002. LNCS, vol. 2576, pp. 174–185. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  4. Baignères, T., Junod, P., Vaudenay, S.: How far can we go beyond linear cryptanalysis? In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 432–450. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  5. Biham, E., Shamir, A.: Differential cryptanalysis of DES-like cryptosystems. In: Menezes, A., Vanstone, S.A. (eds.) CRYPTO 1990. LNCS, vol. 537, pp. 2–21. Springer, Heidelberg (1991)

    Google Scholar 

  6. Biryukov, A., Nikolić, I.: Automatic search for related-key differential characteristics in byte-oriented block ciphers: application to AES, Camellia, Khazad and others. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 322–344. Springer, Heidelberg (2010)

    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)

    Google Scholar 

  8. Blondeau, C., Gérard, B.: Multiple differential cryptanalysis: theory and practice. In: Joux, A. (ed.) FSE 2011. LNCS, vol. 6733, pp. 35–54. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  9. Blondeau, C., Gérard, B., Nyberg, K.: Multiple differential cryptanalysis using LLR and statistics. In: Visconti, I., De Prisco, R. (eds.) SCN 2012. LNCS, vol. 7485, pp. 343–360. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  10. Granlund, T., et al.: The GNU Multiple Precision Arithmetic Library, 2.0.2 edn. TMG Datakonsult, Boston (1996)

    Google Scholar 

  11. Knudsen, L.R., Robshaw, M.: The Block Cipher Companion. Springer Science & Business Media, Heidelberg (2011)

    Book  MATH  Google Scholar 

  12. Lu, J., Yap, W.-S., Wei, Y.: Weak keys of the full MISTY1 block cipher for related-key differential cryptanalysis. In: Dawson, E. (ed.) CT-RSA 2013. LNCS, vol. 7779, pp. 389–404. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  13. Matsui, M.: On correlation between the order of S-Boxes and the strength of DES. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 366–375. Springer, Heidelberg (1995)

    Google Scholar 

  14. Neyman, J., Pearson, E.S.: On the Problem of the Most Efficient Tests of Statistical Hypotheses. Springer, New York (1992)

    Book  MATH  Google Scholar 

  15. O’Connor, L., Goli, J.: A unified Markov approach to differential and linear cryptanalysis. In: Safavi-Naini, R., Pieprzyk, J.P. (eds.) ASIACRYPT 1994. LNCS, vol. 917, pp. 385–397. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  16. Özen, O., Varıcı, K., Tezcan, C., Kocair, Ç.: Lightweight block ciphers revisited: cryptanalysis of reduced round PRESENT and HIGHT. In: Boyd, C., González Nieto, J. (eds.) ACISP 2009. LNCS, vol. 5594, pp. 90–107. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  17. Shibutani, K.: On the diffusion of generalized Feistel structures regarding differential and linear cryptanalysis. In: Biryukov, A., Gong, G., Stinson, D.R. (eds.) SAC 2010. LNCS, vol. 6544, pp. 211–228. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  18. Shirai, T., Shibutani, K., Akishita, T., Moriai, S., Iwata, T.: The 128-bit blockcipher CLEFIA (Extended Abstract). In: Biryukov, A. (ed.) FSE 2007. LNCS, vol. 4593, pp. 181–195. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  19. Sun, S., Hu, L., Wang, P., Qiao, K., Ma, X., Song, L.: Automatic security evaluation and (related-key) differential characteristic search: application to SIMON, PRESENT, LBlock, DES(L) and other bit-oriented block ciphers. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8873, pp. 158–178. Springer, Heidelberg (2014)

    Google Scholar 

  20. Suzaki, T., Minematsu, K.: Improving the generalized Feistel. In: Hong, S., Iwata, T. (eds.) FSE 2010. LNCS, vol. 6147, pp. 19–39. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  21. Suzaki, T., Minematsu, K., Morioka, S., Kobayashi, E.: TWINE: a lightweight block cipher for multiple platforms. In: Knudsen, L.R., Wu, H. (eds.) SAC 2012. LNCS, vol. 7707, pp. 339–354. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  22. Wu, W., Zhang, L.: LBlock: a lightweight block cipher. In: Lopez, J., Tsudik, G. (eds.) ACNS 2011. LNCS, vol. 6715, pp. 327–344. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer School, Central China Normal University, Wuhan, 430079, China

    Jiageng Chen

  2. School of Information Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa, 923-1292, Japan

    Atsuko Miyaji & Chunhua Su

  3. Japan Science and Technology Agency (JST) CREST, Kawaguchi Center Building 4-1-8, Honcho, Kawaguchi-shi, Saitama, 332-0012, Japan

    Atsuko Miyaji

  4. Graduate School of Engineering, Osaka University, Osaka, Japan

    Atsuko Miyaji

  5. School of Computer Sciences, Universiti Sains Malaysia, Gelugor, Malaysia

    Je Sen Teh

Authors
  1. Jiageng Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Atsuko Miyaji
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chunhua Su
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Je Sen Teh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiageng Chen .

Editor information

Editors and Affiliations

  1. Chinese Academy of Sciences, SKLOIS Institute of Engineering, Beijing, China

    Dongdai Lin

  2. Center for Security Informatics, Indiana University at Bloomington, Indiana, USA

    XiaoFeng Wang

  3. Computer Science, Columbia University, New York, New York, USA

    Moti Yung

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Chen, J., Miyaji, A., Su, C., Teh, J.S. (2016). Accurate Estimation of the Full Differential Distribution for General Feistel Structures. In: Lin, D., Wang, X., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2015. Lecture Notes in Computer Science(), vol 9589. Springer, Cham. https://doi.org/10.1007/978-3-319-38898-4_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-38898-4_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-38897-7

  • Online ISBN: 978-3-319-38898-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation