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Improved Differential Cryptanalysis on Generalized Feistel Schemes

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Progress in Cryptology – INDOCRYPT 2017 (INDOCRYPT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10698))

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Abstract

Nachef et al. used differential cryptanalysis to study four types of Generalized Feistel Scheme (GFS). They gave the lower bound of maximum number of rounds that is indistinguishable from a random permutation. In this paper, we study the security of several types of GFS by exploiting the asymmetric property. We show that better lower bounds can be achieved for the Type-1 GFS, Type-3 GFS and Alternating Feistel Scheme. Furthermore, we give the first general results regarding to the lower bound of the Unbalanced Feistel Scheme.

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Notes

  1. 1.

    We also examine Type-2 Feistel Scheme, but we cannot improve the previous results since it does not have asymmetric property.

  2. 2.

    The full version will be uploaded to Cryptology ePrint archive soon.

References

  1. Anderson, R., Biham, E.: Two practical and provably secure block ciphers: BEAR and LION. In: Gollmann, D. (ed.) FSE 1996. LNCS, vol. 1039, pp. 113–120. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-60865-6_48

    Chapter  Google Scholar 

  2. Aoki, K., Ichikawa, T., Kanda, M., Matsui, M., Moriai, S., Nakajima, J., Tokita, T.: Camellia: a 128-bit block cipher suitable for multiple platforms — design and analysis. In: Stinson, D.R., Tavares, S. (eds.) SAC 2000. LNCS, vol. 2012, pp. 39–56. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44983-3_4

    Chapter  Google Scholar 

  3. Bertoni, G., Daemen, J., Peeters, M., Van Assche, G.: Keccak Sponge Function Family Main Document. Submission to NIST (Round 2) (2009)

    Google Scholar 

  4. Biham, E., Biryukov, A., Dunkelman, O., Richardson, E., Shamir, A.: Initial observations on skipjack: cryptanalysis of skipjack-3XOR. In: Tavares, S., Meijer, H. (eds.) SAC 1998. LNCS, vol. 1556, pp. 362–375. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48892-8_27

    Chapter  Google Scholar 

  5. Biham, E., Biryukov, A., Shamir, A.: Cryptanalysis of skipjack reduced to 31 rounds using impossible differentials. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 12–23. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48910-X_2

    Google Scholar 

  6. Gueron, S., Mouha, N.: Simpira v2: a family of efficient permutations using the AES round function. In: Cheon, J.H., Takagi, T. (eds.) ASIACRYPT 2016. LNCS, vol. 10031, pp. 95–125. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53887-6_4

    Chapter  Google Scholar 

  7. Hoang, V.T., Rogaway, P.: On generalized feistel networks. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 613–630. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14623-7_33

    Chapter  Google Scholar 

  8. Jutla, C.S.: Generalized birthday attacks on unbalanced Feistel networks. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 186–199. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0055728

    Chapter  Google Scholar 

  9. Knudsen, L.: DEAL - a 128-bit block cipher. In: NIST AES Proposal (1998)

    Google Scholar 

  10. Luby, M., Rackoff, C.: How to construct pseudo-random permutations from pseudo-random functions. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 447–447. Springer, Heidelberg (1986). https://doi.org/10.1007/3-540-39799-X_34

    Chapter  Google Scholar 

  11. Lucks, S.: Faster Luby-Rackoff ciphers. In: Gollmann, D. (ed.) FSE 1996. LNCS, vol. 1039, pp. 189–203. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-60865-6_53

    Chapter  Google Scholar 

  12. Nachef, V., Volte, E., Patarin, J.: Differential attacks on generalized Feistel schemes. In: Abdalla, M., Nita-Rotaru, C., Dahab, R. (eds.) CANS 2013. LNCS, vol. 8257, pp. 1–19. Springer, Cham (2013). https://doi.org/10.1007/978-3-319-02937-5_1

    Chapter  Google Scholar 

  13. Nyberg, K.: Generalized Feistel networks. In: Kim, K., Matsumoto, T. (eds.) ASIACRYPT 1996. LNCS, vol. 1163, pp. 91–104. Springer, Heidelberg (1996). https://doi.org/10.1007/BFb0034838

    Chapter  Google Scholar 

  14. Patarin, J.: Generic attacks on Feistel schemes. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 222–238. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45682-1_14

    Chapter  Google Scholar 

  15. Patarin, J.: Security of random feistel schemes with 5 or more rounds. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 106–122. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-28628-8_7

    Chapter  Google Scholar 

  16. Patarin, J.: Security of Balanced and Unbalanced Feistel Schemes with Linear Non Equalities. Cryptology ePrint Archive, Report 2010/293 (2010). http://eprint.iacr.org/2010/293

  17. Patarin, J., Nachef, V., Berbain, C.: Generic attacks on unbalanced feistel schemes with contracting functions. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 396–411. Springer, Heidelberg (2006). https://doi.org/10.1007/11935230_26

    Chapter  Google Scholar 

  18. Patarin, J., Nachef, V., Berbain, C.: Generic attacks on unbalanced Feistel schemes with expanding functions. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 325–341. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-76900-2_20

    Chapter  Google Scholar 

  19. Schneier, B., Kelsey, J.: Unbalanced Feistel networks and block cipher design. In: Gollmann, D. (ed.) FSE 1996. LNCS, vol. 1039, pp. 121–144. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-60865-6_49

    Chapter  Google Scholar 

  20. 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). https://doi.org/10.1007/978-3-540-74619-5_12

    Chapter  Google Scholar 

  21. Tjuawinata, I., Huang, T., Wu, H.: Cryptanalysis of simpira v2. In: Pieprzyk, J., Suriadi, S. (eds.) ACISP 2017. LNCS, vol. 10342, pp. 384–401. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-60055-0_20

    Chapter  Google Scholar 

  22. Treger, J., Patarin, J.: Generic attacks on feistel networks with internal permutations. In: Preneel, B. (ed.) AFRICACRYPT 2009. LNCS, vol. 5580, pp. 41–59. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-02384-2_4

    Chapter  Google Scholar 

  23. Volte, E., Nachef, V., Patarin, J.: Improved generic attacks on unbalanced feistel schemes with expanding functions. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 94–111. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_6

    Chapter  Google Scholar 

  24. Zheng, Y., Matsumoto, T., Imai, H.: On the construction of block ciphers provably secure and not relying on any unproved hypotheses. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 461–480. Springer, New York (1990). https://doi.org/10.1007/0-387-34805-0_42

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

    Ivan Tjuawinata, Tao Huang & Hongjun Wu

Authors
  1. Ivan Tjuawinata
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  2. Tao Huang
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  3. Hongjun Wu
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Corresponding author

Correspondence to Ivan Tjuawinata .

Editor information

Editors and Affiliations

  1. Indian Institute of Science (IISc), Bengaluru, India

    Arpita Patra

  2. Department of Computer Science, University of Bristol, Bristol, United Kingdom

    Nigel P. Smart

Appendices

A  Expected Value and Variance of Random Variables Concerning Type-1 Feistel Scheme and UFN(\(k',k\)) When \(k'\) Divides k.

The following table summarises the expected value and variance of the random variables used in the analysis of Type-1 Feistel Schemes.

Table 3. Expected value and variance of random variables concerning Type-1 Feistel Schemes
Full size table

The next table summarises the expected values and variances for random variables used in the analysis of UFN(\(k',k\)) when \(k'\) divides k.

Table 4. Expected value and variance for various cases of UFN(\(k',k\))
Full size table
Table 5. Complexity of Unbalanced Feistel Scheme
Full size table

B  Distinguishability Table for UFN(\(k',k\))

The following tables contain the summary of distinguishability of UFN(\(k',k\)) from a random permutation.

Table 6. Summary of distinguishability of Unbalanced Feistel Scheme
Full size table

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Tjuawinata, I., Huang, T., Wu, H. (2017). Improved Differential Cryptanalysis on Generalized Feistel Schemes. In: Patra, A., Smart, N. (eds) Progress in Cryptology – INDOCRYPT 2017. INDOCRYPT 2017. Lecture Notes in Computer Science(), vol 10698. Springer, Cham. https://doi.org/10.1007/978-3-319-71667-1_16

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  • DOI: https://doi.org/10.1007/978-3-319-71667-1_16

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