Designs, Codes and Cryptography

, Volume 80, Issue 3, pp 587–618 | Cite as

Extended meet-in-the-middle attacks on some Feistel constructions

  • Jian Guo
  • Jérémy Jean
  • Ivica Nikolić
  • Yu Sasaki
Article
  • 386 Downloads

Abstract

We show key recovery attacks on generic balanced Feistel ciphers. The analysis is based on the meet-in-the-middle technique and exploits truncated differentials that are present in the ciphers due to the Feistel construction. Depending on the type of round function, we differentiate and show attacks on two types of Feistels. For the first type, which is one of the most practical Feistels, we show a 5-round distinguisher based on a truncated differential, which allows to launch 6-round and 10-round attacks, for single-key and double-key sizes, respectively. For the second type of Feistels, with round functions that follow the SPN structure composed of linear layers with maximal branch number, based on a 7-round distinguisher we show attacks that reach up to 14 rounds. Our attacks outperform all the known attacks for any key sizes and provide new lower bounds on the number of rounds required to achieve a practical and a secure Feistel. The attacks on first type have been experimentally verified with computer implementations of the attacks on small-state ciphers.

Keywords

Feistel Generic attack Key recovery Meet-in-the-middle 

Mathematics Subject Classification

94A60 (cryptography) 

References

  1. 1.
    Aoki K., Guo J., Matusiewicz K., Sasaki Y., Wang L.: Preimages for step-reduced SHA-2. In: Matsui M. (ed.) ASIACRYPT. LNCS, vol. 5912, pp. 578–597. Springer, Berlin (2009).Google Scholar
  2. 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.E. (eds.) Selected Areas in Cryptography. LNCS, vol. 2012, pp. 39–56. Springer, Berlin (2000).Google Scholar
  3. 3.
    Beaulieu R., Shors D., Smith J., Treatman-Clark S., Weeks B., Wingers L.: The SIMON and SPECK families of lightweight block ciphers. Cryptology ePrint Archive, Report 2013/404 (2013).Google Scholar
  4. 4.
    Biham E., Dunkelman O.: The SHAvite-3 hash function. Submission to NIST (Round 2) (2009).Google Scholar
  5. 5.
    CAST: Cryptographic algorithms approved for Canadian government use (2012).Google Scholar
  6. 6.
    Coppersmith D.: The data encryption standard (DES) and its strength against attacks. IBM J. Res. Dev. 38(3), 243–250 (1994).Google Scholar
  7. 7.
    Daemen J., Knudsen L.R., Rijmen V.: The block cipher square. In: Biham, E. (ed.) FSE. LNCS, vol. 1267, pp. 149–165. Springer, Heidelberg (1997).Google Scholar
  8. 8.
    Demirci H., Selçuk A.A.: A meet-in-the-middle attack on 8-round AES. In: Nyberg K. (ed.) FSE. LNCS, vol. 5086, pp. 116–126. Springer, Heidelberg (2008).Google Scholar
  9. 9.
    Derbez P., Fouque P.A., Jean J.: Improved key recovery attacks on reduced-round AES in the single-key setting. IACR Cryptology ePrint Archive 2012, 477 (2012).Google Scholar
  10. 10.
    Derbez P., Fouque P.A., Jean J.: Improved key recovery attacks on reduced-round AES in the single-key setting. In: Johansson T., Nguyen P.Q. (eds.) EUROCRYPT. LNCS, vol. 7881, pp. 371–387. Springer, Heidelberg (2013).Google Scholar
  11. 11.
    Dinur I., Dunkelman O., Keller N., Shamir A.: Efficient dissection of composite problems, with applications to cryptanalysis, knapsacks, and combinatorial search problems. In: Safavi-Naini R., Canetti R. (eds.) CRYPTO. LNCS, vol. 7417, pp. 719–740. Springer, Heidelberg (2012).Google Scholar
  12. 12.
    Dunkelman O., Keller N., Shamir A.: Improved single-key attacks on 8-round AES-192 and AES-256. In: Abe M. (ed.) ASIACRYPT. LNCS, vol. 6477, pp. 158–176. Springer, Heidelberg (2010).Google Scholar
  13. 13.
    Feistel H., Notz W., Smith J.: Some cryptographic techniques for machine-to-machine data communications. Proc. IEEE. 63(11), 1545–1554 (1975).Google Scholar
  14. 14.
    Gilbert H., Minier M.: A collision attack on 7 rounds of Rijndael. In: AES Candidate Conference, pp. 230–241 (2000).Google Scholar
  15. 15.
    Guo J., Ling S., Rechberger C., Wang H.: Advanced meet-in-the-middle preimage attacks: first results on full tiger, and improved results on MD4 and SHA-2. In: Abe M. (ed.) ASIACRYPT. LNCS, vol. 6477, pp. 56–75 Springer, Heidelberg (2010).Google Scholar
  16. 16.
    ISO/IEC: Information technology—security techniques—encryption algorithms—part 3: block ciphers (2010).Google Scholar
  17. 17.
    Isobe T., Shibutani K.: All subkeys recovery attack on block ciphers: extending meet-in-the-middle approach. In: Knudsen LR, Wu H. (eds.) Selected Areas in Cryptography. LNCS, vol. 7707, pp. 202–221. Springer, Heidelberg (2012).Google Scholar
  18. 18.
    Isobe T., Shibutani K.: Generic key recovery attack on feistel scheme. In: Sako K., Sarkar P. (eds.) ASIACRYPT (1). LNCS, vol. 8269, pp. 464–485. Springer, Heidelberg (2013).Google Scholar
  19. 19.
    Knudsen L.R.: The security of feistel ciphers with six rounds or less. J. Cryptol. 15(3), 207–222 (2002).Google Scholar
  20. 20.
    Luby M., Rackoff C.: How to construct pseudorandom permutations from pseudorandom functions. SIAM J. Comput. 17(2), 373–386 (1988).Google Scholar
  21. 21.
    Merkle R.C., Hellman M.E.: On the security of multiple encryption. Commun. ACM 24(7), 465–467 (1981).Google Scholar
  22. 22.
    Sasaki Y., Aoki K.: Finding preimages in full MD5 faster than exhaustive search. In: Joux A. (ed.) EUROCRYPT. LNCS, vol. 5479, pp. 134–152. Springer, Heidelberg (2009).Google Scholar
  23. 23.
    Shibutani K., Bogdanov A.: Towards the optimality of Feistel ciphers with substitution-permutation functions. Des. Codes Cryptogr. 73(2), 667–682 (2014).Google Scholar
  24. 24.
    Shibutani K., Isobe T., Hiwatari H., Mitsuda A., Akishita T., Shirai T.: Piccolo: an ultra-lightweight blockcipher. In: Preneel B., Takagi T. (eds.) CHES. LNCS, vol. 6917, pp. 342–357. Springer, Heidelberg (2011).Google Scholar
  25. 25.
    Todo Y.: Upper bounds for the security of several feistel networks. In: Boyd C., Simpson L. (eds.) ACISP. LNCS, vol. 7959, pp. 302–317. Springer, Heidelberg (2013).Google Scholar
  26. 26.
    Wu W., Zhang L.: LBlock: a lightweight block cipher. In: Lopez J., Tsudik G. (eds.) ACNS. LCNS, vol. 6715, pp. 327–344. Springer, Berlin (2011).Google Scholar
  27. 27.
    Zhang L., Wu W., Wang Y., Wu S., Zhang J.: LAC: a lightweight authenticated encryption cipher. Submitted to the CAESAR competition (2014).Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Jian Guo
    • 1
  • Jérémy Jean
    • 1
  • Ivica Nikolić
    • 1
  • Yu Sasaki
    • 1
    • 2
  1. 1.Division of Mathematical Sciences, School of Physical and Mathematical SciencesNanyang Technological UniversitySingaporeSingapore
  2. 2.NTT Information Sharing Platform LaboratoriesNTT CorporationMusashino-shiJapan

Personalised recommendations