Differential Cryptanalysis of Keccak Variants

  • Stefan Kölbl
  • Florian Mendel
  • Tomislav Nad
  • Martin Schläffer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8308)

Abstract

In October 2012, NIST has announced Keccak as the winner of the SHA-3 cryptographic hash function competition. Recently, at CT-RSA 2013, NIST brought up the idea to standardize Keccak variants with different parameters than those submitted to the SHA-3 competition. In particular, NIST considers to reduce the capacity to the output size of the SHA-3 standard and additionally, standardize a Keccak variant with a permutation size of 800 instead of 1600 bits. However, these variants have not been analyzed very well during the SHA-3 competition. Especially for the variant using an 800-bit permutation no analysis on the hash function has been published so far.

In this work, we analyze these newly proposed Keccak variants and provide practical collisions for up to 4 rounds for all output sizes by constructing internal collisions. Our attacks are based on standard differential cryptanalysis contrary to the recent attacks by Dinur at al. from FSE 2013. We use a non-linear low probability path for the first two rounds and use methods from coding theory to find a high-probability path for the last two rounds. The low probability path as well as the conforming message pair is found using an automatic differential path search tool. Our results indicate that reducing the capacity slightly improves attacks, while reducing the permutation size degrades attacks on Keccak.

Keywords

hash functions SHA-3 collision attack differential cryptanalysis 

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References

  1. 1.
    Bertoni, G., Daemen, J., Peeters, M., Van Assche, G.: On the Indifferentiability of the Sponge Construction. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 181–197. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  2. 2.
    Bertoni, G., Daemen, J., Peeters, M., Van Assche, G.: The Keccak reference. Submission to NIST (Round 3) (January 2011), http://csrc.nist.gov/groups/ST/hash/sha-3/Round3/submissions_rnd3.html
  3. 3.
    Biham, E., Shamir, A.: Differential Cryptanalysis of DES-like Cryptosystems. J. Cryptology 4(1), 3–72 (1991)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Brier, E., Khazaei, S., Meier, W., Peyrin, T.: Linearization Framework for Collision Attacks: Application to CubeHash and MD6. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 560–577. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Canteaut, A., Chabaud, F.: A New Algorithm for Finding Minimum-Weight Words in a Linear Code: Application to McEliece’s Cryptosystem and to Narrow-Sense BCH Codes of Length 511. IEEE Transactions on Information Theory 44(1), 367–378 (1998)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Daemen, J., Van Assche, G.: Differential Propagation Analysis of Keccak. In: Canteaut, A. (ed.) FSE 2012. LNCS, vol. 7549, pp. 422–441. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  7. 7.
    De Cannière, C., Rechberger, C.: Finding SHA-1 Characteristics: General Results and Applications. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 1–20. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Dinur, I., Dunkelman, O., Shamir, A.: New Attacks on Keccak-224 and Keccak-256. In: Canteaut, A. (ed.) FSE 2012. LNCS, vol. 7549, pp. 442–461. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  9. 9.
    Dinur, I., Dunkelman, O., Shamir, A.: Collision Attacks on Up to 5 Rounds of SHA-3 Using Generalized Internal Differentials. In: Moriai, S. (ed.) FSE. LNCS, Springer (to appear, 2013)Google Scholar
  10. 10.
    Eichlseder, M., Mendel, F., Nad, T., Rijmen, V., Schläffer, M.: Linear Propagation in Efficient Guess-and-Determine Attacks. In: Budaghyan, L., Helleseth, T., Parker, M.G. (eds.) WCC (2013), http://www.selmer.uib.no/WCC2013/
  11. 11.
    Indesteege, S., Preneel, B.: Practical Collisions for EnRUPT. J. Cryptology 24(1), 1–23 (2011)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Mendel, F., Nad, T.: A Distinguisher for the Compression Function of SIMD-512. In: Roy, B., Sendrier, N. (eds.) INDOCRYPT 2009. LNCS, vol. 5922, pp. 219–232. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  13. 13.
    Mendel, F., Nad, T., Schläffer, M.: Finding SHA-2 Characteristics: Searching through a Minefield of Contradictions. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 288–307. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  14. 14.
    Mendel, F., Nad, T., Schläffer, M.: Improving Local Collisions: New Attacks on Reduced SHA-256. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 262–278. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  15. 15.
    National Institute of Standards and Technology: Cryptographic Hash Algorithm Competition (November 2007), http://csrc.nist.gov/groups/ST/hash/sha-3/index.html
  16. 16.
    National Institute of Standards and Technology: SHA-3 Selection Announcement (October 2012), http://csrc.nist.gov/groups/ST/hash/sha-3/sha-3_selection_announcement.pdf
  17. 17.
    Naya-Plasencia, M., Röck, A., Meier, W.: Practical Analysis of Reduced-Round Keccak. In: Bernstein, D.J., Chatterjee, S. (eds.) INDOCRYPT 2011. LNCS, vol. 7107, pp. 236–254. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  18. 18.
    Rijmen, V., Oswald, E.: Update on SHA-1. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 58–71. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  19. 19.
    Wang, X., Lai, X., Feng, D., Chen, H., Yu, X.: Cryptanalysis of the Hash Functions MD4 and RIPEMD. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 1–18. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  20. 20.
    Wang, X., Yu, H.: How to Break MD5 and Other Hash Functions. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 19–35. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Stefan Kölbl
    • 1
  • Florian Mendel
    • 1
  • Tomislav Nad
    • 1
  • Martin Schläffer
    • 1
  1. 1.IAIKGraz University of TechnologyAustria

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