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Speeding up Collision Search for Byte-Oriented Hash Functions

  • Dmitry Khovratovich
  • Alex Biryukov
  • Ivica Nikolic
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5473)

Abstract

We describe a new tool for the search of collisions for hash functions. The tool is applicable when an attack is based on a differential trail, whose probability determines the complexity of the attack. Using the linear algebra methods we show how to organize the search so that many (in some cases — all) trail conditions are always satisfied thus significantly reducing the number of trials and the overall complexity.

The method is illustrated with the collision and second preimage attacks on the compression functions based on Rijndael. We show that slow diffusion in the Rijndael (and AES) key schedule allows to run an attack on a version with a 13-round compression function, and the S-boxes do not prevent the attack. We finally propose how to modify the key schedule to resist the attack and provide lower bounds on the complexity of the generic differential attacks for our modification.

Keywords

Hash Function Free Variable Block Cipher Compression Function Round Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Aumasson, J.-P., Meier, W., Phan, R.C.-W.: The hash function family LAKE. In: Nyberg, K. (ed.) FSE 2008. LNCS, vol. 5086, pp. 36–53. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  2. 2.
    Bentahar, K., Page, D., Saarinen, M.-J.O., Silverman, J.H., Smart, N.: LASH, Tech. report, NIST Cryptographic Hash Workshop (2006)Google Scholar
  3. 3.
    Bertoni, G., Daemen, J., Peeters, M., van Assche, G.: Radiogatun, a belt-and-mill hash function (2006), http://radiogatun.noekeon.org/
  4. 4.
    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
  5. 5.
    Cohen, B.: AES-hash, International Organization for Standardization (2001)Google Scholar
  6. 6.
    Contini, S., Matusiewicz, K., Pieprzyk, J., Steinfeld, R., Jian, G., San, L., Wang, H.: Cryptanalysis of LASH. In: Nyberg, K. (ed.) FSE 2008. LNCS, vol. 5086, pp. 207–223. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Daemen, J., Rijmen, V.: AES proposal: Rijndael, Tech. report (1999), http://csrc.nist.gov/archive/aes/rijndael/Rijndael-ammended.pdf
  8. 8.
    Daemen, J., Rijmen, V.: The wide trail design strategy. In: IMA Int. Conf., pp. 222–238 (2001)Google Scholar
  9. 9.
  10. 10.
    FIPS 180-2. secure hash standard (2002), http://csrc.nist.gov/publications/
  11. 11.
    International Organization for Standardization, The Whirlpool hash function. iso/iec 10118-3:2004 (2004)Google Scholar
  12. 12.
    Knudsen, L.R., Rechberger, C., Thomsen, S.S.: The grindahl hash functions. In: Biryukov, A. (ed.) FSE 2007. LNCS, vol. 4593, pp. 39–57. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    Manuel, S., Peyrin, T.: Collisions on SHA-0 in one hour. In: Nyberg, K. (ed.) FSE 2008. LNCS, vol. 5086, pp. 16–35. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  14. 14.
    Matusiewicz, K., Peyrin, T., Billet, O., Contini, S., Pieprzyk, J.: Cryptanalysis of FORK-256. In: Biryukov, A. (ed.) FSE 2007. LNCS, vol. 4593, pp. 19–38. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  15. 15.
    Peyrin, T.: Cryptanalysis of Grindahl. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 551–567. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  16. 16.
    Preneel, B., Govaerts, R., Vandewalle, J.: Hash functions based on block ciphers: A synthetic approach. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 368–378. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  17. 17.
    Rivest, R.L.: The MD5 message-digest algorithm, request for comments (RFC 1320), Internet Activities Board, Internet Privacy Task Force (1992)Google Scholar
  18. 18.
    Wang, X., Yin, Y.L., Yu, H.: Finding collisions in the full SHA-1. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 17–36. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  19. 19.
    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 2009

Authors and Affiliations

  • Dmitry Khovratovich
    • 1
  • Alex Biryukov
    • 1
  • Ivica Nikolic
    • 1
  1. 1.University of LuxembourgLuxembourg

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