Non-linear Reduced Round Attacks against SHA-2 Hash Family

  • Somitra Kumar Sanadhya
  • Palash Sarkar
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5107)


Most of the attacks against (reduced) SHA-2 family in literature have used local collisions which are valid for linearized version of SHA-2 hash functions. Recently, at FSE ’08, an attack against reduced round SHA-256 was presented by Nikolić and Biryukov which used a local collision which is valid for the actual SHA-256 function. It is a 9-step local collision which starts by introducing a modular difference of 1 in the two messages. It succeeds with probability roughly 1/3. We build on the work of Nikolić and Biryukov and provide a generalized nonlinear local collision which accepts an arbitrary initial message difference. This local collision succeeds with probability 1. Using this local collision we present attacks against 18-step SHA-256 and 18-step SHA-512 with arbitrary initial difference. Both of these attacks succeed with probability 1. We then present special cases of our local collision and show two different differential paths for attacking 20-step SHA-256 and 20-step SHA-512. One of these paths is the same as presented by Nikolić and Biryukov while the other one is a new differential path. Messages following both these differential paths can be found with probability 1. This improves on the previous result where the success probability of 20-step attack was 1/3. Finally, we present two differential paths for 21-step collisions for SHA-256 and SHA-512, one of which is a new path. The success probabilities of these paths for SHA-256 are roughly 2− 15 and 2− 17 which improve on the 21-step attack having probability 2− 19 reported earlier. We show examples of message pairs following all the presented differential paths for up to 21-step collisions in SHA-256. We also show first real examples of colliding message pairs for up to 20-step reduced SHA-512.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chabaud, F., Joux, A.: Differential Collisions in SHA-0. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 56–71. Springer, Heidelberg (1998)Google Scholar
  2. 2.
    Gilbert, H., Handschuh, H.: Security Analysis of SHA-256 and Sisters. In: Matsui, M., Zuccherato, R.J. (eds.) Selected Areas in Cryptography, 10th Annual International Workshop, SAC 2003, Ottawa, Canada, August 14-15, 2003. LNCS, vol. 3006, pp. 175–193. Springer, Heidelberg (2003)Google Scholar
  3. 3.
    Hawkes, P., Paddon, M., Rose, G.G.: On Corrective Patterns for the SHA-2 Family. Cryptology eprint Archive (August 2004),
  4. 4.
    Mendel, F., Pramstaller, N., Rechberger, C., Rijmen, V.: Analysis of Step-Reduced SHA-256. In: Robshaw, M.J.B. (ed.) FSE 2006. LNCS, vol. 4047, pp. 126–143. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Mendel, F., Pramstaller, N., Rechberger, C., Rijmen, V.: Analysis of Step-Reduced SHA-256. Cryptology eprint Archive (March 2008),
  6. 6.
    Nikolić, I., Biryukov, A.: Collisions for Step-Reduced SHA-256. In: Nyberg, K. (ed.) Fast Software Encryption 2008. LNCS, pp. 1–16. Springer, Heidelberg (2008)Google Scholar
  7. 7.
    Sanadhya, S.K., Sarkar, P.: New Local Collisions for the SHA-2 Hash Family. In: Nam, K.-H., Rhee, G. (eds.) ICISC 2007. LNCS, vol. 4817, pp. 193–205. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. 8.
    Sanadhya, S.K., Sarkar, P.: Attacking Reduced Round SHA-256. In: Bellovin, S., Gennaro, R. (eds.) ACNS 2008. LNCS. Springer, Heidelberg (to appear, 2008)Google Scholar
  9. 9.
    Sanadhya, S.K., Sarkar, P.: Non-Linear Reduced Round Attacks Against SHA-2 Hash family. Cryptology eprint Archive (April 2008),
  10. 10.
    Shoup, V. (ed.): CRYPTO 2005. LNCS, vol. 3621. Springer, Heidelberg (2005)zbMATHGoogle Scholar
  11. 11.
    Secure Hash Standard. Federal Information Processing Standard Publication 180-2. U.S. Department of Commerce, National Institute of Standards and Technology(NIST) (2002),
  12. 12.
    Wang, X., Yin, Y.L., Yu, H.: Finding Collisions in the Full SHA-1. In: Shoup (ed.) [10], pp. 17–36Google Scholar
  13. 13.
    Wang, X., Yu, H.: How to Break MD5 and Other Hash Functions. In: Cramer, R.J.F. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 19–35. Springer, Heidelberg (2005)Google Scholar
  14. 14.
    Wang, X., Yu, H., Yin, Y.L.: Efficient Collision Search Attacks on SHA-0. In: Shoup [10], pp. 1–16Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Somitra Kumar Sanadhya
    • 1
  • Palash Sarkar
    • 1
  1. 1.Applied Statistics UnitIndian Statistical InstituteKolkataIndia

Personalised recommendations