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Paper: New Local Collisions for the SHA-2 Hash Family

Authors:
Somitra Kumar Sanadhya
Palash Sarkar
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URL: http://eprint.iacr.org/2007/352
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Abstract: The starting point for collision attacks on practical hash functions is a local collision. In this paper, we make a systematic study of local collisions for the SHA-2 family. The possible linear approximations of the constituent Boolean functions are considered and certain impossible conditions for such approximations are identified. Based on appropriate approximations, we describe a general method for finding local collisions. Applying this method, we obtain several local collisions and compute the probabilities of the various differential paths. Previously, only one local collision due to Gilbert-Handschuh was known. We point out two impossible conditions in the GH local collision and provide an example of an impossible differential path for linearized SHA-2 using this local collision. Sixteen new local collisions are obtained none of which have any impossible conditions. The probabilities of these local collisions are a little less than the GH local collision. On the other hand, the absence of impossible conditions may make them more suitable for (reduced round) collision search attacks on the SHA-2 family.
BibTeX
@misc{eprint-2007-13632,
  title={New Local Collisions for the SHA-2 Hash Family},
  booktitle={IACR Eprint archive},
  keywords={foundations / cryptanalysis, hash function, SHA-2, local collision, reduced round collision},
  url={http://eprint.iacr.org/2007/352},
  note={Shorter version of this work accepted in "International Conference on Information Security and Cryptology, Seoul, Korea 2007" somitra_r@isical.ac.in 13797 received 6 Sep 2007, last revised 10 Oct 2007},
  author={Somitra Kumar Sanadhya and Palash Sarkar},
  year=2007
}