Paper 2007/352

New Local Collisions for the SHA-2 Hash Family

Somitra Kumar Sanadhya and Palash Sarkar


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.

Note: This is the revised version of the paper. Revision date : Oct 10th 2007.

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Published elsewhere. Shorter version of this work accepted in "International Conference on Information Security and Cryptology, Seoul, Korea 2007"
cryptanalysishash functionSHA-2local collisionreduced round collision
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somitra_r @ isical ac in
2007-10-11: revised
2007-09-13: received
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      author = {Somitra Kumar Sanadhya and Palash Sarkar},
      title = {New Local Collisions for the SHA-2 Hash Family},
      howpublished = {Cryptology ePrint Archive, Paper 2007/352},
      year = {2007},
      note = {\url{}},
      url = {}
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