Cryptology ePrint Archive: Report 2009/382

Linearization Framework for Collision Attacks: Application to CubeHash and MD6

Eric Brier and Shahram Khazaei and Willi Meier and Thomas Peyrin

Abstract: In this paper, an improved differential cryptanalysis framework for finding collisions in hash functions is provided. Its principle is based on linearization of compression functions in order to find low weight differential characteristics as initiated by Chabaud and Joux. This is formalized and refined however in several ways: for the problem of finding a conforming message pair whose differential trail follows a linear trail, a condition function is introduced so that finding a collision is equivalent to finding a preimage of the zero vector under the condition function. Then, the dependency table concept shows how much influence every input bit of the condition function has on each output bit. Careful analysis of the dependency table reveals degrees of freedom that can be exploited in accelerated preimage reconstruction under the condition function. These concepts are applied to an in-depth collision analysis of reduced-round versions of the two SHA-3 candidates CubeHash and MD6, and are demonstrated to give by far the best currently known collision attacks on these SHA-3 candidates.

Category / Keywords: Hash functions, collisions, differential attack, SHA-3, CubeHash and MD6

Publication Info: The short version appears in the proceeding of ASIACYPT 2009.

Date: received 4 Aug 2009, last revised 3 Sep 2009

Contact author: shahram khazaei at gmail com

Available format(s): PDF | BibTeX Citation

Version: 20090903:153437 (All versions of this report)

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