International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Inside the Hypercube

Jean-Philippe Aumasson
Willi Meier
María Naya-Plasencia
Thomas Peyrin
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Abstract: Bernstein's CubeHash is a hash function family that includes four functions submitted to the NIST Hash Competition. A CubeHash function is parametrized by a number of rounds r, a block byte size b, and a digest bit length h (the compression function makes r rounds, while the finalization function makes 10r rounds). The 1024-bit internal state of CubeHash is represented as a five-dimensional hypercube. The submissions to NIST recommends r=8, b=1, and h in {224,256,384,512}. This paper presents the first external analysis of CubeHash, with: improved standard generic attacks for collisions and preimages; a multicollision attack that exploits fixed points; a study of the round function symmetries; a preimage attack that exploits these symmetries; a practical collision attack on a weakened version of CubeHash; a study of fixed points and an example of nontrivial fixed point; high-probability truncated differentials over 10 rounds. Since the first publication of these results, several collision attacks for reduced versions of CubeHash were published by Dai, Peyrin, et al. Our results are more general, since they apply to any choice of the parameters, and show intrinsic properties of the CubeHash design, rather than attacks on specific versions.
  title={Inside the Hypercube},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography /},
  note={ 14305 received 19 Nov 2008, last revised 2 Mar 2009},
  author={Jean-Philippe Aumasson and Willi Meier and María Naya-Plasencia and Thomas Peyrin},