International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: How to Build a Hash Function from any Collision-Resistant Function

Thomas Ristenpart
Thomas Shrimpton
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Abstract: Recent collision-finding attacks against hash functions such as MD5 and SHA-1 motivate the use of provably collision-resistant (CR) functions in their place. Finding a collision in a provably CR function implies the ability to solve some hard problem (e.g., factoring). Unfortunately, existing provably CR functions make poor replacements for hash functions as they fail to deliver behaviors demanded by practical use. In particular, they are easily distinguished from a random oracle. We initiate an investigation into building hhash functions from provably CR functions. As a method for achieving this, we present the Mix-Compress-Mix (MCM) construction; it envelopes any provably CR function H (with suitable regularity properties) between two injective ``mixing'' stages. The MCM construction simultaneously enjoys (1) provable collision-resistance in the standard model, and (2) indifferentiability from a monolithic random oracle when the mixing stages themselves are indifferentiable from a random oracle that observes injectivity. We instantiate our new design approach by specifying a blockcipher-based construction that appropriately realizes the mixing stages.
  title={How to Build a Hash Function from any Collision-Resistant Function},
  booktitle={IACR Eprint archive},
  keywords={Hash functions, random oracle, collision-resistance, pseudorandom oracles, indifferentiability},
  note={A preliminary version appeared at Asiacrypt 2007. 13995 received 26 Apr 2008, last revised 26 Apr 2008},
  author={Thomas Ristenpart and Thomas Shrimpton},