How to build a hash function from any collision-resistant function

  • Authors:
  • Thomas Ristenpart;Thomas Shrimpton

  • Affiliations:
  • Dept. of Computer Science & Engineering, University of California San Diego, La Jolla, CA;Dept. of Computer Science, Portland State University, Portland, OR and Faculty of Informatics, University of Lugano, Lugano, Switzerland

  • Venue:
  • ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
  • Year:
  • 2007

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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 hash 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.