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Distributional Collision Resistance Beyond One-Way Functions

  • Nir Bitansky
  • Iftach Haitner
  • Ilan Komargodski
  • Eylon YogevEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11478)

Abstract

Distributional collision resistance is a relaxation of collision resistance that only requires that it is hard to sample a collision (xy) where x is uniformly random and y is uniformly random conditioned on colliding with x. The notion lies between one-wayness and collision resistance, but its exact power is still not well-understood. On one hand, distributional collision resistant hash functions cannot be built from one-way functions in a black-box way, which may suggest that they are stronger. On the other hand, so far, they have not yielded any applications beyond one-way functions.

Assuming distributional collision resistant hash functions, we construct constant-round statistically hiding commitment scheme. Such commitments are not known based on one-way functions, and are impossible to obtain from one-way functions in a black-box way. Our construction relies on the reduction from inaccessible entropy generators to statistically hiding commitments by Haitner et al. (STOC ’09). In the converse direction, we show that two-message statistically hiding commitments imply distributional collision resistance, thereby establishing a loose equivalence between the two notions.

A corollary of the first result is that constant-round statistically hiding commitments are implied by average-case hardness in the class \({\textsf {SZK}}\) (which is known to imply distributional collision resistance). This implication seems to be folklore, but to the best of our knowledge has not been proven explicitly. We provide yet another proof of this implication, which is arguably more direct than the one going through distributional collision resistance.

Notes

Acknowledgments

Nir Bitansky is a member of the Check Point Institute of Information Security. Supported by ISF grant 18/484, the Alon Young Faculty Fellowship, and by Len Blavatnik and the Blavatnik Family foundation. Iftach Haitner is a member of the Check Point Institute for Information Security. Research supported by ERC starting grant 638121. Ilan Komargodski is supported in part by an AFOSR grant FA9550-15-1-0262. Eylon Yogev is supported by the European Union’s Horizon 2020 research and innovation program under grant agreement No. 742754.

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Copyright information

© International Association for Cryptologic Research 2019

Authors and Affiliations

  • Nir Bitansky
    • 1
  • Iftach Haitner
    • 1
  • Ilan Komargodski
    • 2
  • Eylon Yogev
    • 3
    Email author
  1. 1.School of Computer ScienceTel Aviv UniversityTel AvivIsrael
  2. 2.Cornell TechNew YorkUSA
  3. 3.TechnionHaifaIsrael

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