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On the Complexity of Collision Resistant Hash Functions: New and Old Black-Box Separations

  • Nir BitanskyEmail author
  • Akshay Degwekar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11891)

Abstract

The complexity of collision-resistant hash functions has been long studied in the theory of cryptography. While we often think about them as a Minicrypt primitive, black-box separations demonstrate that constructions from one-way functions are unlikely. Indeed, theoretical constructions of collision-resistant hash functions are based on rather structured assumptions.

We make two contributions to this study:
  1. 1.

    A New Separation: We show that collision-resistant hashing does not imply hard problems in the class Statistical Zero Knowledge in a black-box way.

     
  2. 2.

    New Proofs: We show new proofs for the results of Simon, ruling out black-box reductions of collision-resistant hashing to one-way permutations, and of Asharov and Segev, ruling out black-box reductions to indistinguishability obfuscation. The new proofs are quite different from the previous ones and are based on simple coupling arguments.

     

Notes

Acknowledgements

Nir Bitansky is a member of the Check Point Institute of Information Security. Supported by the Alon Young Faculty Fellowship, by Len Blavatnik and the Blavatnik Family foundation, and an ISF grant 18/484. Akshay Degwekar did part of this work while visiting the FACT Center in IDC Herzliya, supported in part by ISF grant 1861/16 and AFOSR Award FA9550-17-1-0069. Also supported in part by NSF Grants CNS-1413920 and CNS-1350619, and by the Defense Advanced Research Projects Agency (DARPA) and the U.S. Army Research Office under contracts W911NF-15-C-0226 and W911NF-15-C-0236.

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© International Association for Cryptologic Research 2019

Authors and Affiliations

  1. 1.Tel Aviv UniversityTel AvivIsrael
  2. 2.MITCambridgeUSA

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