Multi-Collision Resistant Hash Functions and Their Applications

  • Itay Berman
  • Akshay Degwekar
  • Ron D. Rothblum
  • Prashant Nalini Vasudevan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10821)

Abstract

Collision resistant hash functions are functions that shrink their input, but for which it is computationally infeasible to find a collision, namely two strings that hash to the same value (although collisions are abundant).

In this work we study multi-collision resistant hash functions (\(\mathsf {MCRH}\)) a natural relaxation of collision resistant hash functions in which it is difficult to find a t-way collision (i.e., t strings that hash to the same value) although finding \((t-1)\)-way collisions could be easy. We show the following:
  • The existence of \(\mathsf {MCRH}\) follows from the average case hardness of a variant of the Entropy Approximation problem. The goal in this problem (Goldreich, Sahai and Vadhan, CRYPTO ’99) is to distinguish circuits whose output distribution has high entropy from those having low entropy.

  • \(\mathsf {MCRH}\) imply the existence of constant-round statistically hiding (and computationally binding) commitment schemes. As a corollary, using a result of Haitner et al. (SICOMP, 2015), we obtain a blackbox separation of \(\mathsf {MCRH}\) from any one-way permutation.

Notes

Acknowledgments

We thank Vinod Vaikuntanathan for helpful discussions and for his support, and Oded Goldreich, Yuval Ishai and the anonymous reviewers for useful comments. We thank Nir Bitansky, Yael Kalai, Ilan Komargodski, Moni Naor, Omer Paneth and Eylon Yogev for helping us provide a good example of a t-way collision. We also thank Nir Bitansky and an anonymous reviewer for pointing out the connection to inaccessible entropy.

This research was 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. The third author was also partially supported by the SIMONS Investigator award agreement dated 6-5-12 and by the Cybersecurity and Privacy Institute at Northeastern University.

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Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  • Itay Berman
    • 1
  • Akshay Degwekar
    • 1
  • Ron D. Rothblum
    • 1
    • 2
  • Prashant Nalini Vasudevan
    • 1
  1. 1.MITCambridgeUSA
  2. 2.Northeastern UniversityBostonUSA

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