**Multi Collision Resistant Hash Functions and their Applications**

*Itay Berman and Akshay Degwekar and Ron D. Rothblum and Prashant Nalini Vasudevan*

**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 (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:

1. The existence of MCRH follows from the average case hardness of a variant of the Entropy Approximation problem. The goal in the entropy approximation problem (Goldreich, Sahai and Vadhan, CRYPTO '99) is to distinguish circuits whose output distribution has high entropy from those having low entropy.

2. 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 MCRH from any one-way permutation.

**Category / Keywords: **foundations / collision resistant hashing, entropy approximation

**Date: **received 29 May 2017, last revised 26 Sep 2017

**Contact author: **ronr at mit edu

**Available format(s): **PDF | BibTeX Citation

**Version: **20170926:195320 (All versions of this report)

**Short URL: **ia.cr/2017/489

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