Multi Collision Resistant Hash Functions and their Applications

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: • The existence of MCRH follows from the average case hardness of a variant of Entropy Approximation, a problem known to be complete for the class NISZK. • MCRH imply the existence of constant-round statistically hiding (and computationally binding) commitment schemes. In addition, we show a blackbox separation of MCRH from any one-way permutation. ∗MIT. Emails: {itayberm, akshayd, ronr, prashvas}@mit.edu. Research 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. ISSN 1433-8092 Electronic Colloquium on Computational Complexity, Report No. 97 (2017)