Cryptology ePrint Archive: Report 2022/173

Collision-Resistance from Multi-Collision-Resistance

Ron D. Rothblum and Prashant Nalini Vasudevan

Abstract: Collision-resistant hash functions (CRH) are a fundamental and ubiquitous cryptographic primitive. Several recent works have studied a relaxation of CRH called t-way multi-collision-resistant hash functions (t-MCRH). These are families of functions for which it is computationally hard to find a t-way collision, even though such collisions are abundant (and even (t-1)-way collisions may be easy to find). The case of t=2 corresponds to standard CRH, but it is natural to study t-MCRH for larger values of t.

Multi-collision-resistance seems to be a qualitatively weaker property than standard collision-resistance. Nevertheless, in this work we show a non-blackbox transformation of any moderately shrinking t-MCRH, for t in {2,4}, into an (infinitely often secure) CRH. This transformation is non-constructive - we can prove the existence of a CRH but cannot explicitly point out a construction.

Our result partially extends to larger values of t. In particular, we show that for suitable values of t>t', we can transform a t-MCRH into a t'-MCRH, at the cost of reducing the shrinkage of the resulting hash function family and settling for infinitely often security. This result utilizes the list-decodability properties of Reed-Solomon codes.

Category / Keywords: foundations / Collision-Resistant Hash Functions, Multicollision Resistance

Date: received 15 Feb 2022, last revised 23 Feb 2022

Contact author: prashant at comp nus edu sg, rothblum at cs technion ac il

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Version: 20220223:083810 (All versions of this report)

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