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Revision #1 to TR22-017 | 23rd February 2022 10:38

Collision-Resistance from Multi-Collision-Resistance

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Revision #1
Authors: Ron D. Rothblum, Prashant Nalini Vasudevan
Accepted on: 23rd February 2022 10:38
Downloads: 51
Keywords: 


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.



Changes to previous version:

Removed references to the blackbox separation of Komargodski et al. (Eurocrypt, 2018) as their proof has a bug.


Paper:

TR22-017 | 15th February 2022 10:46

Collision-Resistance from Multi-Collision-Resistance





TR22-017
Authors: Ron D. Rothblum, Prashant Nalini Vasudevan
Publication: 15th February 2022 17:00
Downloads: 140
Keywords: 


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. In particular, Komargodski et al. (Eurocrypt, 2018) showed that there does not exist a blackbox transformation of MCRH into CRH. Nevertheless, in this work we show a non-blackbox transformation of any moderately shrinking t-MCRH, for t in {3,4}, 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.



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