Collision resistant hashing is a fundamental concept that is the basis for many of the important cryptographic primitives and protocols. Collision resistant hashing is a family of compressing functions such that no efficient adversary can find any collision given a random function in the family. In this work we study a relaxation of collision resistance called distributional collision resistance, introduced by Dubrov and Ishai (STOC ’06). This relaxation of collision resistance only guarantees that no efficient adversary, given a random function in the family, can sample a pair (x, y) where x is uniformly random and y is uniformly random conditioned on colliding with x. Our first result shows that distributional collision resistance can be based on the existence of multi-collision resistance hash (with no additional assumptions). Multi-collision resistance is another relaxation of collision resistance which guarantees that an efficient adversary cannot find any tuple of (formula presented) inputs that collide relative to a random function in the family. The construction is non-explicit, non-black-box, and yields an infinitely-often secure family. This partially resolves a question of Berman et al. (EUROCRYPT ’18). We further observe that in a black-box model such an implication (from multi-collision resistance to distributional collision resistance) does not exist. Our second result is a construction of a distributional collision resistant hash from the average-case hardness of SZK. Previously, this assumption was not known to imply any form of collision resistance (other than the ones implied by one-way functions).
|Title of host publication||Advances in Cryptology – CRYPTO 2018 - 38th Annual International Cryptology Conference, 2018, Proceedings|
|Editors||Alexandra Boldyreva, Hovav Shacham|
|Number of pages||25|
|State||Published - 2018|
|Event||38th Annual International Cryptology Conference, CRYPTO 2018 - Santa Barbara, United States|
Duration: 19 Aug 2018 → 23 Aug 2018
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||38th Annual International Cryptology Conference, CRYPTO 2018|
|Period||19/08/18 → 23/08/18|
Bibliographical noteFunding Information:
I. Komargodski—Supported in part by a Packard Foundation Fellowship and by an AFOSR grant FA9550-15-1-0262. E. Yogev—Supported in part by a grant from the Israel Science Foundation (no. 950/16).
© 2018, International Association for Cryptologic Research.