Welcome to the resource topic for 2021/793
Title:
Property-Preserving Hash Functions for Hamming Distance from Standard Assumptions
Authors: Nils Fleischhacker, Kasper Green Larsen, and Mark Simkin
Abstract:Property-preserving hash functions allow for compressing long inputs x_0 and x_1 into short hashes h(x_0) and h(x_1) in a manner that allows for computing a predicate P(x_0, x_1) given only the two hash values without having access to the original data. Such hash functions are said to be adversarially robust if an adversary that gets to pick x_0 and x_1 after the hash function has been sampled, cannot find inputs for which the predicate evaluated on the hash values outputs the incorrect result. In this work we construct robust property-preserving hash functions for the hamming-distance predicate which distinguishes inputs with a hamming distance at least some threshold t from those with distance less than t. The security of the construction is based on standard lattice hardness assumptions. Our construction has several advantages over the best known previous construction by Fleischhacker and Simkin (Eurocrypt 2021). Our construction relies on a single well-studied hardness assumption from lattice cryptography whereas the previous work relied on a newly introduced family of computational hardness assumptions. In terms of computational effort, our construction only requires a small number of modular additions per input bit, whereas the work of Fleischhacker and Simkin required several exponentiations per bit as well as the interpolation and evaluation of high-degree polynomials over large fields. An additional benefit of our construction is that the description of the hash function can be compressed to \lambda bits assuming a random oracle. Previous work has descriptions of length \mathcal{O}(\ell \lambda) bits for input bit-length \ell. We prove a lower bound on the output size of any property-preserving hash function for the hamming distance predicate. The bound shows that the size of our hash value is not far from optimal.
ePrint: https://eprint.iacr.org/2021/793
Talk: https://www.youtube.com/watch?v=pbnjrAKpcog
Slides: https://iacr.org/submit/files/slides/2022/eurocrypt/eurocrypt2022/257/slides.pdf
See all topics related to this paper.
Feel free to post resources that are related to this paper below.
Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.
For more information, see the rules for Resource Topics .