Adversarially robust property-preserving hash functions
Name
LIPIcs-ITCS-2019-16.pdf
Description
Published version
Size
620.85 KB
Format
Adobe PDF
Checksum (MD5)
08c79df4ba30dea3bf8693d3a4ca137a
Author(s)
LaVigne, Rio (Kristen Rio)
Vaikuntanathan, Vinod
Date Issued
January 2019
Journal
Leibniz International Proceedings in Informatics, LIPIcs
Publisher
Leibniz Center for Informatics
Citation
Boyle, Elette et al. “Adversarially robust property-preserving hash functions.” Paper in the Leibniz International Proceedings in Informatics, LIPIcs, 124, 16, 10th Innovations in Theoretical Computer Science (ITCS 2019), San Diego, California, January 10-12, 2019, Leibniz Center for Informatics: 1-20 © 2019 The Author(s)
Version
Final published version
Abstract
Property-preserving hashing is a method of compressing a large input x into a short hash h(x) in such a way that given h(x) and h(y), one can compute a property P(x, y) of the original inputs. The idea of property-preserving hash functions underlies sketching, compressed sensing and locality-sensitive hashing. Property-preserving hash functions are usually probabilistic: they use the random choice of a hash function from a family to achieve compression, and as a consequence, err on some inputs. Traditionally, the notion of correctness for these hash functions requires that for every two inputs x and y, the probability that h(x) and h(y) mislead us into a wrong prediction of P(x, y) is negligible. As observed in many recent works (incl. Mironov, Naor and Segev, STOC 2008; Hardt and Woodruff, STOC 2013; Naor and Yogev, CRYPTO 2015), such a correctness guarantee assumes that the adversary (who produces the offending inputs) has no information about the hash function, and is too weak in many scenarios. We initiate the study of adversarial robustness for property-preserving hash functions, provide definitions, derive broad lower bounds due to a simple connection with communication complexity, and show the necessity of computational assumptions to construct such functions. Our main positive results are two candidate constructions of property-preserving hash functions (achieving different parameters) for the (promise) gap-Hamming property which checks if x and y are “too far” or “too close”. Our first construction relies on generic collision-resistant hash functions, and our second on a variant of the syndrome decoding assumption on low-density parity check codes.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4230/LIPIcs.ITCS.2019.16
