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Adversarially Robust Property-Preserving Hash Functions

Authors Elette Boyle, Rio LaVigne, Vinod Vaikuntanathan

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Elette Boyle
  • IDC Herzliya, Kanfei Nesharim Herzliya, Israel
Rio LaVigne
  • MIT CSAIL, 32 Vassar Street, Cambridge MA, 02139 USA
Vinod Vaikuntanathan
  • MIT CSAIL, 32 Vassar Street, Cambridge MA, 02139 USA

Funding

  • Boyle, Elette: Supported in part by ISF grant 1861/16, AFOSR Award FA9550-17-1-0069, and ERC grant 742754 (project NTSC).
  • LaVigne, Rio: This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. 1122374. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors(s) and do not necessarily reflect the views of the National Science Foundation. This research was also supported in part by grants of the third author.
  • Vaikuntanathan, Vinod: Research supported in part by NSF Grants CNS-1350619 and CNS-1414119, an MIT-IBM grant and a DARPA Young Faculty Award.

Cite AsGet BibTex

Elette Boyle, Rio LaVigne, and Vinod Vaikuntanathan. Adversarially Robust Property-Preserving Hash Functions. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 16:1-16:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.ITCS.2019.16

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Cryptographic primitives
Keywords
  • Hash function
  • compression
  • property-preserving
  • one-way communication

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