Locality-Preserving Hashing for Shifts with Connections to Cryptography

Elette Boyle, Itai Dinur, Niv Gilboa, Yuval Ishai, Nathan Keller, Ohad Klein

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

Can we sense our location in an unfamiliar environment by taking a sublinear-size sample of our surroundings? Can we efficiently encrypt a message that only someone physically close to us can decrypt? To solve this kind of problems, we introduce and study a new type of hash functions for finding shifts in sublinear time. A function h : {0, 1}n → ℤn is a (d, δ) locality-preserving hash function for shifts (LPHS) if: (1) h can be computed by (adaptively) querying d bits of its input, and (2) Pr [h(x) ≠ h(x ≪ 1) + 1] ≤ δ, where x is random and ≪ 1 denotes a cyclic shift by one bit to the left. We make the following contributions. - Near-optimal LPHS via Distributed Discrete Log. We establish a general two-way connection between LPHS and algorithms for distributed discrete logarithm in the generic group model. Using such an algorithm of Dinur et al. (Crypto 2018), we get LPHS with near-optimal error of δ = Õ(1/d2). This gives an unusual example for the usefulness of group-based cryptography in a post-quantum world. We extend the positive result to non-cyclic and worst-case variants of LPHS. - Multidimensional LPHS. We obtain positive and negative results for a multidimensional extension of LPHS, making progress towards an optimal 2-dimensional LPHS. - Applications. We demonstrate the usefulness of LPHS by presenting cryptographic and algorithmic applications. In particular, we apply multidimensional LPHS to obtain an efficient “packed” implementation of homomorphic secret sharing and a sublinear-time implementation of location-sensitive encryption whose decryption requires a significantly overlapping view.

Original languageEnglish
Title of host publication13th Innovations in Theoretical Computer Science Conference, ITCS 2022
EditorsMark Braverman
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772174
DOIs
StatePublished - 1 Jan 2022
Event13th Innovations in Theoretical Computer Science Conference, ITCS 2022 - Berkeley, United States
Duration: 31 Jan 20223 Feb 2022

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume215
ISSN (Print)1868-8969

Conference

Conference13th Innovations in Theoretical Computer Science Conference, ITCS 2022
Country/TerritoryUnited States
CityBerkeley
Period31/01/223/02/22

Keywords

  • Discrete logarithm
  • Homomorphic secret sharing
  • Metric embeddings
  • Shift finding
  • Sublinear algorithms

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