On the cryptographic hardness of local search

Nir Bitansky, Idan Gerichter

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


We show new hardness results for the class of Polynomial Local Search problems (PLS): Hardness of PLS based on a falsifiable assumption on bilinear groups introduced by Kalai, Paneth, and Yang (STOC 2019), and the Exponential Time Hypothesis for randomized algorithms. Previous standard model constructions relied on non-falsifiable and non-standard assumptions. Hardness of PLS relative to random oracles. The construction is essentially different than previous constructions, and in particular is unconditionally secure. The construction also demonstrates the hardness of parallelizing local search. The core observation behind the results is that the unique proofs property of incrementally-verifiable computations previously used to demonstrate hardness in PLS can be traded with a simple incremental completeness property.

Original languageEnglish
Title of host publication11th Innovations in Theoretical Computer Science Conference, ITCS 2020
EditorsThomas Vidick
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771344
StatePublished - Jan 2020
Event11th Innovations in Theoretical Computer Science Conference, ITCS 2020 - Seattle, United States
Duration: 12 Jan 202014 Jan 2020

Publication series

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


Conference11th Innovations in Theoretical Computer Science Conference, ITCS 2020
Country/TerritoryUnited States


FundersFunder number
Alon Young Faculty Fellowship
Blavatnik Family Foundation
Israel Science Foundation18/484


    • Cryptography
    • Incremental computation
    • Lower bounds
    • PLS


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