Paper 2020/013
On the Cryptographic Hardness of Local Search
Nir Bitansky and Idan Gerichter
Abstract
We show new hardness results for the class of Polynomial Local Search problems ($\mathsf{PLS}$): * Hardness of $\mathsf{PLS}$ 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 $\mathsf{PLS}$ 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 $\mathsf{PLS}$ can be traded with a simple incremental completeness property.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Published elsewhere. Major revision. ITCS 2020
- Keywords
- TFNPPLSLower BoundsIncremental Computation
- Contact author(s)
- idangerichter @ gmail com
- History
- 2020-01-06: received
- Short URL
- https://ia.cr/2020/013
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2020/013,
author = {Nir Bitansky and Idan Gerichter},
title = {On the Cryptographic Hardness of Local Search},
howpublished = {Cryptology ePrint Archive, Paper 2020/013},
year = {2020},
note = {\url{https://eprint.iacr.org/2020/013}},
url = {https://eprint.iacr.org/2020/013}
}
