## Cryptology ePrint Archive: Report 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.

Category / Keywords: foundations / TFNP, PLS, Lower Bounds, Incremental Computation

Original Publication (with major differences): ITCS 2020