One-Way Functions and the Hardness of (Probabilistic) Time-Bounded Kolmogorov Complexity w.r.t. Samplable Distributions

Yanyi Liu*, Rafael Pass

*Corresponding author for this work

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

Abstract

Consider the recently introduced notion of probabilistic time-bounded Kolmogorov Complexity, pKt (Goldberg et al., CCC’22), and let MpKtP denote the language of pairs (x, k) such that pKt(x) ≤ k. We show the equivalence of the following: MpKpolyP is (mildly) hard-on-average w.r.t. any samplable distribution D ;MpKpolyP is (mildly) hard-on-average w.r.t. the uniform distribution;existence of one-way functions. As far as we know, this yields the first natural class of problems where hardness with respect to any samplable distribution is equivalent to hardness with respect to the uniform distribution. Under standard derandomization assumptions, we can show the same result also w.r.t. the standard notion of time-bounded Kolmogorov complexity, Kt.

Original languageEnglish
Title of host publicationAdvances in Cryptology – CRYPTO 2023 - 43rd Annual International Cryptology Conference, CRYPTO 2023, Proceedings, Part II
EditorsHelena Handschuh, Anna Lysyanskaya
PublisherSpringer Science and Business Media Deutschland GmbH
Pages645-673
Number of pages29
ISBN (Print)9783031385445
DOIs
StatePublished - 2023
EventAdvances in Cryptology – CRYPTO 2023 - 43rd Annual International Cryptology Conference, CRYPTO 2023, Proceedings - Santa Barbara, United States
Duration: 20 Aug 202324 Aug 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14082 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

ConferenceAdvances in Cryptology – CRYPTO 2023 - 43rd Annual International Cryptology Conference, CRYPTO 2023, Proceedings
Country/TerritoryUnited States
CitySanta Barbara
Period20/08/2324/08/23

Funding

FundersFunder number
Algorand Centres of Excellence
Algorand Foundation
National Science FoundationCNS 2149305, CNS-2128519, RI-1703846
Air Force Office of Scientific ResearchFA9550-18-1-0267, FA9550-23-1-0312
Defense Advanced Research Projects AgencyHR00110C0086
Simons Institute for the Theory of Computing, University of California Berkeley

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