Gap MCSP Is Not (Levin) NP-Complete in Obfustopia

Noam Mazor*, Rafael Pass*

*Corresponding author for this work

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

1 Scopus citations

Abstract

We demonstrate that under believable cryptographic hardness assumptions, Gap versions of standard meta-complexity problems, such as the Minimum Circuit Size Problem (MCSP) and the Minimum Time-Bounded Kolmogorov Complexity problem (MKTP) are not NP-complete w.r.t. Levin (i.e., witness-preserving many-to-one) reductions. In more detail: Assuming the existence of indistinguishability obfuscation, and subexponentially-secure one-way functions, an appropriate Gap version of MCSP is not NP-complete under randomized Levin-reductions. Assuming the existence of subexponentially-secure indistinguishability obfuscation, subexponentially-secure one-way functions and injective PRGs, an appropriate Gap version of MKTP is not NP-complete under randomized Levin-reductions.

Original languageEnglish
Title of host publication39th Computational Complexity Conference, CCC 2024
EditorsRahul Santhanam
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959773317
DOIs
StatePublished - Jul 2024
Event39th Computational Complexity Conference, CCC 2024 - Ann Arbor, United States
Duration: 22 Jul 202425 Jul 2024

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume300
ISSN (Print)1868-8969

Conference

Conference39th Computational Complexity Conference, CCC 2024
Country/TerritoryUnited States
CityAnn Arbor
Period22/07/2425/07/24

Funding

FundersFunder number
Algorand Foundation
NSFCNS-2149305
DARPAHR00110C0086
AFOSRFA9550-23-1-0387, FA9550-23-1-0312

    Keywords

    • Kolmogorov complexity
    • Levin Reduction
    • MCSP

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