Toward Basing Cryptography on the Hardness of EXP

Yanyi Liu, Rafael Pass

Research output: Contribution to journalArticlepeer-review

Abstract

Let Kt(x) denote the Levin-Kolmogorov Complexity of the string x, and let MKtP denote the language of pairs (x, k) having the property that Kt(x) ≤ k. We demonstrate that: • MKtP Ï HeurnegBPP (i.e., MKtP is two-sided error mildly average-case hard) iff infinitely-often OWFs exist. • MKtP Ï AvgnegBPP (i.e., MKtP is errorless mildly average-case hard) iff EXP ≠ BPP. Taken together, these results show that the only “gap” toward getting (infinitely-often) OWFs from the assumption that EXP ≠ BPP is the seemingly “minor” technical gap between two-sided error and errorless average-case hardness of the MKtP problem.

Original languageEnglish
Pages (from-to)91-99
Number of pages9
JournalCommunications of the ACM
Volume66
Issue number5
DOIs
StatePublished - 21 Apr 2023

Funding

FundersFunder number
National Science FoundationSATC-1704788, RI-1703846
Air Force Office of Scientific ResearchFA9550-18-1-0267
Defense Advanced Research Projects AgencyHR00110C0086

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