Cryptography from sublinear-time average-case hardness of time-bounded Kolmogorov complexity

Yanyi Liu, Rafael Pass

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

Abstract

Let MKtP[s] be the set of strings x such that Kt(x) ? s(|x|), where Kt(x) denotes the t-bounded Kolmogorov complexity of the truthtable described by x. Our main theorem shows that for an appropriate notion of mild average-case hardness, for every ?>0, polynomial t(n) ? (1+?)n, and every "nice"class F of super-polynomial functions, the following are equivalent: (i) the existence of some function T e F such that T-hard one-way functions (OWF) exists (with non-uniform security); (ii) the existence of some function T e F such that MKtP[T-1] is mildly average-case hard with respect to sublinear-time non-uniform algorithms (with running-time n? for some 0<?<1). For instance, existence of subexponentially-hard (resp. quasi-poly-nomially-hard) OWFs is equivalent to mild average-case hardness of MKtP[poly logn] (resp. MKtP[2O(?logn))]) w.r.t. sublinear-time non-uniform algorithms. We additionally note that if we want to deduce T-hard OWFs where security holds w.r.t. uniform T-time probabilistic attackers (i.e., uniformly-secure OWFs), it suffices to assume sublinear time hardness of MKtP w.r.t. uniform probabilistic sublinear-time attackers. We complement this result by proving lower bounds that come surprisingly close to what is required to unconditionally deduce the existence of (uniformly-secure) OWFs: MKtP[polylogn] is worst-case hard w.r.t. uniform probabilistic sublinear-time algorithms, and MKtP[n-logn] is mildly average-case hard for all O(t(n)/n3)-time deterministic algorithms.

Original languageEnglish
Title of host publicationSTOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing
EditorsSamir Khuller, Virginia Vassilevska Williams
Pages722-735
Number of pages14
ISBN (Electronic)9781450380539
DOIs
StatePublished - 15 Jun 2021
Externally publishedYes
Event53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 - Virtual, Online, Italy
Duration: 21 Jun 202125 Jun 2021

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing

Conference

Conference53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021
Country/TerritoryItaly
CityVirtual, Online
Period21/06/2125/06/21

Keywords

  • Kolmogorov complexity
  • One-way functions

All Science Journal Classification (ASJC) codes

  • Software

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