期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2021
卷号：21
语种：English
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：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 ε > 0, polynomial t(n) ≥ (1 + ε)n, and every “nice” class F of super-polynomial functions, the following are equivalent: • the existence of some function T ∈ F such that T-hard one-way functions (OWF) exists (with non-uniform security); • the existence of some function T ∈ F such that MKtP[T −1 ] is mildly average-case hard with respect to sublinear-time non-uniform algorithms (with running-time nδ for some 0 < δ < 1). For instance, existence of subexponentially-hard (resp. quasi-polynomially-hard) OWFs is equivalent to mild average-case hardness of MKtP[poly log n] (resp. MKtP[2O(√ log n) )]) 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. uni?form 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 uncondition?ally deduce the existence of (uniformly-secure) OWFs: MKtP[poly log n] is worst-case hard w.r.t. uniform probabilistic sublinear-time algorithms, and MKtP[n − log n] is mildly average-case hard for all O(t(n)/n3 )-time deterministic algorithms.
关键词：average case complexity;Kolmogorov complexity;one-way function
