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

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