@inproceedings{1e6aa56ab4c74778bf4a5638f07d69d4,
title = "One-Way Functions and the Hardness of (Probabilistic) Time-Bounded Kolmogorov Complexity w.r.t. Samplable Distributions",
abstract = "Consider the recently introduced notion of probabilistic time-bounded Kolmogorov Complexity, pKt (Goldberg et al., CCC{\textquoteright}22), and let MpKtP denote the language of pairs (x, k) such that pKt(x) ≤ k. We show the equivalence of the following: MpKpolyP is (mildly) hard-on-average w.r.t. any samplable distribution D ;MpKpolyP is (mildly) hard-on-average w.r.t. the uniform distribution;existence of one-way functions. As far as we know, this yields the first natural class of problems where hardness with respect to any samplable distribution is equivalent to hardness with respect to the uniform distribution. Under standard derandomization assumptions, we can show the same result also w.r.t. the standard notion of time-bounded Kolmogorov complexity, Kt.",
author = "Yanyi Liu and Rafael Pass",
note = "Publisher Copyright: {\textcopyright} 2023, International Association for Cryptologic Research.; 43rd Annual International Cryptology Conference, CRYPTO 2023 ; Conference date: 20-08-2023 Through 24-08-2023",
year = "2023",
doi = "10.1007/978-3-031-38545-2_21",
language = "الإنجليزيّة",
isbn = "9783031385445",
series = "Lecture Notes in Computer Science",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "645--673",
editor = "Helena Handschuh and Anna Lysyanskaya",
booktitle = "Advances in Cryptology – CRYPTO 2023 - 43rd Annual International Cryptology Conference, CRYPTO 2023, Proceedings",
address = "ألمانيا",
}