Paper 2023/1591 Original: eprint.iacr.org/2023/1591 ↗
One-way Functions and Hardness of (Probabilistic) Time-Bounded Kolmogorov Complexity w.r.t. Samplable Distributions
Abstract
Consider the recently introduced notion of \emph{probabilistic time-bounded Kolmogorov Complexity}, pK^t (Goldberg et al, CCC'22), and let MpK^tP denote the language of pairs (x,k) such that pK^t(x) \leq k. We show the equivalence of the following: - MpK^{poly}P is (mildly) hard-on-average w.r.t. \emph{any} samplable distribution D; - MpK^{poly}P is (mildly) hard-on-average w.r.t. the \emph{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, K^t.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2023-10-13: last updated
- 2023-10-13: published
- Short URL
- https://ia.cr/2023/1591
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2023/1591,
author = {Yanyi Liu and Rafael Pass},
title = {One-way Functions and Hardness of (Probabilistic) Time-Bounded Kolmogorov Complexity w.r.t. Samplable Distributions},
howpublished = {Cryptology {ePrint} Archive, Paper 2023/1591},
year = {2023},
url = {https://eprint.iacr.org/2023/1591}
}