### On One-way Functions and Kolmogorov Complexity

Yanyi Liu and Rafael Pass

##### Abstract

We prove that the equivalence of two fundamental problems in the theory of computing. For every polynomial $t(n)\geq (1+\varepsilon)n, \varepsilon>0$, the following are equivalent: - One-way functions exists (which in turn is equivalent to the existence of secure private-key encryption schemes, digital signatures, pseudorandom generators, pseudorandom functions, commitment schemes, and more); - $t$-time bounded Kolmogorov Complexity, $K^t$, is mildly hard-on-average (i.e., there exists a polynomial $p(n)>0$ such that no $\PPT$ algorithm can compute $K^t$, for more than a $1-\frac{1}{p(n)}$ fraction of $n$-bit strings). In doing so, we present the first natural, and well-studied, computational problem characterizing the feasibility of the central private-key primitives and protocols in Cryptography.

Available format(s)
Category
Foundations
Publication info
Preprint.
Keywords
one-way functionsKolmogorov complexityaverage-case hardness
Contact author(s)
yl2866 @ cornell edu
rafael @ cs cornell edu
History
2020-09-24: last of 3 revisions
See all versions
Short URL
https://ia.cr/2020/423

CC BY

BibTeX

@misc{cryptoeprint:2020/423,
author = {Yanyi Liu and Rafael Pass},
title = {On One-way Functions and Kolmogorov Complexity},
howpublished = {Cryptology ePrint Archive, Paper 2020/423},
year = {2020},
note = {\url{https://eprint.iacr.org/2020/423}},
url = {https://eprint.iacr.org/2020/423}
}

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