Cryptology ePrint Archive: Report 2020/423

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.

Category / Keywords: foundations / one-way functions, Kolmogorov complexity, average-case hardness

Date: received 14 Apr 2020, last revised 24 Sep 2020

Contact author: yl2866 at cornell edu, rafael at cs cornell edu

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Version: 20200924:062756 (All versions of this report)

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