On One-way Functions and Kolmogorov Complexity

Yanyi Liu; Rafael Pass

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arXiv · 2009.11514

On One-way Functions and Kolmogorov Complexity

Yanyi Liu·Rafael Pass

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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.

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Yanyi Liu, Rafael Pass. 2020-09-24. On One-way Functions and Kolmogorov Complexity. https://arxiv.org/abs/2009.11514

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