On One-way Functions and Kolmogorov Complexity

09/24/2020

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by   Yanyi Liu, et al.

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We prove that the equivalence of two fundamental problems in the theory of computing. For every polynomial t(n)≥ (1+ε)n, ε>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 1-1/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.