期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2020
卷号：2020
页码：1-22
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：We prove the equivalence of two fundamental problems in the theory of computation: • Existence of one-way functions: the existence of one-way functions (which in turn are equivalent to pseudorandom generators, pseudorandom functions, private-key encryption schemes, digital signatures, commitment schemes, and more). • Mild average-case hardness of Kpoly-complexity: the existence of polynomials t, p such that no PPT algorithm can determine the t-time bounded Kolmogorov Complexity, Kt , 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 “non-trivial” complexity-based Cryptography: “Non-trivial” complexity-based Cryptography is possible iff Kpoly is mildly hard-on average.
