On One-way Functions and Kolmogorov Complexity
2020 IEEE 61ST ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS 2020)(2020)
摘要
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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关键词
pseudorandom functions,commitment schemes,t-time bounded Kolmogorov Complexity,hard-on-average,PPT algorithm,n-bit strings,computational problem,private-key primitives,digital signatures,pseudorandom generators,secure private-key encryption schemes
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