On one-way functions and kolmogorov complexity

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.