Speaker: Marius Zimand
Affiliation: Towson University

Title: An operational characterization of mutual information in algorithmic information theory

Abstract: An operational interpretation of the concept of mutual information in the framework of Kolmogorov complexity has been elusive till now. We show that the mutual information of any pair of strings x and y is equal, up to logarithmic precision, to the length of the longest shared secret key that two parties, one having x and the complexity profile of the pair and the other one having y and the complexity profile of the pair, can establish via a probabilistic protocol with interaction on a public channel. We establish the communication complexity of secret key agreement protocols that produce a secret key of maximal length, for protocols with public randomness. We show that if the communication complexity drops below the established threshold then only very short secret keys can be obtained.

This is joint work with Andrei Romashchenko.