# An operational characterization of mutual information in algorithmic information theory

1 ESCAPE - Systèmes complexes, automates et pavages
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We show that the mutual information, in the sense of Kolmogorov complexity, 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. For $\ell > 2$, the longest shared secret that can be established from a tuple of strings $(x_1, . . . , x_\ell)$ by $\ell$ parties, each one having one component of the tuple and the complexity profile of the tuple, is equal, up to logarithmic precision, to the complexity of the tuple minus the minimum communication necessary for distributing the tuple to all parties. We establish the communication complexity of secret key agreement protocols that produce a secret key of maximal length, for protocols with public randomness. We also show that if the communication complexity drops below the established threshold then only very short secret keys can be obtained.
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Cited literature [28 references]

https://hal-lirmm.ccsd.cnrs.fr/lirmm-01618559
Contributor : Andrei Romashchenko <>
Submitted on : Friday, June 28, 2019 - 3:40:15 PM
Last modification on : Wednesday, September 25, 2019 - 4:55:40 PM

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Andrei Romashchenko, Marius Zimand. An operational characterization of mutual information in algorithmic information theory. ICALP: International Colloquium on Automata, Languages, and Programming, Jul 2018, Prague, Czech Republic. pp.95:1-95:14, ⟨10.4230/LIPIcs.ICALP.2018.95⟩. ⟨lirmm-01618559⟩

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