Communication Complexity of the Secret Key Agreement in Algorithmic Information Theory - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier Access content directly
Conference Papers Year : 2020

Communication Complexity of the Secret Key Agreement in Algorithmic Information Theory

Abstract

It is known that the mutual information, in the sense of Kolmogorov complexity, of any pair of strings x and y is equal to the length of the longest shared secret key that two parties can establish via a probabilistic protocol with interaction on a public channel, assuming that the parties hold as their inputs x and y respectively. We determine the worst-case communication complexity of this problem for the setting where the parities can use private sources of random bits. We show that for some pairs x, y the communication complexity of the secret key agreement does not decrease even if the parties have to agree on a secret key whose size is much smaller than the mutual information between x and y. On the other hand, we discuss examples of x, y such that the communication complexity of the protocol declines gradually with the size of the resulting secret key. The proof of the main result uses spectral properties of appropriate graphs and the expander mixing lemma, as well as information theoretic inequalities.
Fichier principal
Vignette du fichier
LIPIcs-MFCS-2020-44.pdf (421.59 Ko) Télécharger le fichier
Loading...

Dates and versions

lirmm-02558566 , version 1 (29-04-2020)

Licence

Attribution

Identifiers

Cite

Emirhan Gürpınar, Andrei Romashchenko. Communication Complexity of the Secret Key Agreement in Algorithmic Information Theory. MFCS 2020 - 45th International Symposium on Mathematical Foundations of Computer Science, Aug 2020, Prague, Czech Republic. pp.44:1-44:14, ⟨10.4230/LIPIcs.MFCS.2020.44⟩. ⟨lirmm-02558566⟩
116 View
55 Download

Altmetric

Share

Gmail Facebook X LinkedIn More