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Communication Complexity of the Secret Key Agreement in Algorithmic Information Theory

Emirhan Gürpınar 1 Andrei Romashchenko 1, 2
1 ESCAPE - Systèmes complexes, automates et pavages
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
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.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-02558566
Contributor : Andrei Romashchenko <>
Submitted on : Wednesday, April 29, 2020 - 5:05:06 PM
Last modification on : Monday, June 29, 2020 - 11:38:26 PM

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  • HAL Id : lirmm-02558566, version 1
  • ARXIV : 2004.13411

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Emirhan Gürpınar, Andrei Romashchenko. Communication Complexity of the Secret Key Agreement in Algorithmic Information Theory. 45th International Symposium on Mathematical Foundations of Computer Science, Aug 2020, Prague, Czech Republic. ⟨lirmm-02558566⟩

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