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International Conference on Information Theoretic Security

ICITS 2011: Information Theoretic Security pp 76–93Cite as

Common Randomness and Secret Key Capacities of Two-Way Channels

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6673))

Abstract

Common Randomness Generation (CRG) and Secret Key Establishment (SKE) are fundamental primitives in information theory and cryptography. We study these two problems over the two-way communication channel model, introduced by Shannon. In this model, the common randomness (CK) capacity is defined as the maximum number of random bits per channel use that the two parties can generate. The secret key (SK) capacity is defined similarly when the random bits are also required to be secure against a passive adversary. We provide lower bounds on the two capacities. These lower bounds are tighter than those one might derive based on the previously known results. We prove our lower bounds by proposing a two-round, two-level coding construction over the two-way channel. We show that the lower bound on the common randomness capacity can also be achieved using a simple interactive channel coding (ICC) method. We furthermore provide upper bounds on these capacities and show that the lower and the upper bounds coincide when the two-way channel consists of two independent (physically degraded) one-way channels. We apply the results to the case where the channels are binary symmetric.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Calgary, Canada

    Hadi Ahmadi & Reihaneh Safavi-Naini

Authors
  1. Hadi Ahmadi
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  2. Reihaneh Safavi-Naini
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Editor information

Editors and Affiliations

  1. Centrum Wiskunde & Incormatica (CWI), Science Park 123, 1098, Amsterdem, XG, The Netherlands

    Serge Fehr

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© 2011 Springer-Verlag Berlin Heidelberg

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Ahmadi, H., Safavi-Naini, R. (2011). Common Randomness and Secret Key Capacities of Two-Way Channels. In: Fehr, S. (eds) Information Theoretic Security. ICITS 2011. Lecture Notes in Computer Science, vol 6673. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20728-0_8

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  • DOI: https://doi.org/10.1007/978-3-642-20728-0_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20727-3

  • Online ISBN: 978-3-642-20728-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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