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International Symposium on Foundations and Practice of Security

FPS 2012: Foundations and Practice of Security pp 78–94Cite as

Message Transmission and Key Establishment: Conditions for Equality of Weak and Strong Capacities

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7743))

Abstract

Secure communication using noisy resources has been first studied in the contexts of secure message transmission (SMT) by Wyner as well as Csiszár-and-Körner, and secret key establishment (SKE) by Ahlswede-and-Csiszár as well as Maurer. The work defines secrecy (resp. secret-key (SK)) capacity as the highest achievable rate of secure transmission (resp. key establishment). Maurer and Wolf later focused on SKE and noticed that the secrecy requirement in the SK capacity definition was weak as it required only the “ratio” between the adversary’s information and the key length to be negligible. They suggested a stronger definition of the SK capacity by requiring absolute information leakage to be negligible. They provided an interesting proof for the equality of weak and strong SK capacities in the above scenarios (setups).

Followup work has since studied several setups for SKE by considering the weak SK capacity without discussing whether the results also hold for the strong definition. In this paper, we pose the question whether the equality of weak and strong SK capacities can be derived in general for all discrete memoryless communication setups. We also extend this study to message transmission and investigate the equality of weak and strong secrecy capacities. For SKE, we show that weak and strong SK capacities are equal for any setup that allows reliable transmission in any direction. For SMT, the secrecy capacities are equal when the setup allows the sender to use randomness. We furthermore provide trivial counterexamples that show these sufficient conditions are not always necessary for the equality of the capacities. Whether the conditions can be removed or relaxed by tight (necessary and sufficient) conditions remains an interesting question for future.

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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. TELECOM SudParis, 9 rue Charles Fourier, 91011, Evry, CEDEX, France

    Joaquin Garcia-Alfaro

  2. TELECOM Bretagne, 2 rue de la Châtaigneraie, 35512, Cesson Sévigné, CEDEX, France

    Frédéric Cuppens  & Nora Cuppens-Boulahia  & 

  3. Ryerson University, 245 Church Street, M5B 2K3, Toronto, ON, Canada

    Ali Miri

  4. Université Laval, 1065 avenue de la médecine, G1V 0A6, Quebec, Canada

    Nadia Tawbi

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Ahmadi, H., Safavi-Naini, R. (2013). Message Transmission and Key Establishment: Conditions for Equality of Weak and Strong Capacities. In: Garcia-Alfaro, J., Cuppens, F., Cuppens-Boulahia, N., Miri, A., Tawbi, N. (eds) Foundations and Practice of Security. FPS 2012. Lecture Notes in Computer Science, vol 7743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37119-6_6

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  • DOI: https://doi.org/10.1007/978-3-642-37119-6_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37118-9

  • Online ISBN: 978-3-642-37119-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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