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Distributions Attaining Secret Key at a Rate of the Conditional Mutual Information

  • Eric Chitambar
  • Benjamin Fortescue
  • Min-Hsiu Hsieh
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9216)

Abstract

In this paper we consider the problem of extracting secret key from an eavesdropped source \(p_{XYZ}\) at a rate given by the conditional mutual information. We investigate this question under three different scenarios: (i) Alice (X) and Bob (Y) are unable to communicate but share common randomness with the eavesdropper Eve (Z), (ii) Alice and Bob are allowed one-way public communication, and (iii) Alice and Bob are allowed two-way public communication. Distributions having a key rate of the conditional mutual information are precisely those in which a “helping” Eve offers Alice and Bob no greater advantage for obtaining secret key than a fully adversarial one. For each of the above scenarios, strong necessary conditions are derived on the structure of distributions attaining a secret key rate of I(X : Y|Z). In obtaining our results, we completely solve the problem of secret key distillation under scenario (i) and identify H(S|Z) to be the optimal key rate using shared randomness, where S is the Gács-Körner Common Information. We thus provide an operational interpretation of the conditional Gács-Körner Common Information. Additionally, we introduce simple example distributions in which the rate I(X : Y|Z) is achievable if and only if two-way communication is allowed.

Keywords

Information-theoretic security Public key agreement Gács-Körner Common Information 

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Copyright information

© International Association for Cryptologic Research 2015

Authors and Affiliations

  • Eric Chitambar
    • 1
  • Benjamin Fortescue
    • 1
  • Min-Hsiu Hsieh
    • 2
  1. 1.Department of Physics and AstronomySouthern Illinois UniversityCarbondaleUSA
  2. 2.Faculty of Engineering and Information Technology (FEIT), Centre for Quantum Computation & Intelligent Systems (QCIS)University of Technology Sydney (UTS)SydneyAustralia

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