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A Secret Common Information Duality for Tripartite Noisy Correlations

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Security in Computing and Communications (SSCC 2015)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 536))

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Abstract

We explore the duality between the simulation and extraction of secret correlations in light of a similar well-known operational duality between the two notions of common information due to Wyner, and Gács and Körner. For the inverse problem of simulating a tripartite noisy correlation from noiseless secret key and unlimited public communication, we show that Winter’s (2005) result for the key cost in terms of a conditional version of Wyner’s common information can be simply reexpressed in terms of the existence of a bipartite protocol monotone. For the forward problem of key distillation from noisy correlations, we construct simple distributions for which the conditional Gács and Körner common information achieves a tight bound on the secret key rate. We conjecture that this holds in general for non-communicative key agreement models. We also comment on the interconvertibility of secret correlations under local operations and public communication.

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Notes

  1. 1.

    Given jointly distributed RVs \((X,Y,Z,\bar{Z})\) with \(\bar{Z}:XY - Z - \bar{Z}\), it does not hold in general that \(C_W(X;Y|\bar{Z}) \ge C_W(X;Y|Z)\).

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Acknowledgments

PKB wishes to thank Amin Gohari for valuable comments and Paul Cuff for short useful discussions over email. This work is based in part on PKB’s master’s thesis [19] and was supported in part by the AVLSI Consortium, IIT Kharagpur.

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Authors and Affiliations

  1. Indian Institute of Technology Kharagpur, Kharagpur, India

    Pradeep Kr. Banerjee

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  1. Pradeep Kr. Banerjee
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Correspondence to Pradeep Kr. Banerjee .

Editor information

Editors and Affiliations

  1. Deakin University, Geelong, Victoria, Australia

    Jemal H. Abawajy

  2. IBM Research-India, New Delhi, India

    Sougata Mukherjea

  3. Indian Institute of Information Technology and Management, Kerala, India

    Sabu M. Thampi

  4. University of Murcia, Espinardo, Murcia, Spain

    Antonio Ruiz-Martínez

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Banerjee, P.K. (2015). A Secret Common Information Duality for Tripartite Noisy Correlations. In: Abawajy, J., Mukherjea, S., Thampi, S., Ruiz-Martínez, A. (eds) Security in Computing and Communications. SSCC 2015. Communications in Computer and Information Science, vol 536. Springer, Cham. https://doi.org/10.1007/978-3-319-22915-7_31

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  • DOI: https://doi.org/10.1007/978-3-319-22915-7_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22914-0

  • Online ISBN: 978-3-319-22915-7

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