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.
Keywords
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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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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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