Allerton Conference on Communication, Control, and Computing

Secure source coding with a helper

Ravi Tandon, Şennur Ulukuş, Kannan Ramchandran

Published Sep 1, 2009• 10 citations

Abstract

We consider a secure lossless source coding problem with a rate-limited helper. In particular, Alice observes an i.i.d. source Xnand wishes to transmit this source loss-lessly to Bob at a rate Rx. A helper, say Helen, observes a correlated source Ynand transmits at a rate Ryto Bob. A passive eavesdropper can observe the coded output of Alice. The equivocation ¿ is measured by the conditional entropy H(Xn\ Jx)/n, where Jxis the coded output of Alice. We first completely characterize the rate-equivocation region for this secure source coding model, where we show that Slepian-Wolf type coding is optimal. We next study two generalizations of this model and provide single-letter characterizations for the respective rate-equivocation regions. In particular, we first consider the case of a two-sided helper where Alice also has access to the coded output of Helen. We show that for this case, Slepian-Wolf type coding is suboptimal and one can further decrease the information leakage to the eavesdropper by utilizing the side-information at Alice. We finally generalize this result to the case when there are both secure and insecure rate-limited links from Helen and additional uncoded side informations Wnand Znavailable at Bob and Eve, respectively. For this model, we provide a complete characterization of the rate-equivocation region when Yn¿ Xn¿ (Wn, Zn) forms a Markov chain.

DOI: 10.1109/allerton.2009.5394875

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