Secure source coding with a helper

  • Authors:

  • Ravi Tandon;Sennur Ulukus;Kannan Ramchandran

  • Affiliations:

  • Department of Electrical and Computer Engineering, University of Maryland, College Park, MD;Department of Electrical and Computer Engineering, University of Maryland, College Park, MD;Department of EECS, University of California, Berkeley

  • Venue:
  • Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
  • Year:
  • 2009

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Abstract

We consider a secure lossless source coding problem with a rate-limited helper. In particular, Alice observes an i.i.d. source Xn and wishes to transmit this source losslessly to Bob at a rate Rx. A helper, say Helen, observes a correlated source Yn and transmits at a rate Ry to Bob. A passive eavesdropper can observe the coded output of Alice. The equivocation Δ is measured by the conditional entropy H(Xn|Jx)/n, where Jx is 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 Wn and Zn available 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.