Secure source coding with a helper

Ravi Tandon, Sennur Ulukus, Kannan Ramchandran

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

Abstract

We consider a secure lossless source coding problem with a rate-limited helper. In particular, Alice observes an independent and identically distributed (i.i.d.) source and wishes to transmit this source losslessly to Bob over a rate-limited link of capacity not exceeding . A helper, say Helen, observes an i.i.d. correlated source Ynand can transmit information to Bob over another link of capacity not exceeding Ry. A passive eavesdropper (say Eve) can observe the coded output of Alice, i.e., the link from Alice to Bob is public. The uncertainty about the source at Eve (denoted by ) is measured by the conditional entropy , where is the coded output of Alice and is the block length. We completely characterize the rate-equivocation region for this secure source coding model, where we show that Slepian-Wolf binning of X n with respect to the coded side information received at Bob is optimal. We next consider a modification of this model in which Alice also has access to the coded output of Helen. We call this model as the two-sided helper model. For the two-sided helper model, we characterize the rate-equivocation region. While the availability of side information at Alice does not reduce the rate of transmission from Alice, it significantly enhances the resulting equivocation at Eve. In particular, the resulting equivocation for the two-sided helper case is shown to be , i.e., one bit from the two-sided helper provides one bit of uncertainty at Eve. From this result, we infer that Slepian-Wolf binning of is suboptimal and one can further decrease the information leakage to the eavesdropper by utilizing the side information at Alice. We, finally, generalize both of these results to the case in which there is additional uncoded side information Wn available at Bob and characterize the rate-equivocation regions under the assumption that forms a Markov chain.

Original languageEnglish (US)
Article number6399603
Pages (from-to)2178-2187
Number of pages10
JournalIEEE Transactions on Information Theory
Volume59
Issue number4
DOIs
StatePublished - Apr 2013
Externally publishedYes

Keywords

  • Equivocation
  • Helper problem
  • Lossless source coding

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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