Secure source coding with a helper

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 loss-lessly to Bob at a rate R x . A helper, say Helen, observes a correlated source Yn and transmits at a rate R y to Bob. A passive eavesdropper can observe the coded output of Alice. The equivocation Δ is measured by the conditional entropy H(Xn\ J x )/n, where J x 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.