Secure Source Coding with a Helper

Details Secure Source Coding with a Helper Secure Source Coding with a Helper

2009-10-30

arxiv.org/abs/0910.5759v2

Computer Science

Information Theory

Submitted to IEEE Transactions on Information Theory, October 2009

Scientific paper

We consider a secure lossless source coding problem with a rate-limited helper. In particular, Alice observes an i.i.d. source $X^{n}$ and wishes to transmit this source losslessly to Bob at a rate $R_{x}$. A helper, say Helen, observes a correlated source $Y^{n}$ and transmits at a rate $R_{y}$ to Bob. A passive eavesdropper can observe the coded output of Alice. The equivocation $\Delta$ is measured by the conditional entropy $H(X^{n}|J_{x})/n$, 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 $W^{n}$ and $Z^{n}$ are available at Bob and Eve, respectively. For this model, we provide a complete characterization of the rate-equivocation region when $Y^{n}\to X^{n} \to (W^{n},Z^{n})$ forms a Markov chain.

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