On secure distributed hypothesis testing

The distributed binary hypothesis testing problem with communication and security constraints is investigated. A legitimate statistician (referred to as Bob) is interested in detecting the joint probability distribution of two remotely located sources. To this end, Bob has access to analog and coded data where the later is observed at another node (referred to as Alice) and communicated over a public noise-less channel of finite rate. An eavesdropper (referred to as Eve) has access to the encoded bits. In this framework, we study the tradeoff between the maximum achievable error exponent at Bob, i.e., the minimum Type II error probability for a fixed Type I probability of error, the rate and the equivocation rate. We first derive an achievable rate-exponent-equivocation region. Then, we investigate the special case of testing against independence for which we provide the optimal rate-exponent-equivocation region. An application example to binary sources is also considered.