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We study a distributed binary hypothesis testing (HT) problem withcommunication and security constraints, involving three parties: a remotesensor called Alice, a legitimate decision centre called Bob, and aneavesdropper called Eve, all having their own source observations. In thissystem, Alice conveys a rate R description of her observation to Bob, and Bobperforms a binary hypothesis test on the joint distribution underlying his andAlice's observations. The goal of Alice and Bob is to maximise the exponentialdecay of Bob's miss-detection (type II-error) probability under twoconstraints: Bob's false alarm-probability (type-I error) probability has tostay below a given threshold and Eve's uncertainty (equivocation) about Alice'sobservations should stay above a given security threshold even when Eve learnsAlice's message. For the special case of testing against independence, wecharacterise the largest possible type-II error exponent under the describedtype-I error probability and security constraints.

Testing Against Independence with an Eavesdropper