  We study a distributed binary hypothesis testing (HT) problem with
communication and security constraints, involving three parties: a remote
sensor called Alice, a legitimate decision centre called Bob, and an
eavesdropper called Eve, all having their own source observations. In this
system, Alice conveys a rate R description of her observation to Bob, and Bob
performs a binary hypothesis test on the joint distribution underlying his and
Alice's observations. The goal of Alice and Bob is to maximise the exponential
decay of Bob's miss-detection (type II-error) probability under two
constraints: Bob's false alarm-probability (type-I error) probability has to
stay below a given threshold and Eve's uncertainty (equivocation) about Alice's
observations should stay above a given security threshold even when Eve learns
Alice's message. For the special case of testing against independence, we
characterise the largest possible type-II error exponent under the described
type-I error probability and security constraints.
