  In this paper, we study a secure integrated sensing and communication (ISAC)
system where one multi-antenna base station (BS) simultaneously serves a
downlink communication user and senses the location of a target that may
potentially serve as an eavesdropper via its reflected echo signals.
Specifically, the location information of the target is unknown and random,
while its a priori distribution is available for exploitation. First, to
characterize the sensing performance, we derive the posterior Cram\'er-Rao
bound (PCRB) which is a lower bound of the mean squared error (MSE) for target
sensing exploiting prior distribution. Due to the intractability of the PCRB
expression, we further derive a novel approximate upper bound of it which has a
closed-form expression. Next, under an artificial noise (AN) based beamforming
structure at the BS to alleviate information eavesdropping and enhance the
target's reflected signal power for sensing, we formulate a transmit
beamforming optimization problem to maximize the worst-case secrecy rate among
all possible target (eavesdropper) locations, under a sensing accuracy
threshold characterized by an upper bound on the PCRB. Despite the
non-convexity of the formulated problem, we propose a two-stage approach to
obtain its optimal solution by leveraging the semi-definite relaxation (SDR)
technique. Numerical results validate the effectiveness of our proposed
transmit beamforming design and demonstrate the non-trivial trade-off between
secrecy performance and sensing performance in secure ISAC systems.
