This letter studies the problem of maintaining information freshness under passive eavesdropping attacks. The classical three-node wiretap channel model is considered, in which a source aims to send its latest status wirelessly to its intended destination, while protecting the message from being overheard by an eavesdropper. Considering that conventional channel capacity-based secrecy metrics are no longer adequate to measure the information timeliness in status update systems, we define two new age of information-based metrics to characterize the secrecy performance of the considered system. We further propose, analyze, and optimize a randomized stationary transmission policy implemented at the source for further enhancing the secrecy performance. Simulation results are provided to validate our analysis and optimization.