We study the problem of remote state estimation, in the presence of an eavesdropper. An authorized user estimates the state of a linear plant, based on the data received from a sensor, while the data may also be intercepted by the eavesdropper. To maintain confidentiality with respect to state, we introduce a novel control-theoretic definition of perfect secrecy requiring that the user's expected error remains bounded while the eavesdropper's expected error grows unbounded. We propose a secrecy mechanism which guarantees perfect secrecy by randomly withholding sensor information, under the condition that the user's packet reception rate is larger than the eavesdropper's interception rate. Given this mechanism, we also explore the tradeoff between user's utility and confidentiality with respect to the eavesdropper, via an optimization problem. Finally, some examples are studied to provide insights about this tradeoff.