  Linear queries can be submitted to a server containing private data. The
server provides a response to the queries systematically corrupted using an
additive noise to preserve the privacy of those whose data is stored on the
server. The measure of privacy is inversely proportional to the trace of the
Fisher information matrix. It is assumed that an adversary can inject a false
bias to the responses. The measure of the security, capturing the ease of
detecting the presence of the false data injection, is the sensitivity of the
Kullback-Leiber divergence to the additive bias. An optimization problem for
balancing privacy and security is proposed and subsequently solved. It is shown
that the level of guaranteed privacy times the level of security equals a
constant. Therefore, by increasing the level of privacy, the security
guarantees can only be weakened and vice versa. Similar results are developed
under the differential privacy framework.
