  The differential privacy is a widely accepted conception of privacy
preservation and the Laplace mechanism is a famous instance of differential
privacy mechanisms to deal with numerical data. In this paper, we find that the
differential privacy does not take liner property of queries into account,
resulting in unexpected information leakage. In specific, the linear property
makes it possible to divide one query into two queries such as
$q(D)=q(D_1)+q(D_2)$ if $D=D_1\cup D_2$ and $D_1\cap D_2=\emptyset$. If
attackers try to obtain an answer of $q(D)$, they not only can issue the query
$q(D)$, but also can issue the $q(D_1)$ and calculate the $q(D_2)$ by
themselves as long as they know $D_2$. By different divisions of one query,
attackers can obtain multiple different answers for the query from differential
privacy mechanisms. However, from attackers' perspective and from differential
privacy mechanisms' perspective, the totally consumed privacy budget is
different if divisions are delicately designed. The difference leads to
unexpected information leakage because the privacy budget is the key parameter
to control the amount of legally released information from differential privacy
mechanisms. In order to demonstrate the unexpected information leakage, we
present a membership inference attacks against the Laplace mechanism.
