Differential privacy is among the most prominent techniques for preserving
privacy of sensitive data, oweing to its robust mathematical guarantees and
general applicability to a vast array of computations on data, including
statistical analysis and machine learning. Previous work demonstrated that
concrete implementations of differential privacy mechanisms are vulnerable to
statistical attacks. This vulnerability is caused by the approximation of real
values to floating point numbers. This paper presents a practical solution to
the finite-precision floating point vulnerability, where the inverse transform
sampling of the Laplace distribution can itself be inverted, thus enabling an
attack where the original value can be retrieved with non-negligible advantage.
The proposed solution has the advantages of being (i) mathematically sound,
(ii) generalisable to any infinitely divisible probability distribution, and
(iii) of simple implementation in modern architectures. Finally, the solution
has been designed to make side channel attack infeasible, because of inherently
exponential, in the size of the domain, brute force attacks.