Secure Random Sampling in Differential Privacy

Differentialprivacyisamongthemostprominenttechniques for preserving privacy of sensitive data, oweing to its robust mathe- matical guarantees and general applicability to a vast array of com- putations on data, including statistical analysis and machine learning. Previous work demonstrated that concrete implementations of differ- ential 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 sam- pling 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 distribu- tion, and (iii) of simple implementation in modern architectures. Fi- nally, the solution has been designed to make side channel attack in- feasible, because of inherently exponential, in the size of the domain, brute force attacks.