Evaluating Laplace Noise Addition to Satisfy Differential Privacy for Numeric Data

Laplace noise addition is often advanced as an approach for satisfying differential privacy. There have been several illustrations of the application of Laplace noise addition for count data, but no evaluation of its performance for numeric data. In this study we evaluate the privacy and utility performance of Laplace noise addition for numeric data. Our results indicate that Laplace noise addition delivers the promised level of privacy only by adding a large quantity of noise for even relatively large subsets. Because of this, even for simple mean queries, the responses for a masking mechanism that uses Laplace noise addition is of little value. We also show that Laplace noise addition may be vulnerable to a tracker attack. In order to avoid this, it may be necessary to increase the variance of the noise added as a function of the number of queries issued. This implies that the utility of the responses would be further reduced. These results raise serious questions regarding the viability of Laplace based noise addition for masking numeric data.