Toward Optimal Additive Noise Distribution for Privacy Protection in Mobile Statistics Aggregation

In emerging mobile aggregation applications (e.g., large-scale mobile survey), individual privacy is a crucial factor to determine the effectiveness, for which the noise-addition method (i.e., a random noise value is added to the true value) is a simple yet powerful approach. However, improper additive noise could result in bias for the aggregate result. It demands an optimal noise distribution to reduce the deviation. In this paper, we develop a mathematical framework to derive the optimal noise distribution that provides privacy protection under the constraint of a limited value deviation. Specifically, we first derive a generic system dynamic function that the optimal noise distribution must satisfy, and further investigate two special cases for the distribution of the original value (i.e., Gaussian and Truncated Gaussian distribution). Our theoretical analysis suggests that the Gaussian distribution is the optimal solution for the Gaussian input, and can be regarded as the optimal solution for the truncated Gaussian input under some suitable conditions.