Trustworthy Systems

The Laplace mechanism has optimal utility for differential privacy over continuous queries


Natasha Fernandes, Annabelle McIver and Carroll Morgan

    School of Computer Science and Engineering
    Sydney 2052, Australia


Differential Privacy protects individuals’ data when statistical queries are published from aggregated databases: applying “obfuscating” mechanisms to the query results makes the released information less specific but, unavoidably, also decreases its utility. Yet it has been shown that for discrete data (e.g. counting queries), a mandated degree of privacy and a reasonable interpretation of loss of utility, the Geometric obfuscating mechanism is optimal: it loses as little utility as possible.

For continuous query results however (e.g. real numbers) the optimality result does not hold. Our contribution here is to show that optimality is regained by using the Laplace mechanism for the obfuscation.

The technical apparatus involved includes the earlier discrete result [Ghosh], recent work on abstract channels and their geometric representation as hyper-distributions, and the dual interpretations of distance between distributions provided by the Kantorovich-Rubinstein Theorem.

Index Terms: Differential privacy, utility, optimal mechanisms, quantitative information flow, abstract channels, hyper-distributions.

BibTeX Entry

    journal          = {36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)},
    paperurl         = {},
    author           = {Natasha Fernandes and Annabelle McIver and Carroll Morgan},
    year             = {2021},
    title            = {The {Laplace} Mechanism has optimal utility for differential privacy over continuous queries},
    pages            = {1-12}