Deciding Differential Privacy of Online Algorithms with Multiple Variables
Rohit Chadha, A. Prasad Sistla, Mahesh Viswanathan, and Bishnu Bhusal
In Proceedings of the 2023 ACM SIGSAC Conference on Computer and Communications Security , , Copenhagen, Denmark, , 2023
We consider the problem of checking the differential privacy of online randomized algorithms that process a stream of inputs and produce outputs corresponding to each input. This paper generalizes an automaton model called DiP automata [10] to describe such algorithms by allowing multiple real-valued storage variables. A DiP automaton is a parametric automaton whose behavior depends on the privacy budget ∈. An automaton A will be said to be differentially private if, for some D, the automaton is D∈-differentially private for all values of ∈ > 0. We identify a precise characterization of the class of all differentially private DiP automata. We show that the problem of determining if a given DiP automaton belongs to this class is PSPACE-complete. Our PSPACE algorithm also computes a value for D when the given automaton is differentially private. The algorithm has been implemented, and experiments demonstrating its effectiveness are presented.