Deciding Differential Privacy of Online Algorithms with Multiple Variables

• URL: http://arxiv.org/abs/2309.06615v1
• Date: Tue, 12 Sep 2023 22:03:01 GMT
• Title: Deciding Differential Privacy of Online Algorithms with Multiple Variables
• Authors: Rohit Chadha, A. Prasad Sistla, Mahesh Viswanathan, Bishnu Bhusal,
• Abstract summary: This paper generalizes an automaton model called DiP automata to describe such algorithms. Our PSPACE algorithm also computes a value for $mathfrakD$ when the given automaton is differentially private.
• Score: 0.41248472494152805
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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 (See arXiv:2104.14519) 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 $\epsilon$. An automaton $A$ will be said to be differentially private if, for some $\mathfrak{D}$, the automaton is $\mathfrak{D}\epsilon$-differentially private for all values of $\epsilon>0$. 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 $\mathfrak{D}$ when the given automaton is differentially private. The algorithm has been implemented, and experiments demonstrating its effectiveness are presented.

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