The Complexity of Verifying Boolean Programs as Differentially Private

We study the complexity of the problem of verifying differential privacy for while-like programs working over boolean values and making probabilistic choices. Programs in this class can be interpreted into finite-state discrete-time Markov Chains (DTMC). We show that the problem of deciding whether...

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Bibliographic Details
Published in2022 IEEE 35th Computer Security Foundations Symposium (CSF) pp. 396 - 411
Main Authors Bun, Mark, Gaboardi, Marco, Glinskih, Ludmila
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.08.2022
Subjects
Complexity theory
Computer security
Differential privacy
Markov processes
Privacy
Probabilistic logic
probabilistic programs
while programs
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Summary:We study the complexity of the problem of verifying differential privacy for while-like programs working over boolean values and making probabilistic choices. Programs in this class can be interpreted into finite-state discrete-time Markov Chains (DTMC). We show that the problem of deciding whether a program is differentially private for specific values of the privacy parameters is PSPACE-complete. To show that this problem is in PSPACE, we adapt classical results about computing hitting probabilities for DTMC. To show PSPACE-hardness we use a reduction from the problem of checking whether a program almost surely terminates or not. We also show that the problem of approximating the privacy parameters that a program provides is PSPACE-hard. Moreover, we investigate the complexity of similar problems also for several relaxations of differential privacy: Renyi differential privacy, concentrated differential privacy, and truncated concentrated differential privacy. For these notions, we consider gap-versions of the problem of deciding whether a program is private or not and we show that all of them are PSPACE-complete.
DOI:10.1109/CSF54842.2022.9919653