Quantitative Information Flow in Boolean Programs

Chadha, Rohit; Kini, Dileep; Viswanathan, Mahesh

doi:10.1007/978-3-642-54792-8_6

Cited by 4 publications

(2 citation statements)

References 31 publications

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“…Kaminski et al [35] studied the arithmetic complexity of almost sure termination for general probabilistic programs with unbounded data types. Chadha et al [13] showed PSPACE-completeness for the problem of bounding quantitative information flow for boolean programs with loops and probabilistic choice. A bound on pure differential privacy entails a bound on quantitative information flow, but not the other way around, and hence their result does not directly apply in our context.…”

Section: Related Workmentioning

confidence: 99%

The Complexity of Verifying Boolean Programs as Differentially Private

Bun

Gaboardi

Glinskih

2022

2022 IEEE 35th Computer Security Foundations Symposium (CSF)

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We study the complexity of the problem of verifying differential privacy for whilelike 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: Rényi 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.

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Section: Related Workmentioning

confidence: 99%

The Complexity of Verifying Boolean Programs as Differentially Private

Bun

Gaboardi

Glinskih

2022

2022 IEEE 35th Computer Security Foundations Symposium (CSF)

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“…However, when quantifying over all distributions the question is coNP-complete [35]. Checking whether the quantitative information flow of a program is less than a threshold has been shown to be PP-hard [34] (but in PSPACE) for loop-free boolean programs and to be PSPACE-complete for boolean programs with loops [10].…”

Section: Related Workmentioning

confidence: 99%

The Complexity of Verifying Loop-Free Programs as Differentially Private

Gaboardi,

Nissim,

Purser

2019

Preprint

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We study the problem of verifying differential privacy for straight line programs with probabilistic choice. Programs in this class can be seen as randomized Boolean circuits. We focus on two different questions: first, deciding whether a program satisfies a prescribed level of privacy; second, approximating the privacy parameters a program realizes. We show that the problem of deciding whether a program satisfies ε-differential privacy is coNP #P -complete. In fact, this is the case when either the input domain or the output range of the program is large. Further, we show that deciding whether a program is (ε, δ)differentially private is coNP #P -hard, and in coNP #P for small output domains, but always in coNP #P #P. Finally, we show that the problem of approximating the level of differential privacy is both NP-hard and coNP-hard.

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Time-Bounded Reachability for Initialized Hybrid Automata with Linear Differential Inclusions and Rectangular Constraints

Roohi

Viswanathan

2014

Lecture Notes in Computer Science

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Quantitative Information Flow in Boolean Programs

Cited by 4 publications

References 31 publications

The Complexity of Verifying Boolean Programs as Differentially Private

The Complexity of Verifying Boolean Programs as Differentially Private

The Complexity of Verifying Loop-Free Programs as Differentially Private

Time-Bounded Reachability for Initialized Hybrid Automata with Linear Differential Inclusions and Rectangular Constraints

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