Recent work on formal verification of differential privacy
shows a trend toward usability and expressiveness – generating a correctness proof of sophisticated algorithm while
minimizing the annotation burden on programmers. Sometimes, combining those two requires substantial changes to
program logics: one recent paper is able to verify Report
Noisy Max automatically, but it involves a complex verification system using customized program logics and verifiers.
In this paper, we propose a new proof technique, called
shadow execution, and embed it into a language called ShadowDP. ShadowDP uses shadow execution to generate proofs
of differential privacy with very few programmer annotations and without relying on customized logics and verifiers.
In addition to verifying Report Noisy Max, we show that it
can verify a new variant of Sparse Vector that reports the gap
between some noisy query answers and the noisy threshold.
Moreover, ShadowDP reduces the complexity of verification:
for all of the algorithms we have evaluated, type checking
and verification in total takes at most 3 seconds, while prior
work takes minutes on the same algorithms.
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Free gap information from the differentially private sparse vector and noisy max mechanisms
Noisy Max and Sparse Vector are selection algorithms for differential privacy and serve as building blocks for more complex algorithms. In this paper we show that both algorithms can release additional information for free (i.e., at no additional privacy cost). Noisy Max is used to return the approximate maximizer among a set of queries. We show that it can also release for free the noisy gap between the approximate maximizer and runner-up. This free information can improve the accuracy of certain subsequent counting queries by up to 50%. Sparse Vector is used to return a set of queries that are approximately larger than a fixed threshold. We show that it can adaptively control its privacy budget (use less budget for queries that are likely to be much larger than the threshold) in order to increase the amount of queries it can process. These results follow from a careful privacy analysis.
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- NSF-PAR ID:
- 10251221
- Date Published:
- Journal Name:
- Proceedings of the VLDB Endowment
- Volume:
- 13
- Issue:
- 3
- ISSN:
- 2150-8097
- Page Range / eLocation ID:
- 293 to 306
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.14778/3368289.3368295
