Deciding accuracy of differential privacy schemes
| Autor: | A. Prasad Sistla, Gilles Barthe, Paul Krogmeier, Mahesh Viswanathan, Rohit Chadha |
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| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Class (set theory) Computer Science - Cryptography and Security Computer Science - Programming Languages Theoretical computer science Conjecture Computer science Probabilistic logic 020207 software engineering 0102 computer and information sciences 02 engineering and technology Mathematical proof 01 natural sciences Decidability Undecidable problem 010201 computation theory & mathematics 0202 electrical engineering electronic engineering information engineering Differential privacy F.3.1 Safety Risk Reliability and Quality Cryptography and Security (cs.CR) Software Programming Languages (cs.PL) Counterexample |
| Zdroj: | Proceedings of the ACM on Programming Languages. 5:1-30 |
| ISSN: | 2475-1421 |
| DOI: | 10.1145/3434289 |
| Popis: | Differential privacy is a mathematical framework for developing statistical computations with provable guarantees of privacy and accuracy. In contrast to the privacy component of differential privacy, which has a clear mathematical and intuitive meaning, the accuracy component of differential privacy does not have a generally accepted definition; accuracy claims of differential privacy algorithms vary from algorithm to algorithm and are not instantiations of a general definition. We identify program discontinuity as a common theme in existing ad hoc definitions and introduce an alternative notion of accuracy parametrized by, what we call, — the of an input x w.r.t. a deterministic computation f and a distance d , is the minimal distance d ( x , y ) over all y such that f ( y )≠ f ( x ). We show that our notion of accuracy subsumes the definition used in theoretical computer science, and captures known accuracy claims for differential privacy algorithms. In fact, our general notion of accuracy helps us prove better claims in some cases. Next, we study the decidability of accuracy. We first show that accuracy is in general undecidable. Then, we define a non-trivial class of probabilistic computations for which accuracy is decidable (unconditionally, or assuming Schanuel’s conjecture). We implement our decision procedure and experimentally evaluate the effectiveness of our approach for generating proofs or counterexamples of accuracy for common algorithms from the literature. |
| Databáze: | OpenAIRE |
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