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Relational $\star$-Liftings for Differential Privacy
Logical methods in computer science, 2019-12, Vol.15, Issue 4
[Peer Reviewed Journal]
EISSN: 1860-5974 ;DOI: 10.23638/LMCS-15(4:18)2019
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Title:
Relational $\star$-Liftings for Differential Privacy
Author:
Gilles Barthe
;
Thomas Espitau
;
Justin Hsu
;
Tetsuya Sato
;
Pierre-Yves Strub
Subjects:
computer science - logic in computer science
;
computer science - programming languages
Is Part Of:
Logical methods in computer science, 2019-12, Vol.15, Issue 4
Description:
Recent developments in formal verification have identified approximate liftings (also known as approximate couplings) as a clean, compositional abstraction for proving differential privacy. This construction can be defined in two styles. Earlier definitions require the existence of one or more witness distributions, while a recent definition by Sato uses universal quantification over all sets of samples. These notions have each have their own strengths: the universal version is more general than the existential ones, while existential liftings are known to satisfy more precise composition principles. We propose a novel, existential version of approximate lifting, called $\star$-lifting, and show that it is equivalent to Sato's construction for discrete probability measures. Our work unifies all known notions of approximate lifting, yielding cleaner properties, more general constructions, and more precise composition theorems for both styles of lifting, enabling richer proofs of differential privacy. We also clarify the relation between existing definitions of approximate lifting, and consider more general approximate liftings based on $f$-divergences.
Publisher:
Logical Methods in Computer Science e.V
Language:
English
Identifier:
EISSN: 1860-5974
DOI: 10.23638/LMCS-15(4:18)2019
Source:
Alma/SFX Local Collection
ROAD: Directory of Open Access Scholarly Resources
DOAJ Directory of Open Access Journals
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