Distributed Transition Systems with Tags for Privacy Analysis

Siva Anantharaman (1) , Sabine Frittella (2) , Benjamin Nguyen (2)

1 LMV - Langages, Modèles et Vérification
2 SDS - Sécurité des Données et des Systèmes

Abstract: We present a logical framework that formally models how a given private information P stored on a given database D, can get captured progressively, by an agent/adversary querying the database repeatedly. Named DLTTS (Distributed Labeled Tagged Transition System), the frame- work borrows ideas from several domains: Probabilistic Automata of Segala, Probabilistic Concurrent Systems, and Probabilistic labelled tran- sition systems. To every node on a DLTTS is attached a tag that repre- sents the ‘current’ knowledge of the adversary, acquired from the responses of the answering mechanism of the DBMS to his/her queries, at the nodes traversed earlier, along any given run; this knowledge is completed at the same node, with further relational deductions, possibly in combina- tion with ‘public’ information from other databases given in advance. A ‘blackbox’ mechanism is also part of a DLTTS, and it is meant as an or- acle; its role is to tell if the private information has been deduced by the adversary at the current node, and if so terminate the run. An additional special feature is that the blackbox also gives information on how ‘close’, or how ‘far’, the knowledge of the adversary is, from the private infor- mation P , at the current node. A metric is defined for that purpose, on the set of all ‘type compatible’ tuples from the given database, the data themselves being typed with the headers of the base. Despite the transi- tion systems flavor of our framework, this metric is not ‘behavioral’ in the sense presented in some other works. It is exclusively database oriented, and allows to define new notions of adjacency and of -indistinguishabilty between databases, more generally than those usually based on the Ham- ming metric (and a restricted notion of adjacency). Examples are given all along to illustrate how our framework works. Keywords: Database, Privacy, Transition System, Probability, Distribution.

Mots clés: Database; Privacy; Transition System; Probability; Distribution

Domaines: Informatique et langage [cs.CL]

Siva Anantharaman, Sabine Frittella, Benjamin Nguyen. Distributed Transition Systems with Tags for Privacy Analysis. 2022. ⟨hal-03623522v3⟩