Programmation sûre en précision finie : Contrôler les erreurs et les fuites d'informations

Ivan Gazeau 1, 2, 3
1 PARSIFAL - Proof search and reasoning with logic specifications
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
2 COMETE - Concurrency, Mobility and Transactions
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
3 COMETE / PARSIFAL
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
Abstract : In this thesis, we analyze the problem of the finite representation of real numbers and we control the deviation due to this approximation. We particularly focus on two complex problems. First, we study how finite precision interacts with differentially private protocols. We present a methodology to study the perturbations on the probabilistic distribution induced by finite representation. Then we show that a direct implementation of differential privacy protocols is not safe while, with addition of some safeguards, differential privacy is preserved under finite precision up to some quantified inherent leakage. Next, we propose a method to analyze programs that cannot be analyzed by a compositional analysis due to ''erratic'' control flow. This method based on rewrite system techniques allows us to use the proof of correction of the program in the exact semantics to prove the program is still safe in the finite representation.
Document type :
Theses
Complete list of metadatas

Cited literature [41 references]  Display  Hide  Download

https://pastel.archives-ouvertes.fr/pastel-00913469
Contributor : Ivan Gazeau <>
Submitted on : Tuesday, December 3, 2013 - 6:07:09 PM
Last modification on : Wednesday, March 27, 2019 - 4:41:29 PM
Long-term archiving on : Monday, March 3, 2014 - 11:36:01 PM

Identifiers

  • HAL Id : pastel-00913469, version 1

Collections

Citation

Ivan Gazeau. Programmation sûre en précision finie : Contrôler les erreurs et les fuites d'informations. Analyse numérique [cs.NA]. Ecole Polytechnique X, 2013. Français. ⟨pastel-00913469⟩

Share

Metrics

Record views

406

Files downloads

433