delo diplomskega seminarja
Luka Lodrant (Author), Aljoša Peperko (Mentor)

Abstract

V delu najprej predstavimo pojem diferencirane zasebnosti, kot strogo matematično definicijo zasebnosti podatkov, ki pride do izraza pri njihovi javni objavi. Definiramo splošno okolje za numerične podatke, nato pa ocenimo spodnjo mejo napake, ki jo zaseben odzivni mehanizem mora vnesti v podatke. Predstavimo Laplaceov mehanizem, podrobneje pa še $K$-normni in rekurzivni NIM mehanizem. Za vse izpeljemo tudi zgornjo mejo napake in tako za $K$-normni ter NIM mehanizem ocenimo, da sta na določenih razredih poizvedb asimptotsko optimalna. Mehanizme implementiramo in obravnavamo težave, ki pri tem nastanejo.

Keywords

matematika;diferencirana zasebnost;odzivni mehanizem;K-normni mehanizem;izotropski položaj;

Data

Language: Slovenian
Year of publishing:
Typology: 2.11 - Undergraduate Thesis
Organization: UL FS - Faculty of Mechanical Engineering
Publisher: [L. Lodrant]
UDC: 519.2
COBISS: 18723161 Link will open in a new window
Views: 912
Downloads: 143
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Other data

Secondary language: English
Secondary title: On the Geometry of Differential Privacy
Secondary abstract: In this work we present the concept of differential privacy as a rigorous mathematical definition of privacy, which is required for publishing private data. We define a general setting for numerical data and derive a lower bound for the required error of private mechanisms. Laplace mechanism, $K$-norm mechanism and recursive NIM mechanism are presented, each with an upper bound on its error. We conclude that NIM and $K$-norm mechanism are asimptotically optimal for specific classes of queries. Mechanisms are implemented and problems which arise during the implementation are addressed.
Secondary keywords: mathematics;differential privacy;response mechanism;K-norm mechanism;isotropic position;
Type (COBISS): Final seminar paper
Study programme: 0
Embargo end date (OpenAIRE): 1970-01-01
Thesis comment: Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages: 28 str.
ID: 11223560