20.500.12556/RUL-110365 O geometriji diferencirane zasebnosti delo diplomskega seminarja On the Geometry of Differential Privacy 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. 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. diferencirana zasebnost odzivni mehanizem K-normni mehanizem izotropski položaj differential privacy response mechanism K-norm mechanism isotropic position true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2019-09-14 07:15:53 2019-09-14 07:15:58 2024-05-30 10:23:26 0000-00-00 00:00:00 2019 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.2 99109 18723161 1037.pdf 1037.pdf 1 E358894708B9C42EF68310BD51D97EB5 647c5653ba402f6b9b1cd9a135c04257e22724893fde400de3f385fc246ecb43 19238a44-a1b7-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=122021 Fakulteta za matematiko in fiziko 0 0 0