Privaatsust säilitav lineaarne planeerimine
Date
2013
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Tartu Ülikool
Abstract
Rakendusmatemaatikat kasutatakse paljudes reaalse maailma probleemides. Nende probleemide lahendamine võib olla seotud tundlike andmetega. Sellisel juhul läheb tarvis krüptograafilisi meetodeid. Kuigi on tõestatud, et iga funktsiooni saab arvutada turvaliselt, on küsimus selles, kuidas teha seda efektiivselt. Üldiselt võib olla keeruline lahendada optimeerimisülesandeid nii turvaliselt kui ka efektiivselt, kuid häid lahendeid saab leida kitsamatele ülesannete klassidele, näiteks lineaarse planeerimise ülesannetele. Käesolev töö annab ülevaate teisenduspõhisest privaatsust säilitavast lineaarsest planeerimisest, tutvustades mõningaid probleeme eelmistes töödes ja näidates teisenduspõhise meetodi ebaturvalisust. Töö esitab konkreetseid ründeid olemasolevate teisendusmeetodite vastu. Töös pakutakse välja võimalikud viisid nende rünnete eest kaitsmiseks ja seejärel näidatakse, et mõned teisenduspõhise meetodi puudused ei ole üldse ületatavad, vähemalt eelmistes töödes kasutatud teatud teisenduste klassi raamesse jäädes.
Applied mathematics is used in many real-world problems. Solving some of these problems may involve sensitive data. In this case, cryptographic techniques become necessary. Although it has been proven that any function can be computed securely, it is still a question how to do it efficiently. While it may be difficult to solve optimization tasks securely and efficiently in general, there may still be solutions for some particular classes of tasks, such as linear programming. This thesis gives an overview of the transformation-based privacy-preserving linear programming. The thesis introduces some problems of this approach that have been present in the previous works and demonstrates its insecurity. It presents concrete attacks against published methods following this approach. Possible methods of protection against these attacks are proposed. It has been proven that there are issues that cannot be resolved at all using the particular known class of efficient transformations that has been used before.
Applied mathematics is used in many real-world problems. Solving some of these problems may involve sensitive data. In this case, cryptographic techniques become necessary. Although it has been proven that any function can be computed securely, it is still a question how to do it efficiently. While it may be difficult to solve optimization tasks securely and efficiently in general, there may still be solutions for some particular classes of tasks, such as linear programming. This thesis gives an overview of the transformation-based privacy-preserving linear programming. The thesis introduces some problems of this approach that have been present in the previous works and demonstrates its insecurity. It presents concrete attacks against published methods following this approach. Possible methods of protection against these attacks are proposed. It has been proven that there are issues that cannot be resolved at all using the particular known class of efficient transformations that has been used before.