Kvantkrüptograafiline positsiooni verifitseerimine juhusliku oraakli mudelis
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2016
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Juhul kui kasutaja õigsuse kontrollimiseks on võimalik kasutada ainult tema asukohta, nimetatakse seda positsiooni verifitseerimiseks. Lihtsaim viis positsiooni verifitseerimisest on kasutaja kauguse mõõtmine keskpunktist (distance bounding). Verifitseerija paikneb kontrollitava ala keskel, saadab informatsiooni tõestajale ning kontrollib vastuse aega. Kuna selline ülesehitus ei ole alati soovitud, on võimalik kasutada ka teistsugust verifitseerijate asetust. Verifitseerijaid saab seada ümber tõestatava piirkonna, teatud liiki triangulatsioonis. Antud lõputöö muudab artiklis [Dominique Unruh, Quantum position verification in the random oracle model, CRYPTO 2014] esitatud positsiooni verifitseerimise protokolli, esitades uue versiooni protokollist, mis on turvaline väiksemal tõestataval piirkonnal. Algse protokolli\n\rturvalisuse tõestus kasutab kahe mängijaga põimunud kvantsüsteemide monogaamsuse mängu teoreemi. Lisades juurde ühe verifitseerija, defineerime uue kolme mängijaga põimunud kvantsüsteemide monogaamsuse mängu.\n\rTõestame et muudetud protokolli turvalisus sõltub uue kolme mängijaga mängu võidu tõenäosusest. Selgitame probleeme ja edusamme antud\n\rmonogaamsuse mängu tõestamisel. Võrdleme erinevaid kolme mängijaga monogaamsuse mänge ning tõestame mõned võidu tõenäosuste tulemused.
Consider a situation where we wish to verify an entity solely by its location. This is called position verification. The simplest form of position verification is distance bounding where the verifier is located in the middle of the provers region, he sends information to the prover and checks how long it takes for the prover to respond. Since this is not always desirable one can place verifiers around the provers region forming a kind of triangulation. This thesis improves on the precision of the quantum position verification protocol form [Dominique Unruh, Quantum position verification in the random oracle model, CRYPTO 2014] i.e. presents a modification of the protocol that is sound for a smaller region. This is done by adding an additional receiving verifier. The previous result uses a two-player monogamy game. We define the three player monogamy game needed for the proof of the new protocol and explain our progress on the proof of this monogamy game. We also compare different three-player monogamy games and prove some results on their winning probabilities.
Consider a situation where we wish to verify an entity solely by its location. This is called position verification. The simplest form of position verification is distance bounding where the verifier is located in the middle of the provers region, he sends information to the prover and checks how long it takes for the prover to respond. Since this is not always desirable one can place verifiers around the provers region forming a kind of triangulation. This thesis improves on the precision of the quantum position verification protocol form [Dominique Unruh, Quantum position verification in the random oracle model, CRYPTO 2014] i.e. presents a modification of the protocol that is sound for a smaller region. This is done by adding an additional receiving verifier. The previous result uses a two-player monogamy game. We define the three player monogamy game needed for the proof of the new protocol and explain our progress on the proof of this monogamy game. We also compare different three-player monogamy games and prove some results on their winning probabilities.