{"id":{"repo_id":"oldenburg","oai_identifier":"oai:oops.uni-oldenburg.de:905"},"canonical_url":"https://search.dev.ndltd.org/etd/oldenburg/oai:oops.uni-oldenburg.de:905","repository":{"repo_id":"oldenburg","name":"Carl von Ossietzky Universität Oldenburg","base_url":"http://oops.uni-oldenburg.de/cgi/oai2"},"display":{"title":"The Arithmetic of Elliptic and Hyperelliptic Curves with Applications to Pairing-Based Cryptography","abstract":"After giving an extensive treatment of the theory of algebraic curves and their connection to the theory of algebraic function fields of one variable, the thesis concentrates on pairings (such as the Tate pairing) defined on groups related to a given absolutely irreducible non-singular curve over a finite field. Those pairings are being studied in terms of their usability in cryptography. Important special cases, such as elliptic and hyperelliptic curves are being discussed, whereas the arithmetic of those curves lies in the focus.","abstract_html":"After giving an extensive treatment of the theory of algebraic curves and their connection to the theory of algebraic function fields of one variable, the thesis concentrates on pairings (such as the Tate pairing) defined on groups related to a given absolutely irreducible non-singular curve over a finite field. Those pairings are being studied in terms of their usability in cryptography. Important special cases, such as elliptic and hyperelliptic curves are being discussed, whereas the arithmetic of those curves lies in the focus.","abstract_has_math":false,"creators":["Peter, Andreas"],"institution":"Universität Oldenburg","degree_name":null,"degree_level":"Diplom","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009","date_published":"2009","updated_at":"2026-07-27T20:27:51Z","subjects":["Hyperelliptische Kurve , Miller Algorithmus , Tate Paarung , Weil Paarung"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://oops.uni-oldenburg.de/905","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Peter, Andreas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["BIS der Universität Oldenburg"]},{"key":"dc:type","label":"Dc Type","values":["masterThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Diplom"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Universität Oldenburg"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Hyperelliptische Kurve , Miller Algorithmus , Tate Paarung , Weil Paarung"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["After giving an extensive treatment of the theory of algebraic curves and their connection to the theory of algebraic function fields of one variable, the thesis concentrates on pairings (such as the Tate pairing) defined on groups related to a given absolutely irreducible non-singular curve over a finite field. Those pairings are being studied in terms of their usability in cryptography. Important special cases, such as elliptic and hyperelliptic curves are being discussed, whereas the arithmetic of those curves lies in the focus.","Die Arbeit gibt zunächst eine Einführung in die Theorie algebraischer Kurven und algebraischer Funktionenkörper. Es wird ein detaillierter Zusammenhang zwischen diesen beiden Theorien hergestellt, welcher komplett auf die moderne Grothendieck-Theorie verzichtet. Danach liegen Paarungen auf solchen Kurven (wie z.B. die Tate Paarung) im Fokus, welche intensiv bzgl. ihrer Nutzbarkeit in der Kryptologie studiert werden. Wichtige Spezialfälle, wie elliptische und hyperelliptische Kurven werden diskutiert, wobei die Arithmetik solcher Kurven im Vordergrund steht."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["The Arithmetic of Elliptic and Hyperelliptic Curves with Applications to Pairing-Based Cryptography"]}]}],"canonical_facts":{"dc:creator":["Peter, Andreas"],"dc:description.abstract":["After giving an extensive treatment of the theory of algebraic curves and their connection to the theory of algebraic function fields of one variable, the thesis concentrates on pairings (such as the Tate pairing) defined on groups related to a given absolutely irreducible non-singular curve over a finite field. Those pairings are being studied in terms of their usability in cryptography. Important special cases, such as elliptic and hyperelliptic curves are being discussed, whereas the arithmetic of those curves lies in the focus.","Die Arbeit gibt zunächst eine Einführung in die Theorie algebraischer Kurven und algebraischer Funktionenkörper. Es wird ein detaillierter Zusammenhang zwischen diesen beiden Theorien hergestellt, welcher komplett auf die moderne Grothendieck-Theorie verzichtet. Danach liegen Paarungen auf solchen Kurven (wie z.B. die Tate Paarung) im Fokus, welche intensiv bzgl. ihrer Nutzbarkeit in der Kryptologie studiert werden. Wichtige Spezialfälle, wie elliptische und hyperelliptische Kurven werden diskutiert, wobei die Arithmetik solcher Kurven im Vordergrund steht."],"dc:format.medium":["application/pdf"],"dc:publisher":["BIS der Universität Oldenburg"],"dc:subject":["Hyperelliptische Kurve , Miller Algorithmus , Tate Paarung , Weil Paarung"],"dc:title":["The Arithmetic of Elliptic and Hyperelliptic Curves with Applications to Pairing-Based Cryptography"],"dc:type":["masterThesis"],"thesis:degree_level":["Diplom"],"thesis:institution_name":["Universität Oldenburg"]},"updated_at":"2026-07-27T20:27:51Z"}