Isomorphism classes of elliptic curves over finite fields of characteristic two

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Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Uygulamalı Matematik Enstitüsü, Türkiye

Tezin Onay Tarihi: 2005

Öğrenci: BARIŞ BÜLENT KIRLAR

Danışman: ERSAN AKYILDIZ

Özet:

In this thesis, the work of Menezes on the isomorphism classes of elliptic curves over finite fields of characteristic two is studied. Basic definitions and some facts of the elliptic curves required in this context are reviewed and group structure of elliptic curves are constructed. A fairly detailed investigation is made for the isomorphism classes of elliptic curves due to Menezes and Schoof. This work plays an important role in Elliptic Curve Digital Signature Algorithm. In this context, those isomorphism classes of elliptic curves recommended by National Institute of Standards and Technology are listed and their properties are discussed.