Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
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There are many bilinear pairings that naturally appear when one studies elliptic curves, abelian varieties, and related groups. Some of these pairings, notably the Weil and Lichtenbaum-Tate pairings, can be defined over finite fields and have important applications in cryptography. Others, such as the Néron-Tate canonical height pairing and the Cassels-Tate pairing on the Shafarevich-Tate group, are of fundamental importance in number theory and arithmetic geometry, but have seen limited use in cryptography. In this article I will present a survey of some of the pairings that are used to study elliptic curves and abelian varieties. I will attempt to show why they are natural pairings and how they fit into a wider framework.