Single angle Group structures of elliptic curves #1
Auteurs : Shparlinski, Igor
CIRM (Editeur )
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Résumé : We give a survey of results which address the following generic question: How does a random elliptic curve over a finite field look like.11G20 - Curves over finite and local fields
This question has a rich variety of specfic interpretations, which depend on how one defines a random curve and what properties which are of interest. The former may include randomisation of the coefficients of the Weierstrass equation or the prime power defining the field, or both. The latter may include studying the group structure, arithmetic structure of the number of points (primality, smoothness, etc.) and certain divisibility conditions.
These questions are related to such celebrated problems as Lang-Trotter and Sato-Tate conjectures. More recently the interest to these questions was re-fueled by the needs of pairing based cryptography.
In a series of talks we will describe the state of art in some of these directions, demonstrate the richness of underlying mathematics and pose some open questions.
14G15 - Finite ground fields
14H52 - Elliptic curves