Explicit maximal and minimal curves over finite fields of odd characteristics

On maximal curves over finite fields of small order

Elliptic curves with weak coverings over cubic extensions of finite fields with odd characteristics

In this paper, we present a classification of classes of elliptic curves defined over cubic extension of finite fields with odd characteristics, which have coverings over the finite fields therefore can be attacked by the GHS attack. We then show the density of these weak curves with hyperelliptic and non-hyperelliptic coverings respectively. In particular, we shown for elliptic curves defined ...

Elliptic Curves over Finite Fields

In this chapter, we study elliptic curves defined over finite fields. Our discussion will include the Weil conjectures for elliptic curves, criteria for supersingularity and a description of the possible groups arising as E(Fq). We shall use basic algebraic geometry of elliptic curves. Specifically, we shall need the notion and properties of isogenies of elliptic curves and of the Weil pairing....

Elliptic Curves over Finite Fields

Counting curves over finite fields

Article history: Received 25 August 2014 Received in revised form 10 September 2014 Accepted 18 September 2014 Available online 4 November 2014 Communicated by H. Stichtenoth MSC: 11G20 10D20 14G15 14H10