Topic In Elliptic Curves Over Finite Fields: The Groups of Points

TL;DR

This paper provides an introductory overview of the groups of points on elliptic curves over finite fields, emphasizing their role in elliptic curve cryptography and algebraic curves.

Contribution

It offers a focused, elementary exposition on the structure and properties of elliptic curve groups relevant to cryptographic applications.

Findings

Highlights the importance of elliptic curve groups in cryptography

Summarizes elementary properties of elliptic curve groups over finite fields

Connects algebraic curve theory with practical cryptographic systems

Abstract

This article is a short introduction to the theory of the groups of points of elliptic curves over finite fields. It is concerned with the elementary theory and practice of elliptic curves cryptography, the new generation of public key systems. The material and coverage are focused on the groups of points of elliptic curves and algebraic curves, but not exclusively.