Abelian varieties and cryptography

Let A be an Abelian variety over a finite field F. The possibility of using the group A(F) of points on A in F as the basis of a public-key cryptography scheme is still at an early stage of exploration. In this article, we will discuss some of the issues and their current staus. In particular, we will discuss arithmetic on Abelian varieties, methods for point counting, and attacks on the Discrete Logarithm Problem, especially those that are peculiar to higher-dimensional varieties.