Primality Testing and Abelian Varieties Over Finite Fields

From Gauss to G|del, mathematicians have sought an efficient
algorithm to distinguish prime numbers from composite
numbers. This book presents a random polynomial time
algorithm for the problem. The methods used are from
arithmetic algebraic geometry, algebraic number theory and
analyticnumber theory. In particular, the theory of two
dimensional Abelian varieties over finite fields is
developed.
The book will be of interest to both researchers and
graduate students in number theory and theoretical computer
science.