Elliptic curves have been intensively studied in algebraic geometry and number theory. In
recent years they have been used in devising efficient algorithms for factoring integers and …

This book is intended as a text for a course on cryptography with emphasis on algebraic
methods. It is written so as to be accessible to graduate or advanced undergraduate …

This book is mainly devoted to some computational and algorithmic problems in finite fields
such as, for example, polynomial factorization, finding irreducible and primitive polynomials …

This paper gives some details about howWeil descent can be used to solve the discrete
logarithm problem on elliptic curves which are defined over finite fields of small …

We generalize Sudan's (see J. Compl., vol. 13, p. 180-93, 1997) results for Reed-Solomon
codes to the class of algebraic-geometric codes, designing algorithms for list decoding of …

This paper is concerned with algorithms for computing in the divisor class group of a
nonsingular plane curve of the form $ y^ n= c (x) $ which has only one point at infinity …

We present an index calculus algorithm which is particularly well suited to solve the discrete
logarithm problem (DLP) in degree 0 class groups of curves over finite fields which are …

We use an embedding of the symmetric $ d $ th power of any algebraic curve $ C $ of genus
$ g $ into a Grassmannian space to give algorithms for working with divisors on $ C $, using …

We derive an explicit method of computing the composition step in Cantor's algorithm for
group operations on Jacobians of hyperelliptic curves. Our technique is inspired by the …

Let $ C $ be a curve of genus $ g $ over a field $ k $. We describe probabilistic algorithms
for addition and inversion of the classes of rational divisors in the Jacobian of $ C $. After a …