We develop a simple and efficient algorithm to compute Riemann–Roch spaces of divisors
in general algebraic function fields which does not use the Brill–Noether method of adjoints …

We provide a convenient mathematical framework that essentially encompasses all known
pairing functions based on the Tate pairing and also applies to the Weil pairing. We prove …

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 …

When a pairing e: G _1 * G _2 → G _ T e: G 1× G 2→ GT, on an elliptic curve E defined over
a finite field F _q F q, is exploited for an identity-based protocol, there is often the need to …

This paper presents the first study of pairing computation on curves with embedding degree
$15 $. We compute the Ate and the twisted Ate pairing for a family of curves with parameter …

Sei F ein algebraischer Zahlkörper oder ein algebraischer Funktionenkörper über Q oder
einem endlichen Körper. In dieser Arbeit beschreiben wir einen effizienten Algorithmus zur …

The goal of this paper is to describe a practical and efficient algorithm for computing in the
Jacobian of a large class of algebraic curves over a finite field. For elliptic and hyperelliptic …

We develop a simple and e cient algorithm to compute Riemann-Roch spaces of divisors in
general algebraic function elds which does not use the Brill-Noether method of adjoints nor …

We propose a polynomial time f-algorithm (a deterministic algorithm which uses an oracle
for factoring univariate polynomials over F _q F q) for computing an isomorphism (if there is …

We present two algorithms for the arithmetic of cubic curves with a totally ramified prime at
infinity. The first algorithm, inspired by Cantor's reduction for hyperelliptic curves, is easily …