The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference
book for the theory and applications of finite fields. It is not intended to be an introductory …

Public key cryptography is a major interdisciplinary subject with many real-world
applications, such as digital signatures. A strong background in the mathematics underlying …

In 1986, DV Chudnovsky and GV Chudnovsky proposed to use formulae coming from Theta
functions for the arithmetic in Jacobians of genus 2 curves. We follow this idea and derive …

We propose a novel scheme for selective distribution of content, encoded as documents,
that preserves the privacy of the users to whom the documents are delivered and is based …

For counting points of Jacobians of genus 2 curves over a large prime field, the best known
approach is essentially an extension of Schoof's genus 1 algorithm. We propose various …

We study the complexity of computing one or several terms (not necessarily consecutive) in
a recurrence with polynomial coefficients. As applications, we improve the best currently …

We present an implementation of elliptic curves and of hyperelliptic curves of genus 2 and 3
over prime fields. To achieve a fair comparison between the different types of groups, we …

Groups of unknown order are of major interest due to their applications including time-lock
puzzles, verifiable delay functions, and accumulators. In this paper we focus on trustless …

We propose fast algorithms for computing composed products and composed sums, as well
as diamond products of univariate polynomials. These operations correspond to special …

Groups of unknown order are of major interest due to their applications including time-lock
puzzles, verifiable delay functions, and accumulators. In this paper we focus on trustless …