Background Elliptic curve cryptographic schemes were proposed independently in 1985 by
Neal Koblitz (Koblitz 1987) and Victor Miller (Miller 1986). They are the elliptic curve …

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 …

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 present a variation of the index calculus attack by Gaudry which can be used to solve the
discrete logarithm problem in the Jacobian of hyperelliptic curves. The new algorithm has a …

Given a polynomial system of n equations in n unknowns that depends on some parameters,
we define the notion of parametric geometric resolution as a means to represent some …

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 …

For most of the time since they were proposed, it was widely believed that hyperelliptic curve
cryptosystems (HECC) carry a substantial performance penalty compared to elliptic curve …

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 …

CONSTRUCTING HYPERELLIPTIC CURVES OF GENUS 2 SUITABLE FOR
CRYPTOGRAPHY 1. Introduction In 1986 Atkin [1] proposed an algorithm f Page 1 …