Empirical optimization of divisor arithmetic on hyperelliptic curves over $\mathbf{F}_{2^m}$ - LIRMM - Laboratoire d’Informatique, de Robotique et de Microélectronique de Montpellier Access content directly
Journal Articles Advances in Mathematics of Communications Year : 2013

Empirical optimization of divisor arithmetic on hyperelliptic curves over $\mathbf{F}_{2^m}$

Abstract

A significant amount of effort has been devoted to improving divisor arithmetic on low-genus hyperelliptic curves via explicit versions of generic algorithms. Moderate and high genus curves also arise in cryptographic applications, for example, via the Weil descent attack on the elliptic curve discrete logarithm problem, but for these curves, the generic algorithms are to date the most efficient available. Nagao~\cite{Nagao2000} described how some of the techniques used in deriving efficient explicit formulas can be used to speed up divisor arithmetic using Cantor's algorithm on curves of arbitrary genus. In this paper, we describe how Nagao's methods, together with a sub-quadratic complexity partial extended Euclidean algorithm using the half-gcd algorithm can be applied to improve arithmetic in the degree zero divisor class group. We present numerical results showing which combination of techniques is more efficient for hyperelliptic curves over $\mathbb{F}_{2^n}$ of various genera.

Dates and versions

lirmm-00870376 , version 1 (07-10-2013)

Identifiers

Cite

Laurent Imbert, Michael J. Jacobson Jr. Empirical optimization of divisor arithmetic on hyperelliptic curves over $\mathbf{F}_{2^m}$. Advances in Mathematics of Communications, 2013, 7 (4), pp.485-502. ⟨10.3934/amc.2013.7.485⟩. ⟨lirmm-00870376⟩
187 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More