2006/03/21 by David Kohel, David R. Kohel, Benjamin Smith +3
Computer Science · Mathematics · #11G #11Y16 #14Q05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11G #msc:11Y16 #msc:14Q05
paper · pdf · doi:10.48550/arxiv.math/0603505
15 pages, LaTeX with xy-pic and algorithmicx packages. To appear in the proceedings of the 7th Algorithmic Number Theory Symposium (ANTS-VII), Berlin, July 2006
arxiv created 2006/03/21 · openalex publication_date 2006/03/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Elliptic curves have a well-known and explicit theory for the construction and application of endomorphisms, which can be applied to improve performance in scalar multiplication. Recent work has extended these techniques to hyperelliptic Jacobians, but one obstruction is the lack of explicit models of curves together with an efficiently computable endomorphism. In the case of hyperelliptic curves there are limited examples, most methods focusing on special CM curves or curves defined over a small field. In this article we describe three infinite families of curves which admit an efficiently computable endomorphism, and give algorithms for their efficient application.