2009/04/15 by François Morain, Morain, François · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT
paper · pdf · doi:10.48550/arxiv.0904.2243
arxiv created 2009/04/15 · openalex publication_date 2009/04/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Edwards curves are a particular form of elliptic curves that admit a fast, unified and complete addition law. Relations between Edwards curves and Montgomery curves have already been described. Our work takes the view of parameterizing elliptic curves given by their j-invariant, a problematic that arises from using curves with complex multiplication, for instance. We add to the catalogue the links with Kubert parameterizations of X0(2) and X0(4). We classify CM curves that admit an Edwards or Montgomery form over a finite field, and justify the use of isogenous curves when needed.