2009/05/14 by Romain Cosset · 1 citation
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #Edwards curve #Elliptic curve #Factoring #Factorization #Genus #Hyperelliptic curve #Hyperelliptic curve cryptography #Polynomial and algebraic computation #Supersingular elliptic curve #math.NT #msc:11Y05 #msc:11Y16 #msc:11Y40
paper · pdf · doi:10.1090/s0025-5718-09-02295-9
arxiv created 2009/05/14 · openalex publication_date 2009/08/20 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The elliptic curve method (ECM) is one of the best factorization methods available. It is possible to use hyperelliptic curves instead of elliptic curves but it is in theory slower. We use special hyperelliptic curves and Kummer surfaces to reduce the complexity of the algorithm. Our implementation GMP-HECM is faster than GMP-ECM for factoring large numbers.