2009/12/10 by Jean‐François Biasse, Biasse, Jean-François
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Coding theory and cryptography #Cryptography and Residue Arithmetic #Cryptography and Security (cs.CR) #FOS: Computer and information sciences
paper · pdf · doi:10.48550/arxiv.0912.1927
openalex publication_date 2009/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyse the complexity of the computation of the class group structure, regulator, and a system of fundamental units of a certain class of number fields. Our approach differs from Buchmann's, who proved a complexity bound of L(1/2,O(1)) when the discriminant tends to infinity with fixed degree. We achieve a subexponential complexity in O(L(1/3,O(1))) when both the discriminant and the degree of the extension tend to infinity by using techniques due to Enge and Gaudry in the context of algebraic curves over finite fields.