Computing the endomorphism ring of an ordinary abelian surface over a finite field

JOURNAL OF NUMBER THEORY

卷:202

Article

Springer, Caleb¹ 

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

关键词: Abelian variety;    Ideal class group;    Algorithm;    Computation;    Isogeny;    Finite field;    Fndomorphism ring;   

DOI  :  10.1016/j.jnt.2019.01.013

来源: Elsevier

【 摘 要 】

We present a new algorithm for computing the endomorphism ring of an ordinary abelian surface over a finite field which is subexponential and generalizes an algorithm of Bisson and Sutherland for elliptic curves. The correctness of this algorithm only requires the heuristic assumptions required by the algorithm of Biasse and Fieker [2] which computes the class group of an order in a number field in subexponential time. Thus we avoid the multiple heuristic assumptions on isogeny graphs and polarized class groups which were previously required. The output of the algorithm is an ideal in the maximal totally real subfield of the endomorphism algebra, generalizing the elliptic curve case. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free