Computing the endomorphism ring of an ordinary abelian surface over a finite field
Abstract
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 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2018
 DOI:
 10.48550/arXiv.1810.12270
 arXiv:
 arXiv:1810.12270
 Bibcode:
 2018arXiv181012270S
 Keywords:

 Mathematics  Number Theory;
 11G10;
 11Y40;
 11Y16