  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.
