## Cryptology ePrint Archive: Report 2012/525

Computing endomorphism rings of abelian varieties of dimension two

Gaetan Bisson

Abstract: Generalizing a method of Sutherland and the author for elliptic curves, we design a subexponential algorithm for computing the endomorphism ring structure of ordinary abelian varieties of dimension two over finite fields. Although its correctness and complexity bound rely on several assumptions, we report on practical computations showing that it performs very well and can easily handle previously intractable cases.

Category / Keywords: foundations / hyperelliptic curves, complex multiplication, isogenies