## Computing endomorphism rings of abelian varieties of dimension two

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## Abstract:

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

**Note**. Some results of this paper previously appeared in the author’s thesis, [*Endomorphism Rings in Cryptography*, Ph.D. Thesis. Eindhoven University of Technology and Institut National Polytechnique de Lorraine, 2011. ISBN: 90-386-2519-7].

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## Additional Information

**Gaetan Bisson**- Affiliation: University of French Polynesia, BP6570, 98702 Faaa, French Polynesia
- Email: bisson@gaati.org
- Received by editor(s): September 24, 2012
- Received by editor(s) in revised form: October 15, 2013
- Published electronically: January 20, 2015
- © Copyright 2015 American Mathematical Society
- Journal: Math. Comp.
**84**(2015), 1977-1989 - MSC (2010): Primary 11Y40, 14Q15
- DOI: https://doi.org/10.1090/S0025-5718-2015-02938-X
- MathSciNet review: 3335900