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Computing endomorphism rings of abelian varieties of dimension two

2015; American Mathematical Society; Volume: 84; Issue: 294 Linguagem: Inglês

10.1090/s0025-5718-2015-02938-x

1088-6842

Gaetan Bisson,

Cryptography and Residue Arithmetic

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].