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Computing endomorphism rings of elliptic curves under the GRH

Gaetan Bisson 1, 2 
2 CARAMEL - Cryptology, Arithmetic: Hardware and Software
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : We design a probabilistic algorithm for computing endomorphism rings of ordinary elliptic curves defined over finite fields that we prove has a subexponential runtime in the size of the base field, assuming solely the generalized Riemann hypothesis. Additionally, we improve the asymptotic complexity of previously known, heuristic, subexponential methods by describing a faster isogeny-computing routine.
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Submitted on : Thursday, January 27, 2011 - 6:10:29 PM
Last modification on : Wednesday, February 2, 2022 - 4:30:55 PM

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Gaetan Bisson. Computing endomorphism rings of elliptic curves under the GRH. Journal of Mathematical Cryptology, 2011, 5 (2), pp.101-113. ⟨10.1515/JMC.2011.008⟩. ⟨inria-00560258⟩



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