Computing endomorphism rings of elliptic curves under the GRH

DOI10.1515/JMC.2011.008zbMath1250.11106arXiv1101.4323OpenAlexW3105727631MaRDI QIDQ3096951

Gaetan Bisson

Publication date: 15 November 2011

Published in: Journal of Mathematical Cryptology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.4323

zbMATH Keywords

endomorphism ringselliptic curvesgeneralized Riemann hypothesissubexponential algorithm

Mathematics Subject Classification ID

Cryptography (94A60) Curves over finite and local fields (11G20) Algebraic number theory computations (11Y40) Applications to coding theory and cryptography of arithmetic geometry (14G50)

Related Items (11)

On the hardness of the computational ring-LWR problem and its applications ⋮ -adic images of Galois for elliptic curves over (and an appendix with John Voight) ⋮ Computing the endomorphism ring of an ordinary abelian surface over a finite field ⋮ On the computation of overorders ⋮ Fast heuristic algorithms for computing relations in the class group of a quadratic order, with applications to isogeny evaluation ⋮ CSIDH: an efficient post-quantum commutative group action ⋮ A low-memory algorithm for finding short product representations in finite groups. ⋮ On the computation of the endomorphism rings of abelian surfaces ⋮ On the elliptic curve endomorphism generator ⋮ Subexponential time relations in the class group of large degree number fields ⋮ Computing endomorphism rings of abelian varieties of dimension two

Cites Work

• Expander graphs based on GRH with an application to elliptic curve cryptography
• Linearizing torsion classes in the Picard group of algebraic curves over finite fields
• Counting points on elliptic curves over finite fields
• Computing the endomorphism ring of an ordinary elliptic curve over a finite field
• A hyperelliptic smoothness test. I
• Pairing the Volcano

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