Universitat de Lleida
Volcanoes of ℓ–isogenies of elliptic curves are a special case of graphs with a cycle called crater. In this paper, given an elliptic curve E of a volcano of ℓ–isogenies, we present a condition over an endomorphism ϕ of E in order to determine which ℓ–isogenies of E are non-descending. The endomorphism ϕ is defined as the crater cycle of an m–volcano where E is located, with m 6= ℓ. The condition is feasible when ϕ is a distortion map for a subgroup of order ℓ of E. We also provide some relationships among the crater sizes of volcanoes of m–isogenies whose elliptic curves belong to a volcano of ℓ–isogenies.
Research of the authors was partially supported by grants MTM2013-46949-P (Spanish MINECO) and 2014 SGR1666 (Generalitat de Catalunya).
English
Finite field; Elliptic curve; Isogeny; Volcano; Distortion map
Elsevier
info:eu-repo/grantAgreement/MINECO//MTM2013-46949-P/ES/CRIPTOGRAFIA CON CURVAS ALGEBRAICAS PARA LA E-SOCIEDAD/
Versió postprint del document publicat a https://doi.org/10.1016/j.ffa.2017.09.006
Finite Fields and Their Applications, 2018, vol. 49, núm. C, p. 108-125
cc-by-nc-nd (c) Elsevier, 2018
http://creativecommons.org/licenses/by-nc-nd/4.0/
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