Isogeny volcanoes of elliptic curves and sylow subgroups
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Given an ordinary elliptic curve over a finite field located in the floor of its volcano of ℓ-isogenies, we present an efficient procedure to take an ascending path from the floor to the level of stability and back to the floor. As an application for regular volcanoes, we give an algorithm to compute all the vertices of their craters. In order to do this, we make use of the structure and generators of the ℓ-Sylow subgroups of the elliptic curves in the volcanoes.
NoteInternational Conference on Cryptology and Information Security in Latin America LATINCRYPT 2014: Progress in Cryptology - LATINCRYPT 2014 pp 162-175
Is part ofLecture Notes in Computer Science, 2015, vol. 8895
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Miret, Josep M. (Josep Maria); Pujolàs Boix, Jordi; Valera Martín, Javier (Springer Verlag, 2015)Let E be an elliptic curve defined over a finite field Fq of odd characteristic. Let l≠2 be a prime number different from the characteristic and dividing #E(Fq). We describe how the l-adic valuation of the number of points ...
Fouquet, Mireille; Miret, Josep M. (Josep Maria); Valera Martín, Javier (Elsevier, 2018)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 ...
Miret, Josep M. (Josep Maria); Sadornil Renedo, Daniel; Tena Ayuso, Juan; Tomàs Cuñat, Rosa Ana; Valls Marsal, Magda (Universitat Autònoma de Barcelona. Departament de Matemàtiques, 2007)This paper is devoted to the study of the volcanoes of l-isogenies of elliptic curves over a finite field, focusing on their height as well as on the location of curves across its different levels. The core of the paper ...