Distorting the volcano
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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.
Is part ofFinite Fields and Their Applications, 2018, vol. 49, núm. C, p. 108-125
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