Papers › Fast computation of elliptic curve isogenies in characteristic two
Fast computation of elliptic curve isogenies in characteristic two
Xavier Caruso, Elie Eid, Reynald Lercier
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We propose an algorithm that calculates isogenies between elliptic curves defined over an extension K of ℚ₂. It consists in efficiently solving with a logarithmic loss of 2-adic precision the first order differential equation satisfied by the isogeny. We give some applications, especially computing over finite fields of characteristic 2 isogenies of elliptic curves and irreducible polynomials, both in quasi-linear time in the degree.
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