Quasi-quadratic elliptic curve point counting using rigid cohomology

• Autores: Hendrik Hubrechts
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 44, Nº 9, 2009, págs. 1255-1267
• Idioma: inglés
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• Resumen

  • Let E be a nonsupersingular elliptic curve over the finite field with pn elements. We present a deterministic algorithm that computes the zeta function and hence the number of points of such a curve E in time quasi-quadratic in n. An older algorithm having the same time complexity uses the canonical lift of E, whereas our algorithm uses rigid cohomology combined with a deformation approach. An implementation in small odd characteristic turns out to give very good results.