Quasi-quadratic elliptic curve point counting using rigid cohomology

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We present a deterministic algorithm that computes the zeta function of a nonsupersingular elliptic curve E over a finite field with p^n elements 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.
14 pages

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Number Theory, Algebraic Geometry, 14H52; 11G20

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http://salesiana.dossiersoluciones.com/handle/123456789/122909

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0701850
 http://arxiv.org/abs/math/0701850

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arXiv