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Quasi-quadratic elliptic curve point counting using rigid cohomology

Hendrik Hubrechts
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Abstract

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.

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Hendrik Hubrechts. 2007-01-29. Quasi-quadratic elliptic curve point counting using rigid cohomology. https://arxiv.org/abs/math/0701850

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