Quasi-quadratic elliptic curve point counting using rigid cohomology
Abstract
We present a deterministic algorithm that computes the zeta function of a nonsupersingular elliptic curve E over a finite field with pn 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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