Quasi-quadratic elliptic curve point counting using rigid cohomology
نویسندگان
چکیده
منابع مشابه
Quasi-quadratic elliptic curve point counting using rigid cohomology
We present a deterministic algorithm that computes the zeta function of a nonsupersingular elliptic curve E over a finite field with p 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 g...
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I consider the problem of computing the zeta function of an algebraic variety defined over a finite field. This problem has been pushed into the limelight in recent years because of its importance in cryptography, at least in the case of curves. Wan’s excellent survey article gives an overview of what has been achieved, and what remains to be done, on the topic [15]. The purpose of this exposit...
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I discuss some algorithms for computing the zeta function of an algebraic variety over a finite field which are based upon rigid cohomology. Two distinct approaches are illustrated with a worked example.
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2009
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2008.02.015