Counting Rational Points on Curves over Finite Fields (Extended Abstract)
نویسندگان
چکیده
We consider the problem of counting the number of points on a plane curve, given by a homogeneous polynomial F E Fp[x, y, 21, which is rational over the ground field IFp. More precisely, we show that if we are given a projective plane curve C of degree n, and if C has only ordinary multiple points, then one can compute the number of IFp-rational points on C in randomized time (logp)" where A = (degF)O('). The complexity of this construction improves previously known bounds for this problem by a t least an order of magnitude.
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