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Counting rational points on curves over finite fields

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2 Author(s)
Ming-Deh Huang ; Dept. of Comput. Sci., Univ. of Southern California, Los Angeles, CA, USA ; Ierardi, D.

We consider the problem of counting the number of points on a plane curve, given by a homogeneous polynomial F∈Fp [x, y, z], which is rational over the ground field Fp. 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 Fp -rational points on C in randomized time (log p)Δ where Δ=(degF)O(1). The complexity of this construction improves previously known bounds for this problem by at least an order of magnitude

Published in:

Foundations of Computer Science, 1993. Proceedings., 34th Annual Symposium on

Date of Conference:

3-5 Nov 1993