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• W1609652510 abstract "We consider the problem of counting the number of points on a plane curve, given by a homogeneous polynomial F/spl isin/F/sub p/[x, y, z], which is rational over the ground field F/sub p/. 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 F/sub p/-rational points on C in randomized time (log p)/sup /spl Delta// where /spl Delta/=(degF)/sup O(1/). The complexity of this construction improves previously known bounds for this problem by at least an order of magnitude. >" @default.
• W1609652510 created "2016-06-24" @default.
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• W1609652510 date "2002-12-30" @default.
• W1609652510 modified "2023-09-26" @default.
• W1609652510 title "Counting rational points on curves over finite fields" @default.
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• W1609652510 doi "https://doi.org/10.1109/sfcs.1993.366825" @default.
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