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FOCM
2008

Modular Counting of Rational Points over Finite Fields

9 years 1 months ago
Modular Counting of Rational Points over Finite Fields
Let Fq be the finite field of q elements, where q = ph. Let f(x) be a polynomial over Fq in n variables with m non-zero terms. Let N(f) denote the number of solutions of f(x) = 0 with coordinates in Fq. In this paper, we give a deterministic algorithm which computes the reduction of N(f) modulo pb in O(n(8m)(h+b)p) bit operations. This is singly exponential in each of the parameters {h, b, p}, answering affirmatively an open problem proposed in [5].
Daqing Wan
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2008
Where FOCM
Authors Daqing Wan
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