Sciweavers

FOCM
2008

Modular Counting of Rational Points over Finite Fields

13 years 11 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
Comments (0)