  We describe an algorithm for counting points on an arbitrary hyperelliptic
curve over a finite field of odd characteristic, using Monsky-Washnitzer
cohomology to compute a p-adic approximation to the characteristic polynomial
of Frobenius. For fixed p, the asymptotic running time for a curve of genus g
over the field of p^n elements is O(g^{4+\epsilon} n^{3+\epsilon}).
