On the discrete logarithm in the divisor class group of curves

@article{Rck1999OnTD,
title={On the discrete logarithm in the divisor class group of curves},
author={Hans-Georg R{\"u}ck},
journal={Math. Comput.},
year={1999},
volume={68},
pages={805-806}
}

Let X be a curve which is defined over a finite field k of characteristic p. We show that one can evaluate the discrete logarithm in Pic0(X)pn by O(n2 log p) operations in k. This generalizes a result of Semaev for elliptic curves to curves of arbitrary genus. Let k be a finite field of characteristic p. We consider a projective irreducible nonsingular curve X of genus g ≥ 1 which is defined over k. We assume that the curve X has a k-rational point P0. Let Pic0(X)m be the subgroup of the m… CONTINUE READING