A particular application is that heuristically, ``essentially all'' instances of the DLP in degree 0 class groups of non-hyperelliptic curves of genus 3 (represented by plane curves of degree 4) can be solved in an expected time of $\tilde{O}(q)$.
We also provide a method to represent ``sufficiently general'' (non-hyperelliptic) curves of genus $g \geq 3$ by plane models of degree $g+1$. We conclude that on heuristic grounds the DLP in degree 0 class groups of ``sufficiently general'' curves of genus $g \geq 3$ (represented initially by plane models of bounded degree) can be solved in an expected time of $\tilde{O}(q^{2 -2/(g-1)})$.
Category / Keywords: public-key cryptography / discrete logarithm problem Date: received 18 Apr 2005 Contact author: diem at iem uni-due de Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation Version: 20050421:174335 (All versions of this report) Short URL: ia.cr/2005/119 Discussion forum: Show discussion | Start new discussion