While Cantor's general composition involves arithmetic in the polynomial ring $F_q[x]$, the algorithm we propose solves a linear system over the base field which can be written down directly from the Mumford coordinates of the group elements.
We apply this method to give more efficient formulas for group operations in both affine and projective coordinates for cryptographic systems based on Jacobians of genus 2 hyperelliptic curves in general form.
Category / Keywords: Hyperelliptic curves, group law, Jacobian arithmetic, genus 2. Date: received 8 Jun 2011, last revised 19 Sep 2011 Contact author: craig costello at qut edu au Available formats: PDF | BibTeX Citation Version: 20110919:121422 (All versions of this report) Discussion forum: Show discussion | Start new discussion