Traces of the Group Law on the Kummer Surface of a Curve of Genus 2 in Characteristic 2

In the early 1990s, Flynn gave an explicit description of the Jacobian of a genus 2 hyperelliptic curve to perform efficient arithmetic on these objects. In this paper, we give a generalization of Flynn’s work when the ground field has characteristic 2. More precisely, we give an explicit description of both the Jacobian and the Kummer surface. We also give (and explain how we found) explicit formulas for the structure of the group law on the Jacobian preserved on the Kummer surface.

• Type: Journal
• Year: 2010
• Where: MICS
• Authors: Sylvain Duquesne
• Keywords: Explicit Description, Hyperelliptic Curve, Kummer Surface, MICS 2010