Montgomery scalar multiplication for genus 2 curves
Résumé
Using powerful tools on genus 2 curves like the Kummer variety, we generalize the Montgomery method for scalar multiplication to the jacobian of these curves. Previously this method was only known for elliptic curves. We obtain an algorithm that is competitive compared to the usual methods of scalar multiplication and that has additional properties such as resistance to timings attacks. This algorithm has very important applications in cryptography using hyperelliptic curves and more particularly for people interested in cryptography on smart cards.