Explicit endomorphism of the Jacobian of a hyperelliptic function field\n of genus 2 using base field operations

We present an efficient endomorphism for the Jacobian of a curve $C$ of genus\n2 (hyperelliptic) for divisors having a Non disjoint support. This extends the\nwork of Costello and Lauter in [12] who calculated explicit formulae for\ndivisor doubling and addition of divisors with disjoint support in\n$\\mathbb{J}(C)$ using only base field operations. Explicit formulae is\npresented for this third case and a slightly different approach for divisor\ndoubling.\n