International Association
for Cryptologic Research

We present an efficient endomorphism for the Jacobian of a curve $C$ of genus 2 for divisors having a Non disjoint support. This extends the work of Costello in ~\\cite{Costello} who calculated explicit formul\\ae\\space for divisor doubling and addition of divisors with disjoint support in $\\jacobian(C)$ using only base field operations. Explicit formul\\ae\\space is presented for this third case and a different approach for divisor doubling.