Cryptology ePrint Archive: Report 2014/359

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

Eduardo Ruiz Duarte and Octavio Páez Osuna

Abstract: 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.

Category / Keywords: public-key cryptography / hyperelliptic curves