[Resource Topic] 2014/359: Explicit endomorphism of the Jacobian of a hyperelliptic function field of genus 2 using base field operations

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

Authors: Eduardo Ruiz Duarte, 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.

ePrint: https://eprint.iacr.org/2014/359

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