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

Eduardo Ruiz Duarte; Octavio Páez Osuna

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Paper 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.

Note: Presented at CECC2014

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint. MINOR revision.
Keywords: hyperelliptic curves
Contact author(s): rduarte @ ciencias unam mx
History: 2014-05-23: received
Short URL: https://ia.cr/2014/359
License: CC BY

BibTeX

@misc{cryptoeprint:2014/359,
      author = {Eduardo Ruiz Duarte and Octavio Páez Osuna},
      title = {Explicit endomorphism of the Jacobian of a hyperelliptic function field of genus 2 using base field operations},
      howpublished = {Cryptology ePrint Archive, Paper 2014/359},
      year = {2014},
      note = {\url{https://eprint.iacr.org/2014/359}},
      url = {https://eprint.iacr.org/2014/359}
}