Reduced Mumford divisors of a genus 2 curve through its jacobian function field

Eduardo Ruiz Duarte

Paper 2017/006

Reduced Mumford divisors of a genus 2 curve through its jacobian function field

Eduardo Ruiz Duarte

Abstract

We explore the function field of the jacobian JH of a hyperelliptic curve H of genus 2 in order to find reduced coordinates to represent points of JH and do arithmetic. We show how this relates to the usual Mumford representation of points of JH. Moreover we identify the open subsets of JH where our reduced coordinates are defined, characterizing the elements which can be reduced and we discuss the group operation with them.

Metadata

Available format(s): PDF
Publication info: Preprint. MINOR revision.
Keywords: hyperelliptic Mumford arithmetic
Contact author(s): e ruiz duarte @ rug nl
History: 2017-01-11: received
Short URL: https://ia.cr/2017/006
License: CC BY

BibTeX

@misc{cryptoeprint:2017/006,
      author = {Eduardo Ruiz Duarte},
      title = {Reduced Mumford divisors of a genus 2 curve through its jacobian function field},
      howpublished = {Cryptology {ePrint} Archive, Paper 2017/006},
      year = {2017},
      url = {https://eprint.iacr.org/2017/006}
}