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

Eduardo Ruíz Duarte

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Abstract

We explore the function field of the jacobian of a hyperelliptic curve of genus 2 in order to find reduced coordinates to represent points of int he abelian variety and do arithmetic.

We show how this relates to the usual Mumford representation of points of the Jacobian. Moreover we identify the open subsets where our reduced coordinates are defined, characterizing the elements which can be reduced and we discuss the group operation with them.
Original languageEnglish
Number of pages15
Publication statusPublished - 2017

Publication series

NameIACR Cryptology ePrint
No.Report 2017/006

Keywords

  • hyperelliptic
  • Mumford
  • arithmetic

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