Cryptology ePrint Archive: Report 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.

Category / Keywords: hyperelliptic, Mumford, arithmetic

Date: received 6 Jan 2017

Contact author: e ruiz duarte at rug nl

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Version: 20170111:130626 (All versions of this report)

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