Vol. 2, 2019

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Fast Jacobian arithmetic for hyperelliptic curves of genus 3

Andrew V. Sutherland

Vol. 2 (2019), No. 1, 425–442
Abstract

We consider the problem of efficient computation in the Jacobian of a hyperelliptic curve of genus 3 defined over a field whose characteristic is not 2. For curves with a rational Weierstrass point, fast explicit formulas are well known and widely available. Here we address the general case, in which we do not assume the existence of a rational Weierstrass point, using a balanced divisor approach.

Keywords
hyperelliptic curve, Jacobian, genus 3
Mathematical Subject Classification 2010
Primary: 14H40
Secondary: 11G10, 11G40, 14H25, 14K15
Supplementary material

Formulas for algorithms

Milestones
Received: 2 March 2018
Revised: 9 June 2018
Accepted: 9 September 2018
Published: 13 February 2019
Authors
Andrew V. Sutherland
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States