Fast Jacobian arithmetic for hyperelliptic curves of genus 3

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.

Minor corrections, updated references; 15 pages

References in corpus (3)

• Computing Hasse-Witt matrices of hyperelliptic curves in average polynomial time
• Computing Hasse-Witt matrices of hyperelliptic curves in average polynomial time, II
• Computing L-series of geometrically hyperelliptic curves of genus three

Cited by in corpus (3)

• Computing L-series of geometrically hyperelliptic curves of genus three
• Mumford representation and Riemann Roch space of a divisor on a hyperelliptic curve
• Improvements to Jacobian Arithmetic in Global Function Fields