#### Vol. 4, No. 1, 2020

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Divisor class group arithmetic on $C_{3,4}$ curves

### Evan MacNeil, Michael J. Jacobson Jr. and Renate Scheidler

Vol. 4 (2020), No. 1, 317–334
##### Abstract

We present novel explicit formulas for arithmetic in the divisor class group of a ${C}_{3,4}$ curve. Our formulas handle all cases of inputs and outputs without having to fall back on a generic method. We also improve on the most commonly occurring case by reducing the number of required field inversions to one at the cost of a small number of additional field operations, resulting in running times that are between 11 and 21% faster than the prior state of the art depending on the field size, and even more for small field sizes when nontypical cases frequently arise.

##### Keywords
computational number theory, computational algebraic geometry, divisor arithmetic, C34 curves, genus 3 nonhyperelliptic curves
##### Mathematical Subject Classification 2010
Primary: 11R65, 14H45, 14Q05