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.

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Mathematical Subject Classification 2010

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