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Computing zeta functions of Artin-Schreier curves over finite fields. (English) Zbl 1067.11078
Summary: The authors present a practical polynomial-time algorithm for computing the zeta function of certain Artin-Schreier curves over finite fields. This yields a method for computing the order of the Jacobian of an elliptic curve in characteristic 2, and more generally, any hyperelliptic curve in characteristic 2 whose affine equation is of a particular form. The algorithm is based upon an efficient reduction method for the Dwork cohomology of one-variable exponential sums.

MSC:
11T23 Exponential sums
11G20 Curves over finite and local fields
11Y16 Number-theoretic algorithms; complexity
14Q05 Computational aspects of algebraic curves
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