Journal of Cryptology
Modern computer algebra
Elliptic curves in cryptography
Elliptic curves in cryptography
Computing Zeta Functions of Hyperelliptic Curves over Finite Fields of Characteristic 2
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
An Extension of Kedlaya's Algorithm to Artin-Schreier Curves in Characteristic 2
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
An Extension of Kedlaya's Algorithm to Artin-Schreier Curves in Characteristic 2
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
On p-adic Point Counting Algorithms for Elliptic Curves over Finite Fields
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Counting points on Cab curves using Monsky--Washnitzer cohomology
Finite Fields and Their Applications
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We describe a method which may be used to compute the zeta function of an arbitrary Artin-Schreier cover of the projective line over a finite field. Specifically, for covers defined by equations of the form Zp -Z =f(X) we present, and give the complexity analysis of, an algorithm for the case in which f(X) is a rational function whose poles all have order 1. However, we only prove the correctness of this algorithm when the field characteristic is at least 5. The algorithm is based upon a cohomological formula for the L-function of an additive character sum. One consequence is a practical method of finding the order of the group of rational points on the Jacobian of a hyperelliptic curve in characteristic 2.