an:01942432
Zbl 1023.14007
Vercauteren, Frederik
Computing zeta functions of hyperelliptic curves over finite fields of characteristic 2
EN
Yung, Moti (ed.), Advances in cryptology - CRYPTO 2002. 22nd annual international cryptology conference, Santa Barbara, CA, USA, August 18-22, 2002. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 2442, 369-384 (2002).
2002
a
14G15 14Q05 94A60 11T71
hyperelliptic curve; Kedlaya's algorithm; Monsky-Washnitzer cohomology; algorithm for computing the zeta-function; complexity
Summary: We present an algorithm for computing the zeta-function of an arbitrary hyperelliptic curve over a finite field \( \mathbb{F}_q\) of characteristic 2, thereby extending Kedlaya's algorithm for small odd characteristic. For a genus \(g\) hyperelliptic curve over \( \mathbb{F}_{2^n}\), the asymptotic running time of the algorithm is \(O(g^{5 + \varepsilon} n^{3 + \varepsilon})\) and the space complexity is \(O (g^{3} n^{3})\).
For the entire collection see [Zbl 0997.00039].