We present an algorithm for computing the zeta function of an arbitrary hyperelliptic curve over a finite field $\FF_q$ of characteristic 2, thereby extending the algorithm of Kedlaya for small odd characteristic. For a genus $g$ hyperelliptic curve over $\FF_2^n$, the asymptotic running time of the algorithm is $O(g^5 + arepsilon n^3 + arepsilon)$ and the space complexity is $O(g^4 n^3)$.
|Translated title of the contribution||Computing zeta functions of hyperelliptic curves over finite fields of characteristic 2|
|Title of host publication||Advances in Cryptology -- CRYPTO 2002|
|Publisher||Springer Berlin Heidelberg|
|Pages||369 - 384|
|Number of pages||15|
|Publication status||Published - Aug 2002|
Bibliographical noteEditors: Moti Yung