### Abstract

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 $O(g^4 n^3)$.

Original language | English |
---|---|

Title of host publication | Advances in Cryptology -- CRYPTO 2002 |

Publisher | Springer Berlin Heidelberg |

Pages | 369 - 384 |

Number of pages | 15 |

Volume | 2442 |

Publication status | Published - Aug 2002 |

### Bibliographical note

Editors: Moti YungPublisher: Springer

## Fingerprint Dive into the research topics of 'Computing zeta functions of hyperelliptic curves over finite fields of characteristic 2'. Together they form a unique fingerprint.

## Cite this

Vercauteren, F. (2002). Computing zeta functions of hyperelliptic curves over finite fields of characteristic 2. In

*Advances in Cryptology -- CRYPTO 2002*(Vol. 2442, pp. 369 - 384). Springer Berlin Heidelberg. http://www.cs.bris.ac.uk/Publications/pub_info.jsp?id=1000652