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Computing zeta functions of hyperelliptic curves over finite fields of characteristic 2

Frederik Vercauteren, Computing zeta functions of hyperelliptic curves over finite fields of characteristic 2. Advances in Cryptology - Crypto 2002. Moti Yung, (eds.). ISSN 0302-9743, pp. 369–384. August 2002. No electronic version available.

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

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