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**2002/105**

**Title:**

An Extension of Kedlaya’s Algorithm to Hyperelliptic Curves in Characteristic 2

**Authors:**
Jan Denef, Frederik Vercauteren

**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 odd characteristic.

For a genus g hyperelliptic curve defined over \FF_{2^n},

the average-case time complexity is O(g^{4 + \varepsilon} n^{3 + \varepsilon})

and the average-case space complexity is O(g^{3} n^{3}), whereas the worst-case time and space

complexities are O(g^{5 + \varepsilon} n^{3 + \varepsilon}) and O(g^{4} n^{3}) respectively.

**ePrint:**
https://eprint.iacr.org/2002/105

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