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Computing zeta functions of hyperelliptic curves over finite fields of characteristic 2. (English) Zbl 1023.14007
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).
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].

##### MSC:
 14G15 Finite ground fields in algebraic geometry 14Q05 Computational aspects of algebraic curves 94A60 Cryptography 11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
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