Point Counting in Families of Hyperelliptic Curves in Characteristic 2
نویسندگان
چکیده
Let ĒΓ be a family of hyperelliptic curves over F cl 2 with general Weierstrass equation given over a very small field F. We describe in this paper an algorithm for computing the zeta function of Ēγ̄, with γ̄ in a degree n extension field of F, which has as time complexity Õ(n3) bit operations and memory requirements O(n2) bits. With a slightly different algorithm we can get time O(n2.667) and memory O(n2.5), and the computation for n curves of the family can be done in time Õ(n3.376). All of these algorithms are polynomial-time in the genus.
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Let ĒΓ be a family of hyperelliptic curves over F alg cl 2 with general Weierstrass equation given over a very small field F. We describe in this paper an algorithm to compute the zeta function of Ēγ̄ for γ̄ in a degree n extension field of F, which has as time complexity Õ(n) and memory requirements O(n). With a slightly different algorithm we can get time O(n) and memory O(n), and the computati...
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