Abstract
AbstractLet EΓ be a family of hyperelliptic curves over F2alg cl with general Weierstrass equation given over a very small field F. The author of this paper describes an algorithm for computing the zeta function of Eγ, with γ in a degree n extension field of F, which has time complexity O(n3 + ε) bit operations and memory requirements O(n2) bits. Using a slightly different algorithm, one 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 O(n3.376). All of these algorithms are polynomial-time in the genus.
Subject
Computational Theory and Mathematics,General Mathematics
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