Point counting in families of hyperelliptic curves in characteristic 2

Details Point counting in families of hyperelliptic curves in characteristic 2 Point counting in families of hyperelliptic curves in characteristic 2

2006-07-14

arxiv.org/abs/math/0607346v1

Mathematics

Number Theory

23 pages

Scientific paper

Let E_G be a family of hyperelliptic curves over F2^(alg cl) with general Weierstrass equation given over a very small field F. We describe in this paper an algorithm to compute the zeta function of E_g for g in a degree n extension field of F, which has as time complexity O(n^3) and memory requirements O(n^2). With a slightly different algorithm we can get time O(n^2,667) and memory O(n^2,5), and the computation of O(n) curves of the family can be done in time and space O(n^3). All these algorithms are polynomial in the genus.

Affiliated with

Also associated with

No associations

Rating

Point counting in families of hyperelliptic curves in characteristic 2 does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Point counting in families of hyperelliptic curves in characteristic 2, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Point counting in families of hyperelliptic curves in characteristic 2 will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-97251