Deterministically generating Picard groups of hyperelliptic curves over finite fields

JOURNAL OF NUMBER THEORY

卷:160

Article

Kosters, Michiel¹ 

[1] UCI, Irvine, CA 92697 USA

关键词: Picard group;    Hyperelliptic curve;    Finite field;    Shape parameter;    Deterministic algorithm;   

DOI  :  10.1016/j.jnt.2015.09.007

来源: Elsevier

【 摘 要 】

Let is an element of > 0. In this article we will present a deterministic algorithm which does the following. The input is a hyperelliptic curve C of genus g over a finite field k of cardinality q given by y(2) + h(x)y = f (x) such that the x-coordinate map is ramified at infinity. In time 0(g(2+is an element of) q(1/2+is an element of)) the algorithm outputs a set of generators of the Picard group Pic(k)(0)(C). This extends results which others have obtained when g = 1. In this article we introduce a combinatorial tool, the shape parameter, which we use together with character sum estimates from class field theory to deduce the statement. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free