Quasi-quadratic elliptic curve point counting using rigid cohomology

被引：1

作者：

Hubrechts, Hendrik ^{[1
]}

机构：

[1] Katholieke Univ Leuven, Dept Math, B-3001 Heverlee, Belgium

来源：

JOURNAL OF SYMBOLIC COMPUTATION | 2009年 / 44卷 / 09期

关键词：

Elliptic curve; Point counting; Rigid cohomology; Cryptography; HYPERELLIPTIC CURVES; ZETA-FUNCTIONS; CRYPTOGRAPHY; COMPUTATION; ALGORITHM;

D O I：

10.1016/j.jsc.2008.02.015

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Let E be a nonsupersingular elliptic curve over the finite field with p(n) elements. We present a deterministic algorithm that computes the zeta function and hence the number of points of such a curve E in time quasi-quadratic in n. An older algorithm having the same time complexity uses the canonical lift of E, whereas our algorithm uses rigid cohomology combined with a deformation approach. An implementation in small odd characteristic turns Out to give very good results. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：1255 / 1267

页数：13

共 28 条

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