On exponential sums and group generators for elliptic curves over finite fields

被引：0
作者：
Kohel, DR [1 ]
Shparlinski, IE
机构：
[1] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia
[2] Macquarie Univ, Dept Comp, N Ryde, NSW 2109, Australia
来源：
ALGORITHMIC NUMBER THEORY | 2000年 / 1838卷
关键词：
D O I：
暂无
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In the paper an upper bound is established for certain exponential sums, analogous to Gaussian sums, defined on the points of an elliptic curve over a prime finite held. The bound is applied to prove the existence of group generators for the set of points on an elliptic curve over F-q among certain sets of bounded size. We apply this estimate to obtain a deterministic O(q(1/2+epsilon)) algorithm for finding generators of the group in echelon form, and in particular to determine its group structure.
引用
收藏
页码：395 / 404
页数：10
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