ELEMENTS OF HIGH ORDER ON FINITE FIELDS FROM ELLIPTIC CURVES

被引：20

作者：

Voloch, Jose Felipe ^{[1
]}

机构：

[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2010年 / 81卷 / 03期

关键词：

finite fields; elliptic curves; multiplicative group;

D O I：

10.1017/S0004972709001075

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We discuss the problem of constructing elements of multiplicative high order in finite fields of large degree over their prime field. We obtain such elements by evaluating rational functions on elliptic curves, at points whose order is small with respect to their degree. We discuss several special cases, including an old construction of Wiedemann, giving the first nontrivial estimate for the order of the elements in this construction.

引用

页码：425 / 429

页数：5

共 5 条

[1] Finite field elements of high order arising from modular curves
Burkhart, Jessica F.
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Gao, Shuhong
Hyde-Volpe, Justine C.
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Manber, Shelly
Ruiz, Jared
Smith, Ethan
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[2] Cohen S. D., 1992, Designs, Codes and Cryptography, V2, P169, DOI 10.1007/BF00124895
[3] Elements of provable high orders in finite fields
Gao, SH
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 127 (06) : 1615 - 1623
[4] Voloch Jose Felipe., 2007, Integers, V7, pA49
[5] WIEDEMANN D, 1988, FIBONACCI QUART, V26, P290

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