On multiplicative order of elements in finite fields based on cyclotomic polynomials

被引：0

作者：

Popovych, Roman ^{[1
]}

机构：

[1] Lviv Polytech Natl Univ, Dept Specialized Comp Syst, Bandery Str 12, UA-79013 Lvov, Ukraine

来源：

NOTES ON NUMBER THEORY AND DISCRETE MATHEMATICS | 2020年 / 26卷 / 02期

关键词：

Finite field; Multiplicative order; Lower bound; Partition;

D O I：

10.7546/nntdm.2020.26.2.47-52

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain explicit lower bound on multiplicative orders of all elements in finite field extensions generated by a root of unity. The bound does not depend on any unknown constant. The result of Ahmadi, Shparlinski and Voloch [1] is a consequence of our main result.

引用

页码：47 / 52

页数：6

共 50 条

[31] A NOTE ON ORDER ONE CYCLOTOMIC POLYNOMIALS
Bamunoba, Alex Samuel
QUAESTIONES MATHEMATICAE, 2016, 39 (01) : 29 - 43
[32] Flat cyclotomic polynomials of order three
Kaplan, Nathan
JOURNAL OF NUMBER THEORY, 2007, 127 (01) : 118 - 126
[33] Cyclotomic orthomorphisms of finite fields
Bell, Jordan
DISCRETE APPLIED MATHEMATICS, 2013, 161 (1-2) : 294 - 300
[34] On small gaps between the elements of multiplicative subgroups of finite fields
Shparlinski, Igor E.
DESIGNS CODES AND CRYPTOGRAPHY, 2016, 80 (01) : 63 - 71
[35] Multiplicative orders of elements in Conway's towers of finite fields
Popovych, Roman
ALGEBRA & DISCRETE MATHEMATICS, 2018, 25 (01): : 137 - 146
[36] On small gaps between the elements of multiplicative subgroups of finite fields
Igor E. Shparlinski
Designs, Codes and Cryptography, 2016, 80 : 63 - 71
[37] On elements of large order on elliptic curves and multiplicative dependent images of rational functions over finite fields
Kerr, Bryce
Mello, Jorge
Shparlinski, Igor E.
ILLINOIS JOURNAL OF MATHEMATICS, 2021, 65 (02) : 499 - 514
[38] Using cyclotomic polynomials to construct efficient discrete logarithm cryptosystems over finite fields
Lenstra, AK
INFORMATION SECURITY AND PRIVACY, 1997, 1270 : 127 - 138
[39] Classes of LDPC Codes Constructed from Elements of Finite Fields and Cyclotomic Cosets
Aly, Salah A.
Maza'ar, Hussein
2009 11TH CANADIAN WORKSHOP ON INFORMATION THEORY, 2009, : 83 - +
[40] A specific family of cyclotomic polynomials of order three
Ji ChunGang
SCIENCE CHINA-MATHEMATICS, 2010, 53 (09) : 2269 - 2274

← 1 2 3 4 5 →