Sequences of irreducible polynomials over odd prime fields via elliptic curve endomorphisms

被引：2

作者：

Ugolini, S. ^{[1
]}

机构：

[1] Univ Trent, Dipartimento Matemat, I-38050 Trento, Italy

来源：

JOURNAL OF NUMBER THEORY | 2015年 / 152卷

关键词：

Irreducible polynomial iterative constructions; Finite fields; Elliptic curves;

D O I：

10.1016/j.jnt.2014.12.027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Text. In this paper we present and analyze a construction of irreducible polynomials over odd prime fields via the transforms which take any polynomial f is an element of F-p[x] of positive degree n to (n/k)n . f (k(x + x(-1))), for some specific values of the odd prime p and k is an element of F-p. Video. For a video summary of this paper, please visit http://youtu.be/Lmw5m_c-i8s. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：21 / 37

页数：17

共 50 条

[11] Number of irreducible polynomials and pairs of relatively prime polynomials in several variables over finite fields
Hou, Xiang-dong
Mullen, Gary L.
FINITE FIELDS AND THEIR APPLICATIONS, 2009, 15 (03) : 304 - 331
[12] Nets and sequences obtained from irreducible polynomials over finite fields
Univ of the Witwatersrand, Johannesburg, South Africa
Applicable Algebra in Engineering, Communications and Computing, 1998, 9 (03): : 265 - 269
[13] Nets and sequences obtained from irreducible polynomials over finite fields
Knopfmacher, A
Ridley, JN
Mullen, GL
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 1998, 9 (03) : 265 - 269
[14] Fast and flexible elliptic curve point arithmetic over prime fields
Longa, Patrick
Miri, Ali
IEEE TRANSACTIONS ON COMPUTERS, 2008, 57 (03) : 289 - 302
[15] Optimized FPGA Implementation of Elliptic Curve Cryptosystem over Prime Fields
Yang, Guoqiang
Kong, Fanyu
Xu, Qiuliang
2020 IEEE 19TH INTERNATIONAL CONFERENCE ON TRUST, SECURITY AND PRIVACY IN COMPUTING AND COMMUNICATIONS (TRUSTCOM 2020), 2020, : 243 - 249
[16] Algebraic Approaches for the Elliptic Curve Discrete Logarithm Problem over Prime Fields
Petit, Christophe
Kosters, Michiel
Messeng, Ange
PUBLIC-KEY CRYPTOGRAPHY - PKC 2016, PT II, 2016, 9615 : 3 - 18
[17] Flexible Hardware Processor for Elliptic Curve Cryptography Over NIST Prime Fields
Ananyi, Kendall
Alrimeih, Hamad
Rakhmatov, Daler
IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS, 2009, 17 (08) : 1099 - 1112
[18] Randomness of Sequences of Numbers Using Permutation Polynomials over Prime Finite Fields
Harish, Mansi
Vinayak, Sagar
Gupta, Shalini
CONTEMPORARY MATHEMATICS, 2023, 4 (03): : 453 - 466
[19] CONSTRUCTING IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS
Ling, San
Ozdemir, Enver
Xing, Chaoping
MATHEMATICS OF COMPUTATION, 2012, 81 (279) : 1663 - 1668
[20] Counting irreducible polynomials over finite fields
Qichun Wang
Haibin Kan
Czechoslovak Mathematical Journal, 2010, 60 : 881 - 886

← 1 2 3 4 5 →