On the differential spectrum of a differentially 3-uniform power function

被引：3

作者：

Pang, Tingting ^{[1
]}

Li, Nian ^{[2
]}

Zeng, Xiangyong ^{[3
]}

机构：

[1] Shandong Univ, Sch Math, Jinan 250100, Peoples R China

[2] Hubei Univ, Sch Cyber Sci & Technol, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China

[3] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2023年 / 87卷

基金：

中国国家自然科学基金;

关键词：

Power function; Differential spectrum; Cyclotomic number;

D O I：

10.1016/j.ffa.2023.102168

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the cardinality of the intersection of four particular cyclotomic classes of order two over the finite field with characteristic 5 by making most use of the cyclotomic numbers of orders two and four. As a consequence, a class of power functions over F5n is shown to be differentially 3-uniform and its differential spectrum is also completely determined.(c) 2023 Elsevier Inc. All rights reserved.

引用

页数：11

共 17 条

[1]

Biham E., 1991, Journal of Cryptology, V4, P3, DOI 10.1007/BF00630563

[2] Differential properties of power functions [J].

Blondeau, Celine ;

Canteaut, Anne ;

Charpin, Pascale .

2010 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, 2010, :2478-2482

[3]

Carlitz L., 1954, Am. J. Math., V76, P137, DOI [10.2307/2372405, DOI 10.2307/2372405]

[4] Differential spectrum of some power functions in odd prime characteristic [J].

Choi, Sung-Tai ;

Hong, Seokbeom ;

No, Jong-Seon ;

Chung, Habong .

FINITE FIELDS AND THEIR APPLICATIONS, 2013, 21 :11-29

[5] Ternary m-sequences with three-valued cross-correlation function:: New decimations of Welch and Niho type [J].

Dobbertin, H ;

Helleseth, T ;

Kumar, PV ;

Martinsen, H .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2001, 47 (04) :1473-1481

[6] Some power mappings with low differential uniformity [J].

Helleseth, T ;

Sandberg, D .

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 1997, 8 (05) :363-370

[7] Differential and boomerang spectrums of some power permutations [J].

Jiang, Sha ;

Li, Kangquan ;

Li, Yubo ;

Qu, Longjiang .

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2022, 14 (02) :371-393

[8] THE DIFFERENTIAL SPECTRUM OF A CLASS OF POWER FUNCTIONS OVER FINITE FIELDS [J].

Lei, Lei ;

Ren, Wenli ;

Fan, Cuiling .

ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2021, 15 (03) :525-537

[9] On the differential properties of the power mapping xpm+2 [J].

Man, Yuying ;

Xia, Yongbo ;

Li, Chunlei ;

Helleseth, Tor .

FINITE FIELDS AND THEIR APPLICATIONS, 2022, 84

[10]

Nyberg K., 1994, Advances in Cryptology - EUROCRYPT '93. Workshop on the Theory and Application of Cryptographic Techniques Proceedings, P55

← 1 2 →