A note on the differential spectrum of a class of power functions

被引：1

作者：

Li, Nian ^{[1
]}

Wu, Yanan ^{[1
]}

Zeng, Xiangyong ^{[1
]}

Tang, Xiaohu ^{[1
,2
]}

机构：

[1] Hubei Univ, Fac Math & Stat, Wuhan 430062, Peoples R China

[2] Southwest Jiaotong Univ, CSNMT Int Coo Res Ctr MoST, Informat Coding & Transmiss Key Lab Sichuan Prov, Chengdu 611756, Peoples R China

来源：

2022 10TH INTERNATIONAL WORKSHOP ON SIGNAL DESIGN AND ITS APPLICATIONS IN COMMUNICATIONS (IWSDA) | 2022年

基金：

中国国家自然科学基金;

关键词：

Differential spectrum; differential uniformity; power function; PROOF;

D O I：

10.1109/IWSDA50346.2022.9870613

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Differential uniformity is a significant concept in cryptography as it quantifies the degree of security of S-boxes with respect to differential attacks. Power functions of the form F(x) = x(d) with low differential uniformity have been extensively studied in the past decades due to their strong resistance to differential attacks and low implementation cost in hardware. In a recent paper, all of us, along with Tu and Jiang gave an affirmative answer to the conjecture about the differential uniformity of F(x) = x(d) over F(2)4n, where n is a positive integer and d = 2(3n) +2(2n) +2(n) - 1, proposed by Budaghyan, Calderini, Carlet, Davidova and Kaleyski (IEEE Trans. Inf. Theory, 68(5), 3389-3403, 2022). In this paper, we show an alternative proof of the conjecture. Also, we completely determine the differential spectrum of F(x).

引用

页码：131 / 135

页数：5

共 17 条

[1]

Berlekamp E. R., 1997, INFORM CONTROL, V10, P553

[2]

BIHAM E, 1991, LECT NOTES COMPUT SC, V537, P2

[3] Differential Properties of x bar right arrow x2t-1 [J].

Blondeau, Celine ;

Canteaut, Anne ;

Charpin, Pascale .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2011, 57 (12) :8127-8137

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

Blondeau, Celine ;

Canteaut, Anne ;

Charpin, Pascale .

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

[5]

Budaghyan L., 2005, Ph.D. dissertation

[6] On Two Fundamental Problems on APN Power Functions [J].

Budaghyan, Lilya ;

Calderini, Marco ;

Carlet, Claude ;

Davidova, Diana ;

Kaleyski, Nikolay S. .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2022, 68 (05) :3389-3403

[7] Niho type cross-correlation functions via Dickson polynomials and Kloosterman sums [J].

Dobbertin, H ;

Felke, P ;

Helleseth, T ;

Rosendahl, P .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2006, 52 (02) :613-627

[8]

Dobbertin H, 2001, FINITE FIELDS AND APPLICATIONS, P113

[9] Another proof of Kasami's theorem [J].

Dobbertin, H .

DESIGNS CODES AND CRYPTOGRAPHY, 1999, 17 (1-3) :177-180

[10] A proof of the Welch and Niho conjectures on cross-correlations of binary m-sequences [J].

Hollmann, HDL ;

Xiang, Q .

FINITE FIELDS AND THEIR APPLICATIONS, 2001, 7 (02) :253-286

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