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

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