On Permutation Quadrinomials and 4-Uniform BCT

被引：24

作者：

Li, Nian ^{[1
,2
]}

Xiong, Maosheng ^{[3
]}

Zeng, Xiangyong ^{[1
,2
]}

机构：

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

[2] State Key Lab Cryptol, Beijing 100878, Peoples R China

[3] Hong Kong Univ Sci & Technol, Dept Math, Hong Kong, Peoples R China

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2021年 / 67卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Boomerang uniformity; differential uniformity; permutation polynomial; BOOMERANG UNIFORMITY; CRYPTANALYSIS;

D O I：

10.1109/TIT.2021.3062681

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Extending previous results, we study a class of general quadrinomials over the field of size 2(2m) with odd m and characterize conditions under which they are permutations with 4-uniform BCT, a new and important parameter related to boomerang-style attacks. These permutations are known to have the best known nonlinearity. Numerical data also show that the inverse of these functions all have large algebraic degree, making them desirable for applications.

引用

页码：4845 / 4855

页数：11

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