New differentially 4-uniform permutations from modifications of the inverse function

被引：3

作者：

Jeong, Jaeseong ^{[1
]}

Koo, Namhun ^{[2
]}

Kwon, Soonhak ^{[1
]}

机构：

[1] Sungkyunkwan Univ, Applied Algebra & Optimizat Res Ctr, Suwon, South Korea

[2] Ewha Womans Univ, Inst Math Sci, Seoul, South Korea

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2022年 / 77卷

基金：

新加坡国家研究基金会;

关键词：

Differential uniformity; Nonlinearity; Differential-linear uniformity; Differentially; 4-uniform; permutations; CONSTRUCTION;

D O I：

10.1016/j.ffa.2021.101931

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Finding permutations with good cryptographic parameters is a good research topic about constructing a secure S box in substitution-permutation networks. In particular constructing differentially 4-uniform permutations has made considerable progress in recent years. In this paper, we present new differentially 4-uniform permutations from the inverse function composed by disjoint cycles. Our new differentially 4-uniform permutations have high nonlinearity and low differential-linear uniformity. We give the differential spectrum and the extended Walsh spectrum of some of our differentially 4-uniform permutations, and then we can see that they are CCZ-inequivalent to some permutations whose differential spectrum and extended Walsh spectrum are known. (c) 2021 Elsevier Inc. All rights reserved.

引用

页数：28

共 31 条

[11] On Z4-linear Goethals codes and Kloosterman sums [J].

Helleseth, T ;

Zinoviev, V .

DESIGNS CODES AND CRYPTOGRAPHY, 1999, 17 (1-3) :269-288

[12] THE WEIGHTS OF THE ORTHOGONALS OF THE EXTENDED QUADRATIC BINARY GOPPA CODES [J].

LACHAUD, G ;

WOLFMANN, J .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1990, 36 (03) :686-692

[13] More Low Differential Uniformity Permutations over F22k with k Odd [J].

Leng, Yue ;

Chen, Jinyang ;

Xie, Tao .

MATHEMATICAL PROBLEMS IN ENGINEERING, 2020, 2020

[14]

Li Y., Constructing differentially 4-uniform permutations over GF(22k) from the inverse function revisited

[15] Constructing differentially 4-uniform permutations over GF(22m ) from quadratic APN permutations over GF(22m+1) [J].

Li, Yongqiang ;

Wang, Mingsheng .

DESIGNS CODES AND CRYPTOGRAPHY, 2014, 72 (02) :249-264

[16]

Nyberg K, 1994, Advances in Cryptology-EUROCRYPT'93. EUROCRYPT 1993. Lecture notes in computer science, V765, DOI DOI 10.1007/3-540-48285-7_6

[17] More New Classes of Differentially 4-Uniform Permutations with Good Cryptographic Properties [J].

Peng, Jie ;

Tan, Chik How ;

Wang, Qichun ;

Gao, Jianhua ;

Kan, Haibin .

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2018, E101A (06) :945-952

[18] New differentially 4-uniform permutations by modifying the inverse function on subfields [J].

Peng, Jie ;

Tan, Chik How .

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2017, 9 (03) :363-378

[19] New explicit constructions of differentially 4-uniform permutations via special partitions of F22k [J].

Peng, Jie ;

Tan, Chik How .

FINITE FIELDS AND THEIR APPLICATIONS, 2016, 40 :73-89

[20]

Peng J, 2016, SCI CHINA MATH, V59, P1221, DOI 10.1007/s11425-016-5122-9

← 1 2 3 4 →