An infinite class of quadratic APN functions which are not equivalent to power mappings

被引：18

作者：

Budaghyan, Lilya ^{[1
]}

Carlet, Claude ^{[2
]}

Felke, Patrick ^{[3
]}

Leander, Gregor ^{[3
]}

机构：

[1] Otto Von Guericke Univ, Inst Algebra & Geometry, Magdeburg, Germany

[2] Inst Natl Rech Informat & Automat, F-78153 Le Chesnay, France

[3] Ruhr Univ Bochum, Dept Mat, D-44780 Bochum, Germany

来源：

2006 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, VOLS 1-6, PROCEEDINGS | 2006年

关键词：

vectorial Boolean function; S-box; nonlinearity; differential uniformity; almost perfect nonlinear; almost bent; affine equivalence; CCZ-equivalence;

D O I：

10.1109/ISIT.2006.262131

中图分类号：

TN [电子技术、通信技术];

学科分类号：

0809 ;

摘要：

We exhibit an infinite class of almost perfect nonlinear quadratic polynomials from F-2n to F-2n (n > 12, n divisible by 3 but not by 9). We prove that these functions are EA-inequivalent to any power function and that they are CCZ-inequivalent to any Gold function. In a forthcoming full paper, we shall also prove that at least some of these functions are CCZ-inequivalent to any Kasami function.

引用

页码：2637 / +

页数：2

共 50 条

[31] On quadratic APN functions and dimensional dual hyperovals
Yves Edel
Designs, Codes and Cryptography, 2010, 57 : 35 - 44
[32] On quadratic APN functions and dimensional dual hyperovals
Edel, Yves
DESIGNS CODES AND CRYPTOGRAPHY, 2010, 57 (01) : 35 - 44
[33] Construction of CCZ transform for quadratic APN functions
Zhang, Xinyang
Zhou, Meng
COGNITIVE SYSTEMS RESEARCH, 2019, 57 : 41 - 45
[34] A matrix approach for constructing quadratic APN functions
Yuyin Yu
Mingsheng Wang
Yongqiang Li
Designs, Codes and Cryptography, 2014, 73 : 587 - 600
[35] REGULAR FUNCTIONS IN A SEMIPLANE WHICH ARE TOPOLOGICALLY EQUIVALENT TO QUASI-ISOMETRIC MAPPINGS
LATFULLIN, TG
SIBERIAN MATHEMATICAL JOURNAL, 1994, 35 (06) : 1157 - 1165
[36] On equivalence between known polynomial APN functions and power APN functions
Wan, Qianhong
Qu, Longjiang
Li, Chao
FINITE FIELDS AND THEIR APPLICATIONS, 2021, 71
[37] A NOTE ON THE PROPERTIES OF ASSOCIATED BOOLEAN FUNCTIONS OF QUADRATIC APN FUNCTIONS
Gorodilova, A. A.
PRIKLADNAYA DISKRETNAYA MATEMATIKA, 2020, (47): : 16 - 21
[38] Some Results on the Known Classes of Quadratic APN Functions
Budaghyan, Lilya
Helleseth, Tor
Li, Nian
Sun, Bo
CODES, CRYPTOLOGY AND INFORMATION SECURITY, C2SI 2017, 2017, 10194 : 3 - 16
[39] On equivalence between known families of quadratic APN functions
Budaghyan, Lilya
Calderini, Marco
Villa, Irene
FINITE FIELDS AND THEIR APPLICATIONS, 2020, 66
[40] Constructing more quadratic APN functions with the QAM method
Yu, Yuyin
Perrin, Leo
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2022, 14 (06): : 1359 - 1369

← 1 2 3 4 5 →