Ambiguity, deficiency and differential spectrum of normalized permutation polynomials over finite fields

被引：3

作者：

Panario, Daniel ^{[1
]}

Santana, Daniel ^{[2
]}

Wang, Qiang ^{[1
]}

机构：

[1] Carleton Univ, Sch Math & Stat, Ottawa, ON, Canada

[2] Univ Fed Santa Catarina, Dept Informat & Stat, Florianopolis, SC, Brazil

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2017年 / 47卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Finite fields; Permutation polynomials; Normalized polynomials; Differential map; Spectrum; Ambiguity; Deficiency;

D O I：

10.1016/j.ffa.2017.06.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain exact formulas for the differential spectrum, deficiency and ambiguity of all normalized permutation polynomials of degree up to six over finite fields. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：330 / 350

页数：21

共 13 条

[1]

[Anonymous], 2013, HDB FINITE FIELDS DI

[2]

Biham E., 1993, Differ. Cryptanal. Data Encrypt. Stand., DOI [10.1007/978-1-4613-9314-6, DOI 10.1007/978-1-4613-9314-6]

[3] Permutation polynomials over finite fields - A survey of recent advances [J].

Hou, Xiang-dong .

FINITE FIELDS AND THEIR APPLICATIONS, 2015, 32 :82-119

[4]

Ireland K., 1990, CLASSICAL INTRO MODE

[5] Permutation polynomials of degree 6 or 7 over finite fields of characteristic 2 [J].

Li, Jiyou ;

Chandler, David B. ;

Xiang, Qing .

FINITE FIELDS AND THEIR APPLICATIONS, 2010, 16 (06) :406-419

[6]

Lidl R., 1997, Encyclopedia Math. Appl.

[7]

Nyberg K., 1994, ADV CRYPTOLOGY PROC, P55

[8]

Omar O., 2015, THESIS

[9] Ambiguity and Deficiency of Permutations Over Finite Fields With Linearized Difference Map [J].

Panario, Daniel ;

Sakzad, Amin ;

Stevens, Brett ;

Thomson, David ;

Wang, Qiang .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2013, 59 (09) :5616-5626

[10] Two New Measures for Permutations: Ambiguity and Deficiency [J].

Panario, Daniel ;

Sakzad, Amin ;

Stevens, Brett ;

Wang, Qiang .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2011, 57 (11) :7648-7657

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