Sparse permutations with low differential uniformity

被引：20
作者：
Charpin, Pascale [1 ]
Kyureghyan, Gohar M. [2 ]
Suder, Valentin [1 ]
机构：
[1] INRIA Projet SECRET, F-78153 Le Chesnay, France
[2] Univ Magdeburg, Dept Math, D-39106 Magdeburg, Germany
来源：
FINITE FIELDS AND THEIR APPLICATIONS | 2014年 / 28卷
关键词：
Permutation; Boolean function; Monomial function; Quadratic fundtion; APN function; AB function; Cryptographic criteria; Differential uniformity;
D O I：
10.1016/j.ffa.2014.02.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the functions F-s,F-t,F-gamma(x) = x(s) + gamma Tr(x(t)) on F-2n We describe the set of such permutations and the explicit expressions of their compositional inverses. Further we consider special classes of such functions, for which we determine the size of their image set, the algebraic degree and the differential uniformity. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：214 / 243
页数：30
相关论文
共 27 条
[1]  
[Anonymous], 2002, ALGEBRA
[2]   On almost perfect nonlinear functions over F2n [J].
Berger, Thierry P. ;
Canteaut, Anne ;
Charpin, Pascale ;
Laigle-Chapuy, Yann .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2006, 52 (09) :4160-4170
[3]  
Blondeau Celine, 2010, International Journal of Information and Coding Theory, V1, P149, DOI 10.1504/IJICOT.2010.032132
[4]  
Blondeau C., 2013, P WORKSH COD CRYPT W
[5]   Differential Properties of x bar right arrow x2t-1 [J].
Blondeau, Celine ;
Canteaut, Anne ;
Charpin, Pascale .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2011, 57 (12) :8127-8137
[6]   Binomial differentially 4 uniform permutations with high nonlinearity [J].
Bracken, Carl ;
Tan, Chik How ;
Tan, Yin .
FINITE FIELDS AND THEIR APPLICATIONS, 2012, 18 (03) :537-546
[7]   A few more quadratic APN functions [J].
Bracken, Carl ;
Byrne, Eimear ;
Markin, Nadya ;
McGuire, Gary .
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2011, 3 (01) :43-53
[8]   FOURIER SPECTRA OF BINOMIAL APN FUNCTIONS [J].
Bracken, Carl ;
Byrne, Eimear ;
Markin, Nadya ;
McGuire, Gary .
SIAM JOURNAL ON DISCRETE MATHEMATICS, 2009, 23 (02) :596-608
[9]   Constructing new APN functions from known ones [J].
Budaghyan, Lilya ;
Carlet, Claude ;
Leander, Gregor .
FINITE FIELDS AND THEIR APPLICATIONS, 2009, 15 (02) :150-159
[10]   Binary m-sequences with three-valued crosscorrelation:: A proof of Welch's conjecture [J].
Canteaut, A ;
Charpin, P ;
Dobbertin, H .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2000, 46 (01) :4-8
123