Permutation polynomials with low differential uniformity over finite fields of odd characteristic  

作　　者：JIA WenJie ZENG XiangYong LI ChunLei HELLESETH Tor HU Lei 

机构地区：[1]Faculty of Mathematics and Computer Science, Hubei University [2]State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences [3]Department of Informatics, University of Bergen

出　　处：《Science China Mathematics》2013年第7期1429-1440,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.61070172,10990011 and 61170257);the External Science and Technology Cooperation Program of Hubei Province(Grant No.2012IHA01402);National Key Basic Research Program of China(Grant No.2013CB834203);the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDA06010702)

摘　　要：In this paper, we propose a construction of functions with low differential uniformity based on known perfect nonlinear functions over finite fields of odd characteristic. For an odd prime power q, it is proved that the proposed functions over the finite field Fq are permutations if and only if q≡3(mod 4).In this paper, we propose a construction of functions with low differential uniformity based on known perfect nonlinear functions over finite fields of odd characteristic. For an odd prime power q, it is proved that the proposed functions over the finite field Fq are permutations if and only if q = 3 （mod 4）.

关 键 词：PERMUTATION perfect nonlinear function almost perfect nonlinear function differential uniformity 

分 类 号：O153.4[理学—数学]