Abstract:
Plateaued function has high nonlinearity, satisfy correlation immune and balanceness, and is applied widely in cryptographic function field. Based on a construction method of single-output Plateaued function proposed by Carlet etc, this paper uses state transition matrix of m-sequence to construct a class of multi-output Plateaued function. By referring to lemma 5 in Johansson’s paper to propose another construction method of multi-output Plateaued function. The functions got are suitable to design S boxes, filtering(combination) functions, hash functions and so on.
Key words:
Walsh spectrum,
Plateaued function,
multi-output Plateaued function,
primitive element,
injection,
m-sequence,
state transition matrix
摘要: Plateaued函数具有很高的非线性度,可以满足相关免疫性、平衡性,在密码函数领域具有重要作用。为此,基于Carlet等提出的单输出Plateaued函数构造方法(FSE’03会议论文集),利用m序列的状态转移矩阵,构造一类多输出Plateaued函数,并参考Johansson方法中的引理5(IEEE Transactions on Information Theory, 2003, No.2),提出另一种多输出Plateaued函数的构造方法,由此得到的2种函数适用于S盒、滤波(组合)函数、杂凑函数等的设计。
关键词:
Walsh谱,
Plateaued函数,
多输出Plateaued函数,
本原元,
单射,
m序列,
状态转移矩阵
CLC Number:
QIAO Tong-Xu, CENG Bing, ZHANG Wen-Zheng, DONG Xin-Feng. Construction Methods of Multi-output Plateaued Function[J]. Computer Engineering, 2012, 38(17): 123-125,128.
谯通旭, 曾兵, 张文政, 董新锋. 多输出Plateaued函数的构造方法[J]. 计算机工程, 2012, 38(17): 123-125,128.