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Construction of highly nonlinear resilient Boolean functions satisfying strict avalanche criterion

Science China(Information Sciences) 2014年第4期57卷 293-298页

作者： ZHANG WeiGuo JIANG FuQiang TANG Deng State Key Laboratory of Integrated Services Networks Xidian University State Key Laboratory of Information Security Graduate University of Chinese Academy of Sciences

Boolean functions with high nonlinearity,high resiliency and strict avalanche criterion(SAC)play an important role in the designs of conventional cryptographic *** this paper,a method is proposed to construct resilient Boolean functions on n variables(n even)satisfying SAC with nonlinearity>2n-1-2n/2.A large class of cryptographic Boolean functions that were not known earlier were obtained.

关键词： Boolean functions cryptography nonlinearity resiliency strict avalanche criterion

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Trace Representations of S-boxes and Their Application

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Wuhan University Journal of Natural Sciences 2004年第2期9卷 173-176页

作者： ZengXiang-yong FuJian-ming LiuHe-guo ZhangHuan-guo SchoolofComputer WuhanUniversityWuhan430072HubeiChina StateKeyLaboratoryofInformationSecurity(GraduateSchoolofChineseAcademyofSciences) Beijing100039China

In the paper, we use trace representations of Boolean functions to obtain that a class mappings including functionsF(x)=x d over field GF(2 n ), withW(d)=n?1, have desirable cryptographic properties. Therefore we generalize an important result of Nyberg. As application, we use these conclusions to analyze cryptographic property of the S-box of AES (the Advanced Encryption Standard) and give its several equivalent representations, proving that the composition of inversion function of AES and any invertible affine transformations is impossible to satisfy strict avalanche criterion, any order propagation criteria and any order correlation immunity. Key words trace function - nonlinearity - differentially uniform - strict avalanche criterion CLC number TP 309 Foundation item: Supported by the National Natural Science Foundation of China (60373089, 60373041), Natural Science Foundation of Hubei Province (2002AB0037) and Chen-guang Plan of Wuhan City (20025001007).Biography: Zeng Xiang-yong (1973-), male, A postdoctoral fellow, research direction: cryptology and the representation theory of algebra.

关键词： trace function nonlinearity differentially uniform strict avalanche criterion

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Construction of plateaued functions satisfying multiple criteria

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High Technology Letters 2005年第4期11卷 364-366页

作者：张卫国 Research Institute of Information Security National Key Laboratory of ISN Xidian University Xi＇an 710071 P.R. China

A class of plateaued functions has been got by using the Maiorana-McFarland construction. A variety of desirable criteria for functions with cryptographic application eouht be satisfied： balancedness, high nonlinearity, correlation immunity of reasonably high order, strict avalanche criterion, non-existence of non-zero linear struetures, good glnbal avalanche characteristics, etc.

关键词： cryptography boolean functious nonlinearity correlation-immunity strict avalanche criterion global avalanche characteristics

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