Nowadays orthogonal arrays play important roles in statistics, computer science, coding theory and cryptography. The usual difference matrices are essential for the construction for many mixed orthogonal arrays. But t...Nowadays orthogonal arrays play important roles in statistics, computer science, coding theory and cryptography. The usual difference matrices are essential for the construction for many mixed orthogonal arrays. But there are also orthogonal arrays which cannot be obtained by the usual difference matrices, such as mixed orthogonal arrays of run size 60. In order to construct these mixed orthogonal arrays, a class of special so-called generalized difference matrices were discovered by Zhang (1989,1990,1993,2006) from the orthogonal decompositions of projection matrices. In this article, an interesting equivalent relationship between orthogonal arrays and the generalized difference matrices is presented and proved. As an application, a lot of new orthogonal arrays of run size 60 have been constructed.展开更多
In this article, we propose a new general approach to constructing asymmetrical orthogonal arrays, namely the Kronecker sum. It is interesting since a lot of new mixed-level orthogonal arrays can be obtained by this m...In this article, we propose a new general approach to constructing asymmetrical orthogonal arrays, namely the Kronecker sum. It is interesting since a lot of new mixed-level orthogonal arrays can be obtained by this method.展开更多
The image's least significant bit(LSB) covers lots of the details that have been commonly used in image encryption analysis. The newly proposed fractal sorting vector(FSV) and FSV-based LSB chaotic permutation(FSV...The image's least significant bit(LSB) covers lots of the details that have been commonly used in image encryption analysis. The newly proposed fractal sorting vector(FSV) and FSV-based LSB chaotic permutation(FSV-LSBCP) is a novel chaotic image encryption cryptosystem introduced in this article. The FSV-LSBCP effectively strengthens the security of the cryptographic scheme concerning the properties of the FSV. Key analysis, statistical analysis, resistance differential attack analysis, and resistance to cropping attacks and noise attacks are the focus of the suggested image encryption cryptosystem. The security experiment shows that the cryptosystem is adequate to achieve the desired degree of security.展开更多
By using the generalized Hadamard product, difference matrix and projection matrices, we present a class of orthogonal projection matrices and related orthogonal arrays of strength two. A new class of orthogonal array...By using the generalized Hadamard product, difference matrix and projection matrices, we present a class of orthogonal projection matrices and related orthogonal arrays of strength two. A new class of orthogonal arrays are constructed.展开更多
Experimental design is an effective statistical tool that is extensively applied in modern industry,engineering,and science.It is proved that experimental design is a powerful and efficient means to screen the relatio...Experimental design is an effective statistical tool that is extensively applied in modern industry,engineering,and science.It is proved that experimental design is a powerful and efficient means to screen the relationships between input factors and their responses,and to distinguish significant and unimportant factor effects.In many practical situations,experimenters are faced with large experiments having four-level factors.Even though there are several techniques provided to design such experiments,the challenge faced by the experimenters is still daunting.The practice has demonstrated that the existing techniques are highly time-consuming optimization procedures,satisfactory outcomes are not guaranteed,and non-mathematicians face a significant challenge in dealing with them.A new technique that can overcome these defects of the existing techniques is presented in this paper.The results demonstrated that the proposed technique outperformed the current techniques in terms of construction simplicity,computational efficiency and achieving satisfactory results capability.For non-mathematician experimenters,the new technique is much easier and simpler than the current techniques,as it allows them to design optimal large experiments without the recourse to optimization softwares.The optimality is discussed from four basic perspectives:maximizing the dissimilarity among experimental runs,maximizing the number of independent factors,minimizing the confounding among factors,and filling the experimental domain uniformly with as few gaps as possible.展开更多
基金supported by Visiting Scholar Foundation of Key Lab in University and by National Natural Science Foundation of China (Grant No. 10571045)Specialized Research Fund for the Doctoral Program of Higher Education of Ministry of Education of China (Grant No. 44k55050)
文摘Nowadays orthogonal arrays play important roles in statistics, computer science, coding theory and cryptography. The usual difference matrices are essential for the construction for many mixed orthogonal arrays. But there are also orthogonal arrays which cannot be obtained by the usual difference matrices, such as mixed orthogonal arrays of run size 60. In order to construct these mixed orthogonal arrays, a class of special so-called generalized difference matrices were discovered by Zhang (1989,1990,1993,2006) from the orthogonal decompositions of projection matrices. In this article, an interesting equivalent relationship between orthogonal arrays and the generalized difference matrices is presented and proved. As an application, a lot of new orthogonal arrays of run size 60 have been constructed.
基金The work was supported by Visiting Scholar Foundation of Key Lab in Universityby Natural Science Foundation No.10571045,No.0224370051(Henan)and No.0211063100(Henan)in China.
文摘In this article, we propose a new general approach to constructing asymmetrical orthogonal arrays, namely the Kronecker sum. It is interesting since a lot of new mixed-level orthogonal arrays can be obtained by this method.
基金supported by the National Natural Science Foundation of China (Grant No. 61672124)the Password Theory Project of the 13th Five-Year Plan National Cryptography Development Fund,China (Grant No. MMJJ20170203)+2 种基金the Liaoning Provincial Science and Technology Innovation Leading Talents Program Project,China (Grant No. XLYC1802013)the Key Research and Development Projects of Liaoning Province,China (Grant No. 2019020105-JH2/103)the Jinan City 20-University Funding Projects for Introducing Innovation Team Program,China (Grant No. 2019GXRC031)。
文摘The image's least significant bit(LSB) covers lots of the details that have been commonly used in image encryption analysis. The newly proposed fractal sorting vector(FSV) and FSV-based LSB chaotic permutation(FSV-LSBCP) is a novel chaotic image encryption cryptosystem introduced in this article. The FSV-LSBCP effectively strengthens the security of the cryptographic scheme concerning the properties of the FSV. Key analysis, statistical analysis, resistance differential attack analysis, and resistance to cropping attacks and noise attacks are the focus of the suggested image encryption cryptosystem. The security experiment shows that the cryptosystem is adequate to achieve the desired degree of security.
基金The research is supported by the National Natural Science Foundation of China under Grant No. 10571045University Backbone Teachers Foundation of the Education Department of Henan ProvinceNatural Science Foundation of Henan Province under Grant No. 0411011100.
文摘By using the generalized Hadamard product, difference matrix and projection matrices, we present a class of orthogonal projection matrices and related orthogonal arrays of strength two. A new class of orthogonal arrays are constructed.
基金partially supported by the UIC Grants(Nos.R201810,R201912 and R202010)the Zhuhai Premier Discipline Grant.
文摘Experimental design is an effective statistical tool that is extensively applied in modern industry,engineering,and science.It is proved that experimental design is a powerful and efficient means to screen the relationships between input factors and their responses,and to distinguish significant and unimportant factor effects.In many practical situations,experimenters are faced with large experiments having four-level factors.Even though there are several techniques provided to design such experiments,the challenge faced by the experimenters is still daunting.The practice has demonstrated that the existing techniques are highly time-consuming optimization procedures,satisfactory outcomes are not guaranteed,and non-mathematicians face a significant challenge in dealing with them.A new technique that can overcome these defects of the existing techniques is presented in this paper.The results demonstrated that the proposed technique outperformed the current techniques in terms of construction simplicity,computational efficiency and achieving satisfactory results capability.For non-mathematician experimenters,the new technique is much easier and simpler than the current techniques,as it allows them to design optimal large experiments without the recourse to optimization softwares.The optimality is discussed from four basic perspectives:maximizing the dissimilarity among experimental runs,maximizing the number of independent factors,minimizing the confounding among factors,and filling the experimental domain uniformly with as few gaps as possible.
