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New insight into linear algebraic technique to construct visual cryptography scheme for general access structure

机译:线性代数技术为一般访问结构构建可视密码方案的新见解

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摘要

The most essential advantage of applying linear algebra to construct visual cryptography scheme (VCS) lies in that it only requires solving linear equations in the construction of initial basis matrices, which are the basis matrices before removing the common columns. In this paper, we give some new insight into linear algebraic technique to construct VCS, where we can take more equations simultaneously. Then based on this knowledge, we propose a construction of VCS for general access structure. The construction is efficient in the sense that it gets the smallest initial pixel expansion compared with some well-known constructions. At the same time, by using the technique of deleting common columns from the initial basis matrices, the proposed construction achieves the optimal pixel expansions in most cases according to our experimental results. However, finding exact number of common columns in the initial basis matrices is a challenging issue. Then we deal with this issue and find out that the exact number of common columns is n - 2 for (2, n) threshold access structures. Finally, we provide some future research directions in the algebraic aspect of VCS.
机译:应用线性代数构建可视密码方案(VCS)的最本质优势在于,它仅需要在构造初始基础矩阵(即除去通用列之前的基础矩阵)的过程中求解线性方程。在本文中,我们对构造VCS的线性代数技术提供了一些新见解,在其中可以同时采用更多的方程式。然后,基于此知识,我们提出了用于通用访问结构的VCS的构造。与某些众所周知的结构相比,该结构在获得最小的初始像素扩展方面是有效的。同时,通过使用从初始基础矩阵中删除公共列的技术,根据我们的实验结果,所提出的构造在大多数情况下均实现了最佳像素扩展。但是,在初始基础矩阵中找到确切的公共列数是一个具有挑战性的问题。然后,我们处理此问题,并发现(2,n)个阈值访问结构的公共列的确切数目为n-2。最后,我们在VCS的代数方面提供了一些未来的研究方向。

著录项

  • 来源
    《Multimedia Tools and Applications》 |2017年第12期|14511-14533|共23页
  • 作者单位

    Zhengzhou Informat Sci & Technol Inst, Zhengzhou, Peoples R China;

    Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing, Peoples R China|Univ Chinese Acad Sci, Sch Cyber Secur, Beijing, Peoples R China;

    Zhengzhou Informat Sci & Technol Inst, Zhengzhou, Peoples R China;

    Zhengzhou Informat Sci & Technol Inst, Dept Comp Sci & Informat Engn, Zhengzhou, Peoples R China;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Visual cryptography; Basis matrices; Linear algebra; More equations; Common columns;

    机译:视觉密码学;基矩阵;线性代数;更多方程;公共列;

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