Designs, Codes and Cryptography

, Volume 50, Issue 2, pp 215–227

The alignment problem of visual cryptography schemes



Pixel expansion is an important parameter for Visual Cryptography Schemes (VCS). However, most papers in the literature are dedicated to reduce pixel expansion on the pixel level, i.e. to reduce the number of subpixels that represent a pixel in the original secret image. It is quite insufficient since the final size of the transparencies of the VCS is affected not only by the number of the subpixels, but also by the size of the subpixels in the transparencies. However, reducing the size of the subpixels in the transparencies results in difficulties of alignment of the transparencies. In this paper, we consider the alignment problem in VCS, and prove that in order to visually recover the original secret image, it is not necessary to align the transparencies precisely. This study is restricted to the case when only one transparency is shifted.


Visual cryptography Pixel expansion Subpixel shift 

Mathematics Subject Classification (2000)



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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.The State Key Laboratory of Information Security, Institute of SoftwareChinese Academy of SciencesBeijingChina
  2. 2.Graduate School of Chinese Academy of SciencesBeijingChina

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