An Optimization Model for Visual Cryptography Schemes with Unexpanded Shares

  • Ching-Sheng Hsu
  • Shu-Fen Tu
  • Young-Chang Hou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4203)


Visual cryptography schemes encrypt a secret image into n shares so that any qualified set of shares enables one to visually decrypt the hidden secret; whereas any forbidden set of shares cannot leak out any secret information. In the study of visual cryptography, pixel expansion and contrast are two important issues. Since pixel-expansion based methods encode a pixel to many pixels on each share, the size of the share is larger than that of the secret image. Therefore, they result in distortion of shares and consume more storage space. In this paper, we propose a method to reach better contrast without pixel expansion. The concept of probability is used to construct an optimization model for general access structures, and the solution space is searched by genetic algorithms. Experimental result shows that the proposed method can reach better contrast and blackness of black pixels in comparison with Ateniese et al.’s.


Access Structure Secret Image Secret Information Black Pixel White Pixel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ching-Sheng Hsu
    • 1
  • Shu-Fen Tu
    • 2
  • Young-Chang Hou
    • 3
  1. 1.Department of Information ManagementMing Chuan UniversityGui Shan Township, Taoyuan County 333Taiwan, R.O.C.
  2. 2.Department of Information ManagementChinese Culture UniversityTaipei City 111Taiwan, R.O.C.
  3. 3.Department of Information ManagementTamkang UniversityTamshui, Taipei County 251Taiwan, R.O.C.

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