Multimedia Tools and Applications

, Volume 73, Issue 3, pp 1177–1193 | Cite as

Optimal pixel expansion of deterministic visual cryptography scheme

  • Zhengxin FuEmail author
  • Bin Yu


The optimal pixel expansion is an important parameter of deterministic visual cryptography scheme (DVCS). There are many researches have been done under different access structures and stacking operations. However, any necessary or sufficient condition has not been found about the optimal pixel expansion. In this paper, we give a necessary condition of the optimal pixel expansion of DVCS for the first time, which is suitable for any access structure and any stacking operation. Furthermore, a pixel expansion optimization algorithm has been designed to improve the existing schemes. It is found that the pixel expansion can be reduced for most DVCS based on XOR operation. Finally, we give some experimental results and comparisons to show the effectiveness of the proposed scheme.


Visual cryptography Deterministic Necessary condition Pixel expansion 



The authors would like to thank the anonymous reviewers for their valuable comments. This work was supported by National Natural Science Foundation of China under Grant No. 61070086.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Zhengzhou Information Science and Technology InstituteZhengzhouPeople’s Republic of China
  2. 2.Department of Computer Science and Information EngineeringZhengzhou Information Science and Technology InstituteZhengzhouPeople’s Republic of China

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