Abstract
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.
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References
Ateniese G., Blundo C., Santis A.D., Stinson D.R.: Visual cryptography for general access structures. Inform. Computat. 129, 86–106 (1996)
Ateniese G., Blundo C., Santis A.D., Stinson D.R.: Extended capabilities for visual cryptography. ACM Theor. Comput. Sci. 250(1–2), 143–161 (2001)
Biham E., Itzkovitz A.: Visual cryptography with polarization. In: The Dagstuhl Seminar on Cryptography, September 1997, and in the RUMP session of CRYPTO ’98 (1997).
Cimato S., Prisco R.D., Santis A.D.: Probabilistic visual cryptography schemes. Comput. J. 49(1), 97–107 (2006)
Droste S.: New results on visual cryptography. In: CRYPTO ’96. LNCS, vol. 1109, pp. 401–415. Springer-Verlag (1996).
Kobara K., Imai H.: Limiting the visible space visual secret sharing schemes and their application to human identification. In: ASIACRYPT ’96. LNCS, vol. 1163, pp. 185–195. Springer-Verlag (1996).
Kuwakado H., Tanaka H.: Size-reduced visual secret sharing scheme. IEICE Trans. Fundam E87-A(5), 1193–1197 (2004)
Ito R., Kuwakado H., Tanaka H.: Image size invariant visual cryptography. IEICE Trans. Fundam. Elect. Commun. Comput. Sci. E82-A(10), 2172–2177 (1999)
Naor M., Shamir A.: Visual cryptography. In: EUROCRYPT ’94. LNCS, vol. 950, pp. 1–12. Springer-Verlag (1995).
Shyu S.J.: Efficient visual secret sharing scheme for color images. Patt. Recogn. 39, 866–880 (2006)
Yan W.Q., Jin D., Kankanhalli M.S.: Visual cryptography for print and scan applications. In: Proceedings of the 2004 International Symposium on Circuits and Systems, vol. 5, pp. 572–575 (2004).
Yang C.N.: New visual secret sharing schemes using probabilistic method. Patt. Recogn. Lett. 25, 481–494 (2004)
Yang C.N., Laih C.S.: New colored visual secret sharing schemes. Des. Codes Cryptogr. 20, 325–335 (2000)
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Liu, F., Wu, C.K. & Lin, X.J. The alignment problem of visual cryptography schemes. Des. Codes Cryptogr. 50, 215–227 (2009). https://doi.org/10.1007/s10623-008-9225-3
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DOI: https://doi.org/10.1007/s10623-008-9225-3