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Visual Secret Sharing Schemes

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Visual secret sharing schemes (VSSS, for shortness) were introduced in 1995 [1]. They form a particular case of secret sharing schemes with the additional restriction that allowed (also called privileged or trusted in access structure) coalitions can recover the secret by visual means.

More precisely, consider the case when just one bit of visual information, i.e., a black or white pixel, has to be distributed as a secret s among n participants of VSSS. To realize this, the dealer uses two sets \( \cal B \) and \( \cal W \) of binary (Boolean) \(n\times m\) matrices in the following way. To distribute a “black” secret (s=1), he randomly chooses a matrix \( B=(b_{i,j})\in \cal B \) and sends to the ith participant a transparency consisting of m subpixels, where the j th subpixel is black if bi,j = 1 and the jth subpixel is white if \(b_{i,j}=0.\). For distributing s = 0, the dealer does the same but with a randomly chosen matrix . An allowed coalition recovers the secret by stacking...

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References

  1. Naor, M. and A. Shamir (1995). “Visual cryptography.” Advances in Cryptology—EUROCRYPT'94, Lecture Notes in Computer Science, vol. 950, ed. A. De Santis. Springer-Verlag, Berlin, 1–12.

    Google Scholar 

  2. Droste, S. (1996). “New results on visual cryptography.” Advances in Cryptology—CRYPTO'96, Lecture Notes in Computer Science, vol. 1109, ed. N. Koblitz. Springer-Verlag, Berlin, 401–415.

    Google Scholar 

  3. Verheul, E.R. H.C.A. van Tilborg (1997). “Constructions and properties of k out of n visual secret sharing schemes.” Designs, Codes and Cryptography, 11 (2), 179–196.

    Article  MATH  MathSciNet  Google Scholar 

  4. Hofmeister, T.M. Krause and H.U. Simon (2000). “Optimal k out of n secret sharing schemes in visual cryptography.” Theoretical Computer Science, vol. 240, 471–485.

    Article  MATH  MathSciNet  Google Scholar 

  5. Krause, M. and H.U. Simon (2000). “On contrast optimal secret sharing schemes in visual cryptography: determining the optimal contrast exactly.” Lecture Notes in Computer Science, vol. 1776, eds. G. H. Gonnet, D. Panario, and A. Viola. Springer, Berlin, 280–291.

    Google Scholar 

  6. Blundo, C.P. D'Arco, A. De Santis, and D.R. Stinson (2003). “Contrast optimal threshold visual cryptography schemes.” SIAM Journal on Discrete Mathematics, vol. 16, 224–261.

    Article  MathSciNet  Google Scholar 

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© 2005 International Federation for Information Processing

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Blakley, R., Kabatiansky, G. (2005). Visual Secret Sharing Schemes. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_456

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