Advertisement

Designs, Codes and Cryptography

, Volume 35, Issue 3, pp 311–335 | Cite as

Optimal Colored Threshold Visual Cryptography Schemes

  • Stelvio Cimato
  • Roberto De PriscoEmail author
  • Alfredo De Santis
Article

Abstract

Visual cryptography schemes allow the encoding of a secret image into n shares which are distributed to the participants. The shares are such that only qualified subsets of participants can “visually” recover the secret image. Usually the secret image consist of black and white pixels. In colored threshold visual cryptography schemes the secret image is composed of pixels taken from a given set of c colors. The pixels expansion and the contrast of a scheme are two measures of the goodness of the scheme.

In this paper, we study c-color (k,n)-threshold visual cryptography schemes and provide a characterization of contrast-optimal schemes. More specifically we prove that there exists a contrast-optimal scheme that is a member of a special set of schemes, which we call canonical schemes, and that satisfy strong symmetry properties.

Then we use canonical schemes to provide a constructive proof of optimality, with respect to the pixel expansion, of c-color (n,n)-threshold visual cryptography schemes.

Finally, we provide constructions of c-color (2,n)-threshold schemes whose pixels expansion improves on previously proposed schemes.

Keywords

visual crytography secret sharing schemes 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ateniese, G, Blundo, C, Santis, A, Stinson, DR 1996Visual Cryptography for General Access StructuresInformation and Computation12986106Google Scholar
  2. Ateniese, G, Blundo, C, Santis, A, Stinson, DR 2001Extended Schemes for Visual CryptographyTheoretical Computer Science250143161Google Scholar
  3. Blundo, C., Bonis, A., Santis, A 2001Improved Schemes for Visual CryptographyDesigns, Codes, and Cryptography24255278Google Scholar
  4. R. L. Grajam, D. E. Kunth and O. Patashnik, Concrete Mathematics, A Foundation for Computer Science, Addison Wesley, 1988.Google Scholar
  5. Lint, JH, Wilson, RM 1992A Course in CombinatoricsCambridge University PressCambridge UKGoogle Scholar
  6. M. Naor and A. Shamir, Visual Cryptography, In Advances in Cryptology – EUROCRYPT ‘94, LNCS 950, pp. 1–12, 1995.Google Scholar
  7. Verheul, ER, Tilborg, HCA 1997Constructions and Properties of k out of n Visual Secret Sharing SchemesDesigns, Codes, and Cryptography11179196Google Scholar
  8. Yang, CN, Laih, CS 2000New Colored Visual Secret Sharing SchemesDesigns, Codes and Cryptography20325335Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Stelvio Cimato
    • 1
  • Roberto De Prisco
    • 1
    Email author
  • Alfredo De Santis
    • 1
  1. 1.Dipartimento di Informatica ed ApplicazioniUniversitá di SalernoBaronissi (SA)Italy

Personalised recommendations