Visual cryptography schemes with optimal pixel expansion

  • Authors:
  • Carlo Blundo;Stelvio Cimato;Alfredo De Santis

  • Affiliations:
  • Dipartimento di Informatica ed Applicazioni, Università degli Studi di Salerno, Baronissi, Italy;Dipartimento di Tecnologie dell'Informazione, Università degli Studi di Milano, Crema, Italy;Dipartimento di Informatica ed Applicazioni, Università degli Studi di Salerno, Baronissi, Italy

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2006

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Abstract

A visual cryptography scheme encodes a black and white secret image into n shadow images called shares which are distributed to the n participants. Such shares are such that only qualified subsets of participants can "visually" recover the secret image. Usually, the reconstructed image will be darker than the background of the image itself. In this paper we consider visual cryptography schemes satisfying the model introduced by Tzeng and Hu [A new approach for visual cryptography, Designs, Codes and Cryptography 27 (3) (2002) 207-227]. In such a model, the recovered secret image can be darker or lighter than the background. We prove a lower bound on the pixel expansion of the scheme and, for (2, n)-threshold visual cryptography schemes, we provide schemes achieving the bound. Our schemes improve on the ones proposed by Tzeng and Hu.