Visual cryptography

  • Moni Naor
  • Adi Shamir
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 950)


In this paper we consider a new type of cryptographic scheme, which can decode concealed images without any cryptographic computations. The scheme is perfectly secure and very easy to implement. We extend it into a visual variant of the k out of n secret sharing problem, in which a dealer provides a transparency to each one of the n users; any k of them can see the image by stacking their transparencies, but any k−1 of them gain no information about it.


  1. 1.
    N. Alon, J. Bruck, J. Naor, M. Naor and R. Roth, Construction of asymptotically good, low-rate error-correcting codes through pseudo-random graphs, IEEE Transactions on Information Theory, 38 (1992), 509–516.CrossRefGoogle Scholar
  2. 2.
    N. Alon, O. Goldreich, J. Hastad and R. Peralta, Simple constructions of almost k-wise independent random variables, Random Structures and Algorithms 3 (1992), 289–304.MathSciNetGoogle Scholar
  3. 3.
    N. Alon and J. Spencer, The probabilistic method, Wiley, 1992.Google Scholar
  4. 4.
    J. L. Carter and M. N. Wegman, Universal classes of hash functions, Journal of Computer and System Sciences 18 (1979), pp. 143–154.CrossRefMathSciNetGoogle Scholar
  5. 5.
    J. Kahn, N. Linial and A. Samorodnitsky, Inclusion-exlusion: exact and approximate, manuscript.Google Scholar
  6. 6.
    N. Linial and N. Nisan, Approximate inclusion-exlusion, Combinatorica 10, 1990, pp. 349–365.CrossRefMathSciNetGoogle Scholar
  7. 7.
    F. J. MacWilliams and N. J. A. Sloane, The theory of error correcting codes, North Holland, Amsterdam, 1977.Google Scholar
  8. 8.
    J. Naor and M. Naor, Small bias probability spaces: efficient constructions and applications, SIAM J. on Computing, vol 22, 1993, pp. 838–856.CrossRefMathSciNetGoogle Scholar
  9. 9.
    M. N. Wegman and J. L. Carter, New hash functions and their use in authentication and set equality, Journal of Computer and System Sciences 22, pp. 265–279 (1981).CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Moni Naor
    • 1
  • Adi Shamir
    • 1
  1. 1.Department of Applied Math and Computer ScienceWeizmann InstituteRehovotIsrael

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