Cheating Immune (2,n)-Threshold Visual Secret Sharing

  • Roberto De Prisco
  • Alfredo De Santis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4116)


Cheating in secret sharing has been considered in several papers. Recently cheating in visual cryptography has been considered in [10], where (2,n)-threshold visual cryptography schemes are provided. In this paper we provide new (2,n)-threshold visual cryptography schemes. Our model is different from the one considered in [10]; in particular we aim at constructing cheating immune schemes without the use of extra information, like additional shares or images as done in [10]. We have provided a formal definition of cheating which requires that a group of cheaters be able to deterministically force a honest participant to reconstruct a wrong secret. The (2,n)-threshold schemes that we provide do not allow such cheating, regardless of the number of cheaters.


Secret Sharing Secret Image Secret Sharing Scheme Threshold Scheme Visual Cryptography 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Blakley, G.R.: Safeguarding Cryptographic keys. In: AFIPS Conference Proceedings, vol. 48, pp. 313–317 (1979)Google Scholar
  2. 2.
    Blakley, G.R., Meadows, C.: Security of Ramp Schemes. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 242–268. Springer, Heidelberg (1985)CrossRefGoogle Scholar
  3. 3.
    Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness Theorems for Non-Cryptographic Fault-Tolerant Distributed Computation. In: Proceedings of STOC 1988, pp. 1–10 (1988)Google Scholar
  4. 4.
    Carpentieri, M.: A perfect threshold secret sharing scheme to identify cheaters. Designs, Codes, and Cryptography (5), 183–187 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Carpentieri, M., De Santis, A., Vaccaro, U.: Size of shares and probability of cheating in threshold schemes. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 118–125. Springer, Heidelberg (1994)Google Scholar
  6. 6.
    Chaum, D., Crépeau, C., Damgård, I.: Multiparty Unconditionally Secure Protocols. In: Proceedings of STOC 1988, pp. 11–19 (1988)Google Scholar
  7. 7.
    Chor, B., Goldwasser, S., Micali, S., Awerbach, B.: Verifiable Secret Sharing and Achieving Simultaneity in Presence of Faults. In: Proceedings of FOCS 1985, pp. 383–395 (1985)Google Scholar
  8. 8.
    D’Arco, P., Kishimoto, W., Stinson, D.: Properties and Constraints of Cheating-Immune Secret Sharing Scheme. Discrete Applied Mathematics (to appear)Google Scholar
  9. 9.
    Feldman, P.: Non-interactive and Information Theoretic Secure Verifiable Secret Sharing. In: Proceedings of FOCS 1987, pp. 427–437 (1987)Google Scholar
  10. 10.
    Horng, G., Chen, T., Tsai, D.-S.: Cheating in Visual Cryptography. Designs, Codes and Cryptography (38), 219–236 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Pieprzyk, J., Zhang, X.M.: Cheating Prevention in Secret Sharing over GF(P t). In: Pandu Rangan, C., Ding, C. (eds.) INDOCRYPT 2001. LNCS, vol. 2247, pp. 79–90. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. 12.
    Pieprzyk, J., Zhang, X.-M.: Constructions of Cheating Immune Secret Sharing. In: Kim, K.-c. (ed.) ICISC 2001. LNCS, vol. 2288, pp. 226–243. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  13. 13.
    Naor, M., Shamir, A.: Visual cryptography. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 1–12. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  14. 14.
    Rabin, T., Ben-Or, M.: Verifiable Secret Sharing and Multiparty Protocols with Honest Majority. In: Proceedings of STOC 1989, pp. 73–85 (1989)Google Scholar
  15. 15.
    Shamir, A.: How to Share a Secret. Communications of the ACM (22), 612–613 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Stinson, D.R.: An Explication of Secret Sharing Schemes. Designs, Codes and Cryptography (2), 357–390 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Stinson, D.R., Wei, R.: Unconditionally Secure Proactive Secret Sharing Scheme with Combinatorial Structures. In: Heys, H.M., Adams, C.M. (eds.) SAC 1999. LNCS, vol. 1758, pp. 200–214. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  18. 18.
    Tompa, M., Woll, H.: How to Share a Secret with Cheaters. Journal of Cryptology (1), 133–138 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Zhang, X.-M., Pieprzyk, J.: Cheating Immune Secret Sharing. In: Qing, S., Okamoto, T., Zhou, J. (eds.) ICICS 2001. LNCS, vol. 2229, pp. 144–149. Springer, Heidelberg (2001)CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Roberto De Prisco
    • 1
  • Alfredo De Santis
    • 1
  1. 1.Dipartimento di Informatica ed ApplicazioniUniversità di SalernoBaronissi (SA)Italy

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