Multi-Secret Sharing Schemes

Extended Abstract
  • Carlo Blundo
  • Alfredo De Santis
  • Giovanni Di Crescenzo
  • Antonio Giorgio Gaggia
  • Ugo Vaccaro
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 839)


A multi-secret sharing scheme is a protocol to share m arbitrarily related secrets s 1, ..., s m among a set of participants \( \mathcal{P} \). In this paper we put forward a general theory of multi-secret sharing schemes by using an information theoretical framework. We prove lower bounds on the size of information held by each participant for various access structures. Finally, we prove the optimality of the bounds by providing protocols.


Secret Sharing Access Structure Sharing Scheme Secret Sharing Scheme Threshold Scheme 
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.


  1. 1.
    J. C. Benaloh and J. Leichter, Generalized Secret Sharing and Monotone Functions, in “Advances in Cryptology — CRYPTO’ 88”, S. Goldwasser Ed., “Lecture Notes in Computer Science”, Vol. 403, Springer-Verlag, Berlin, pp. 27–35, 1990.Google Scholar
  2. 2.
    M. Ben-Or, S. Goldwasser, and A. Wigderson, Completeness Theorems for Non-Cryptographic Fault-Tolerant Distributed Computation, Proceedings of 20th Annual ACM Symposium on Theory of Computing, pp. 1–10, 1988.Google Scholar
  3. 3.
    G. R. Blakley, Safeguarding Cryptographic Keys, Proceedings AFIPS 1979 National Computer Conference, pp. 313–317, June 1979.Google Scholar
  4. 4.
    C. Blundo, A. De Santis, L. Gargano, and U. Vaccaro, On the Information Rate of Secret Sharing Schemes, in “Advances in Cryptology-CRYPTO’ 92”, E. Brickell Ed., “Lecture Notes in Computer Science”, Vol. 740, Springer-Verlag, Berlin, pp. 149–169, 1993. To appear in Theoretical Computer Science.Google Scholar
  5. 5.
    C. Blundo, A De Santis, and U. Vaccaro, Efficient Sharing of Many Secrets, in “Proceedings of STACS’ 93 (10th Symp. on Theoretical Aspects of Computer Science)”, P. Enjalbert, A. Finkel, K. W. Wagner Eds., “Lecture Notes in Computer Science”, Vol. 665, Springer-Verlag, Berlin, pp. 692–703, 1993.Google Scholar
  6. 6.
    R. M. Capocelli, A. De Santis, L. Gargano, and U. Vaccaro, On the Size of Shares for Secret Sharing Schemes, Journal of Cryptology, Vol. 6, pp. 57–167, 1993.CrossRefGoogle Scholar
  7. 7.
    I. Csiszár and J. Körner, Information Theory. Coding Theorems for Discrete Memoryless Systems, Academic Press, 1981.Google Scholar
  8. 8.
    M. Franklin and M. Yung, Communication Complexity of Secure Computation, Proceedings of 24th Annual ACM Symposium on Theory of Computing”, pp. 699–710, 1992.Google Scholar
  9. 9.
    R. G. Gallager, Information Theory and Reliable Communications, John Wiley & Sons, New York, NY, 1968.Google Scholar
  10. 10.
    O. Goldreich, S. Micali, and A. Wigderson, How to Play any Mental Game, Proceedings of 19th ACM Symposium on Theory of Computing, pp. 218–229, 1987.Google Scholar
  11. 11.
    M. Ito, A. Saito, and T. Nishizeki, Secret Sharing Scheme Realizing General Access Structure, Proceedings of IEEE Global Telecommunications Conference, Globecom 87, Tokyo, Japan, pp. 99–102, 1987.Google Scholar
  12. 12.
    W.-A. Jackson, K. M. Martin, and C. M. O’Keefe, Multisecret Threshold Schemes, in “Advances in Cryptology-CRYPTO’ 93”, D.R. Stinson Ed., “Lecture Notes in Computer Science”, Vol. 773, Springer-Verlag, Berlin, pp. 126–135, 1994.Google Scholar
  13. 13.
    W.-A. Jackson, K. M. Martin, and C. M. O’Keefe, A Construction for Multisecret Threshold Schemes, Preprint, 1994.Google Scholar
  14. 14.
    E. D. Karnin, J. W. Greene, and M. E. Hellman, On Secret Sharing Systems, IEEE Trans. on Inform. Theory, Vol. IT-29, no. 1, pp. 35–41, Jan. 1983.CrossRefMathSciNetGoogle Scholar
  15. 15.
    S. C. Kothari, Generalized Linear Threshold Schemes, in “Advances in Cryptology — CRYPTO’ 84”, G. R. Blakley, D. Chaum Eds., “Lecture Notes in Computer Science”, Vol. 196, Springer-Verlag, Berlin, pp. 231–241, 1985.Google Scholar
  16. 16.
    A. Shamir, How to Share a Secret, Communications of the ACM, Vol. 22, n. 11, pp. 612–613, Nov. 1979.zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    G. J. Simmons, An Introduction to Shared Secret and/or Shared Control Schemes and Their Application, Contemporary Cryptology, IEEE Press, pp. 441–497, 1991.Google Scholar
  18. 18.
    D. R. Stinson, An Explication of Secret Sharing Schemes, Design, Codes and Cryptography, Vol. 2, pp. 357–390, 1992.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Carlo Blundo
    • 1
  • Alfredo De Santis
    • 1
  • Giovanni Di Crescenzo
    • 1
  • Antonio Giorgio Gaggia
    • 1
  • Ugo Vaccaro
    • 1
  1. 1.Dipartimento di Informatica ed ApplicazioniUniversità di SalernoBaronissi (SA)Italy

Personalised recommendations