Skip to main content
SpringerLink
Log in

Efficient sharing of many secrets

  • Conference paper
  • First Online:
STACS 93 (STACS 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 665))

Included in the following conference series:

Abstract

A multi-secret sharing scheme is a protocol to distribute n secrets s 1,..., s n among a set of participants \(\mathcal{P}\) in such a way that: 1) any non-qualified subset of participants \(A \subseteq \mathcal{P}\) has absolutely no information on the secrets; 2) any qualified subset can recover all the secrets, but 3) any non-qualified subset knowing the value of a number of secrets might have some information on other secrets.

In this paper we lay foundations for a general theory of multi-secret sharing schemes by using the entropy approach, as done in [4] and [6] to analyze singlesecret sharing schemes. We prove lower bounds on the size of information held by each participant in any multi-secret sharing scheme. We provide an optimal protocol for multi-secret sharing schemes on a particular access structure, where the access structure specifies the subsets of participants qualified to reconstruct the secret.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Benaloh and J. Leichter, Generalized Secret Sharing and Monotone Functions, Lecture Notes in Computer Science, 403:27–35, 1990.

    Google Scholar 

  2. G. R. Blakley, Safeguarding Cryptographic Keys, AFIPS Conference Proceedings, 48:313–317, 1979.

    Google Scholar 

  3. C. Blundo, A. De Santis, D. R. Stinson, and U. Vaccaro, Graph Decomposition and Secret Sharing Schemes, in “Advances in Cryptology — EUROCRYPT 92”, Ed. R. Rueppel, “Lecture Notes in Computer Science”, Springer-Verlag, (to appear).

    Google Scholar 

  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”, Ed. E. Brickell, “Lecture Notes in Computer Science”, Springer-Verlag, (to appear).

    Google Scholar 

  5. E. F. Brickell and D. R. Stinson, Some Improved Bounds on the Information Rate of Perfect Secret Sharing Schemes, in “Advances in Cryptology — CRYPTO 90”, “Lecture Notes in Computer Science”, Springer-Verlag. To appear in J. Cryptology.

    Google Scholar 

  6. R. M. Capocelli, A. De Santis, L. Gargano, and U. Vaccaro, On the Size of Shares for Secret Sharing Schemes, in “Advances in Cryptology — CRYPTO 91”, Ed. J. Feigenbaum, vol. 576 of “Lecture Notes in Computer Science”, Springer-Verlag, pp. 101–113. To appear in J. Cryptology.

    Google Scholar 

  7. I. Csiszár and J. Körner, Information Theory. Coding theorems for discrete memoryless systems, Academic Press, 1981.

    Google Scholar 

  8. R. G. Gallager, Information Theory and Reliable Communications, John Wiley & Sons, New York, NY, 1968.

    Google Scholar 

  9. M. Franklin and M. Yung, Communication Complexity of Secure Computation, STOC 1992, pp. 699–710.

    Google Scholar 

  10. E. D. Karnin, J. W. Greene, and M. E. Hellman, On Secret Sharing Systems, IEEE Trans. on Inform. Theory, vol. IT-29, no. 1, Jan. 1983, pp. 35–41.

    Google Scholar 

  11. S. C. Kothari, Generalized Linear Threshold Schemes, in “Advances in Cryptology — CRYPTO 84”, G. R. Blakley and D. Chaum Eds., vol. 196 of “Lecture Notes in Computer Science”, Springer-Verlag, pp. 231–241.

    Google Scholar 

  12. R. J. McEliece and D. Sarwate, On Sharing Secrets and Reed-Solomon Codes, Communications of the ACM, vol. 24, n. 9, pp. 583–584, September 1981.

    Google Scholar 

  13. A. Shamir, How to Share a Secret, Commun. of the ACM, 22:612–613, 1979.

    Google Scholar 

  14. 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 

  15. D. R. Stinson, An Explication of Secret Sharing Schemes, Technical Report UNL-CSE-92-004, Department of Computer Science and Engineering, University of Nebraska, February 1992. To appear in Codes, Design and Cryptography.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatica ed Applicazioni, Università di Salerno, 84081, Baronissi, SA, Italy

    Carlo Blundo, Alfredo De Santis & Ugo Vaccaro

Authors
  1. Carlo Blundo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alfredo De Santis
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ugo Vaccaro
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

P. Enjalbert A. Finkel K. W. Wagner

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Blundo, C., De Santis, A., Vaccaro, U. (1993). Efficient sharing of many secrets. In: Enjalbert, P., Finkel, A., Wagner, K.W. (eds) STACS 93. STACS 1993. Lecture Notes in Computer Science, vol 665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56503-5_68

Download citation

  • DOI: https://doi.org/10.1007/3-540-56503-5_68

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56503-1

  • Online ISBN: 978-3-540-47574-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation