Skip to main content
SpringerLink
Log in

Secret Sharing Schemes

  • Reference work entry
Encyclopedia of Cryptography and Security

  • 126 Accesses

Informally speaking, a secret sharing scheme (SSS, for short) allows one to share a secret among n participants in a such a way that some sets of participants called allowed coalitions can recover the secret exactly, while any other sets of participants (non-allowed coalitions) cannot get any additional (i.e., a posteriori) information about the possible value of the secret. the SSS with the last property is called perfect. The set Γ of all allowed coalitions is called an access structure.

The history of SSS began in 1979 when this problem was introduced and partially solved by Blakley [2] and Shamir [1] for the case of (n, k)-threshold schemes where the access structure consists of all sets of k or more participants. Consider the simplest example of (n, n)-threshold scheme. There is a dealer who wants to distribute a secret \(s_0\) among n participants. Let \(s_0\) be an element of some finite additive group G. For instance, G is the group of binary strings of length mwith addition...

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

References

  1. Blakley, R. (1979). “Safeguarding cryptographic keys.” Proceedings of AFIPS 1979 National Computer Conference, vol. 48, Va. Arlington, New York, 313–317.

    Google Scholar 

  2. Shamir, A. (1979). “How to share a secret.” Communications of the ACM, 22 (1), 612–613.

    MATH  MathSciNet  Google Scholar 

  3. Ito, M., A. Saito, and T. Nishizeki (1993). “Multiple assignment scheme for sharing secret.” Journal of Cryptology, 6, 15–20.

    MATH  MathSciNet  Google Scholar 

  4. Karnin, E.D., J.W. Greene, and M.E. Hellman (1983). “On secret sharing systems.” IEEE Transactions on Informatiom Theory, 29 (1), 231–241.

    MathSciNet  Google Scholar 

  5. Capocelli, R.M., A. De Santis, L. Gargano, and U. Vaccaro (1993). “On the size of shares for secret sharing schemes.” Journal of Cryptology, 6, 157–167.

    MATH  Google Scholar 

  6. Brickell, E.F. and D.M. Davenport (1991). “On the classification of ideal secret sharing schemes.” Journal of Cryptology, 4, 123–134.

    MATH  Google Scholar 

  7. Blakley, G.R. and G.A. Kabatianski (1997). “Generalized ideal secret sharing schemes and matroids.” Problems of Information Transmission, 33 (3), 102–110.

    MATH  MathSciNet  Google Scholar 

  8. Kurosawa, K., K. Okada, K. Sakano, W. Ogata, and S. Tsujii (1993). “Nonperfect secret sharing schemes and matroids.” Advances in Cryptology—EUROCRYPT'93, Lecture Notes in Computer Science, vol. 765, ed. T. Helleseth. Springer-Verlag, Berlin, 126–141.

    Google Scholar 

  9. Jackson, W.-A. and K.M. Martin (1998). “Combinatorial models for perfect secret sharing schemes.” Journal of Combinatorial Mathematics and Combinatorial Computing, 28, 249–265.

    MATH  MathSciNet  Google Scholar 

  10. Welsh, D.J.A. (1976). Matroid Theory. Academic Press, New York.

    MATH  Google Scholar 

  11. Csirmaz, L. (1995). “The size of a share must be large.” Advances in Cryptology—EUROCRYPT'94, Lecture Notes in Computer Science, vol. 950, ed. A. De Santis. Springer-Verlag, Berlin, 13–22.

    Google Scholar 

  12. Blakley, G.R. and G.A. Kabatianski (1994). “Linear algebra approach to secret sharing schemes.” Error Control, Cryptology and Speech Compression, Lecture Notes in Computer Science, vol. 829, eds. A. Chmora, and S.B. Wicker. Springer, Berlin, 33–40.

    Google Scholar 

  13. van Dijk, M. (1995). “A linear construction of perfect secret sharing schemes.” Advances in Cryptology—EUROCRYPT'94, Lecture Notes in Computer Science, vol. 950, ed. A. De Santis. Springer-Verlag, Berlin, 23–34.

    Google Scholar 

  14. McEliece, R.J. and D.V. Sarwate (1981). “On secret sharing and Reed–Solomon codes.” Communications of the ACM, 24, 583–584.

    MathSciNet  Google Scholar 

  15. Ashihmin, A. and J. Simonis (1998). “Almost affine codes.” Designs, Codes and Cryptography, 14 (2), 179–197.

    MATH  MathSciNet  Google Scholar 

  16. Massey, J. (1993). “Minilal codewords and secret sharing.” Proceedings of Sixth Joint Swedish–Russian Workshop on Information Theory, Molle, Szweden, 246–249.

    Google Scholar 

  17. Beimel, A. and B. Chor (1998). “Secret sharing with public reconstruction.” IEEE Transactions on Informatiom Theory, 44 (5), 1887–1896.

    MATH  MathSciNet  Google Scholar 

Download references

Authors
  1. Robert Blakley
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gregory Kabatiansky
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Eindhoven University of Technology, Eindhoven, The Netherlands

    Henk C. A. van Tilborg

Rights and permissions

Reprints and permissions

Copyright information

© 2005 International Federation for Information Processing

About this entry

Cite this entry

Blakley, R., Kabatiansky, G. (2005). Secret Sharing Schemes. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_373

Download citation

Publish with us

Policies and ethics

Search

Navigation