Skip to main content
SpringerLink
Log in
Book cover

International Conference on Security in Communication Networks

SCN 2002: Security in Communication Networks pp 354–363Cite as

Secret Sharing Schemes on Access Structures with Intersection Number Equal to One

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2576))

Abstract

The characterization of ideal access structures and the search for bounds on the optimal information rate are two important problems in secret sharing. These problems are studied in this paper for access structures with intersection number equal to one, that is, access structures such that there is at most one participant in the intersection of any two minimal qualified subsets. Examples of such access structures are those defined by finite projective planes and those defined by graphs. In this work, ideal access structures with intersection number equal to one are completely characterized and bounds on the optimal information rate are provided for the non-ideal case.

This work was partially supported by the Spanish Ministerio de Ciencia y Tecnología under project TIC 2000-1044.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Blakley, G.R.: Safeguarding cryptographic keys. AFIPS Conference Proceedings 48 (1979) 313–317

    Google Scholar 

  2. Blundo, C., De Santis, A., De Simone, R., Vaccaro, U.: Tight bounds on the information rate of secret sharing schemes. Des. Codes Cryptogr. 11 (1997) 107–122

    Article  MathSciNet  Google Scholar 

  3. Blundo, C., De Santis, A., Gargano, L., Vaccaro, U.: On the information rate of secret sharing schemes. Advances in Cryptology CRYPTO’92. Lecture Notes in Comput. Sci. 740 148–167

    Google Scholar 

  4. Blundo, C., De Santis, A., Stinson, D.R., Vaccaro, U.: Graph decompositions and secret sharing schemes. J. Cryptology 8 (1995) 39–64

    Article  MathSciNet  Google Scholar 

  5. Brickell, E.F.: Some ideal secret sharing schemes. J. Combin. Math. and Combin. Comput. 9 (1989) 105–113

    MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  7. Brickell, E.F., Stinson, D.R.: Some improved bounds on the information rate of perfect secret sharing schemes. J. Cryptology 5 (1992) 153–166

    Article  MathSciNet  Google Scholar 

  8. Capocelli, R.M., De Santis, A., Gargano, L., Vaccaro, U.: On the size of shares of secret sharing schemes. J. Cryptology 6 (1993) 157–168

    Article  Google Scholar 

  9. Dembowski, P.: Finite geometries. Reprint of the 1968 original. Classics in Mathematics. Springer-Verlag, Berlin, 1997

    Google Scholar 

  10. Ito, M., Saito, A., Nishizeki, T.: Secret sharing scheme realizing any access structure. Proc. IEEE Globecom’87 (1987) 99–102

    Google Scholar 

  11. Jackson, W.-A., Martin, K.M.: Geometric secret sharing schemes and their duals. Des. Codes Cryptogr. 4 (1994) 83–95

    Article  MathSciNet  Google Scholar 

  12. Jackson, W.-A., Martin, K.M.: Perfect secret sharing schemes on five participants. Des. Codes Cryptogr. 9 (1996) 267–286

    MathSciNet  MATH  Google Scholar 

  13. Martí-Farré, J., Padró, C.: Secret sharing schemes with three or four minimal qualified subsets. Cryptology ePrint Archive (2002) Report 2002/050, http://eprint.iacr.org/

  14. Padró, C., Sáez, G.: Secret sharing schemes with bipartite access structure. IEEE Trans. Inform. Theory 46 (2000) 2596–2604

    Article  MathSciNet  Google Scholar 

  15. Shamir, A.: How to share a secret. Commun. of the ACM 22 (1979) 612–613

    Google Scholar 

  16. Stinson, D.R.: An explication of secret sharing schemes. Des. Codes Cryptogr. 2 (1992) 357–390

    Article  MathSciNet  Google Scholar 

  17. Stinson, D.R.: Decomposition constructions for secret-sharing schemes. IEEE Trans. Inform. Theory 40 (1994) 118–125

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, C. Jordi Girona, 1-3, Mòdul C3 Campus Nord, 08034, Barcelona, Spain

    Jaume Martí-Farré & Carles Padró

Authors
  1. Jaume Martí-Farré
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Carles Padró
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dipartimento di Informatica ed Applicazioni, Università di Salerno, Via S. Allende, 84081, Baronissi (SA), Italy

    Stelvio Cimato  & Giuseppe Persiano  & 

  2. Dept. of Computer Engineering and Informatics, Computer Technology Institute and University of Patras, 26500, Rio, Greece

    Clemente Galdi

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Martí-Farré, J., Padró, C. (2003). Secret Sharing Schemes on Access Structures with Intersection Number Equal to One. In: Cimato, S., Persiano, G., Galdi, C. (eds) Security in Communication Networks. SCN 2002. Lecture Notes in Computer Science, vol 2576. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36413-7_26

Download citation

  • DOI: https://doi.org/10.1007/3-540-36413-7_26

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00420-2

  • Online ISBN: 978-3-540-36413-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation