Cryptography and Communications

, Volume 9, Issue 5, pp 581–597 | Cite as

Localised multisecret sharing

  • Thalia M. Laing
  • Keith M. Martin
  • Maura B. Paterson
  • Douglas R. Stinson
Article

Abstract

A localised multisecret sharing scheme is a multisecret sharing scheme for an ordered set of players in which players in the smallest sets who are authorised to access secrets are close together in the underlying ordering. We define threshold versions of localised multisecret sharing schemes, we provide lower bounds on the share size of perfect localised multisecret sharing schemes in an information theoretic setting, and we give explicit constructions of schemes to show that these bounds are tight. We then analyse a range of approaches to relaxing the model that provide trade-offs between the share size and the level of security guarantees provided by the scheme, in order to permit the construction of schemes with smaller shares. We show how these techniques can be used in the context of an application to key distribution for RFID-based supply-chain management motivated by the proposal of Juels, Pappu and Parno from USENIX 2008.

Keywords

Multisecret sharing Information-theoretic security Ramp schemes RFID 

Mathematics Subject Classification (2010)

94A60 94A62 

References

  1. 1.
    Abughazalah, S., Markantonakis, K., Mayes, K.: Enhancing the key distribution model in the RFID-enabled supply chains. In: 28th International Conference on Advanced Information Networking and Applications Workshops (WAINA 2014), pp. 871–878 (2014)Google Scholar
  2. 2.
    Blakley, G.R.: Safeguarding cryptographic keys. Federal Inf. Process. Standard Conference Proceedings 48, 313–317 (1979)Google Scholar
  3. 3.
    Blundo, C., Santis, A.D., Crescenzo, G.D., Gaggia, A.G., Vaccaro, U.: Multi-secret sharing schemes. In: Desmedt, Y. (ed.) CRYPTO ’94, volume 839 of LNCS, pp. 150–163. Springer (1994)Google Scholar
  4. 4.
    Blundo, C., Santis, A.D., Vaccaro, U.: Efficient sharing of many secrets. In: Enjalbert, P., Finkel, A., Wagner, K.W. (eds.) STACS ’93, volume 665 of LNCS, pp. 692–703. Springer (1993)Google Scholar
  5. 5.
    Capocelli, R.M., Santis, A.D., Gargano, L., Vaccaro, U.: On the size of shares for secret sharing schemes. In: Feigenbaum, J. (ed.) CRYPTO ’91, volume 576 of LNCS, pp. 101–113. Springer (1991)Google Scholar
  6. 6.
    EPCglobal: Radio-frequency identity protocols class-1 generation-2 UHF RFID protocol for communications at 860 mhz–960 mhz version 1.0. 9. http://www.epcglobalinc.org (2004)
  7. 7.
    Herranz, J., Ruiz, A., Sáez, G.: New results and applications for multi-secret sharing schemes. Des. Codes Crypt. 73(3), 841–864 (2013)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Ito, M., Saito, A., Nishizeki, T.: Secret sharing scheme realizing general access structure. In: IEEE Globecom, pp. 99–102 (1987)Google Scholar
  9. 9.
    Jackson, W.-A., Martin, K.M., O’Keefe, C.M.: Multisecret threshold schemes. In: Stinson, D.R. (ed.) CRYPTO ’93, volume 773 of LNCS, pp. 126–135. Springer (1993)Google Scholar
  10. 10.
    Juels, A., Pappu, R., Parno, B.: Unidirectional key distribution across time and space with applications to RFID security. In: van Oorschot, P.C. (ed.) USENIX Security Symposium, pp. 75–90. USENIX Association (2008)Google Scholar
  11. 11.
    Krawczyk, H.: Secret sharing made short. In: Stinson, D.R. (ed.) CRYPTO ’93, volume 773 of LNCS, pp. 136–146. Springer (1993)Google Scholar
  12. 12.
    Martin, K., Jackson, W.-A.: A combinatorial interpretation of ramp schemes. Aust. J. Commun. 14, 51–60 (1996)MathSciNetMATHGoogle Scholar
  13. 13.
    Massey, J.: Minimal codewords and secret sharing. In: Proceedings 6th Joint Swedish-Russian International Workshop on InformationTheory, pp. 276–279 (1993)Google Scholar
  14. 14.
    Masucci, B.: Sharing multiple secrets: models, schemes and analysis. Des. Codes Crypt. 39(1), 89–111 (2006)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    McEliece, R.J., Sarwate, D.V.: On sharing secrets and R,eed-Solomon codes. Commun. ACM 24(9), 583–584 (1981)CrossRefGoogle Scholar
  16. 16.
    Paterson, M.B., Stinson, D.R.: A simple combinatorial treatment of constructions and threshold gaps of ramp schemes. Cryptogr. Commun. 5(4), 229–240 (2013)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Roberts, C.M.: Radio frequency identification (RFID). Comput. Secur. 25(1), 18–26 (2006)CrossRefGoogle Scholar
  18. 18.
    Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Thalia M. Laing
    • 1
  • Keith M. Martin
    • 1
  • Maura B. Paterson
    • 2
  • Douglas R. Stinson
    • 3
  1. 1.Information Security GroupRoyal Holloway, University of LondonLondonUK
  2. 2.Department of Economics, Mathematics and StatisticsBirkbeck, University of LondonLondonUK
  3. 3.David R. Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada

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