Size of Broadcast in Threshold Schemes with Disenrollment
Threshold schemes are well-studied cryptographic primitives for distributing information among a number of entities in such a way that the information can only be recovered if a threshold of entities cooperate. Establishment of a threshold scheme involves an initialisation overhead. Threshold schemes with disenrollment capability are threshold schemes that enable entities to be removed from the initial threshold scheme at less communication cost than that of establishing a new scheme. We prove a revised version of a conjecture of Blakley, Blakley, Chan and Massey by establishing a bound on the size of the broadcast information necessary in a threshold scheme with disenrollment capability that has minimal entity information storage requirements. We also investigate the characterisation of threshold schemes with disenrollment that meet this bound.
KeywordsDistinct Element Access Structure Secret Data Secret Sharing Scheme Secure Channel
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- 1.G. R. Blakley. Safeguarding cryptographic keys. Proceedings of AFIPS 1979 National Computer Conference, 48 (1979) 313–317.Google Scholar
- 2.B. Blakley, G.R. Blakley, A.H. Chan and J.L. Massey. Threshold schemes with disenrollment. In Advances in Cryptology-CRYPTO’92, LNCS 740 Springer-Verlag, Berlin (1993) 540–548.Google Scholar
- 3.C. Blundo, A. Cresti, A. De Santis and U. Vaccaro. Fully dynamic secret sharing schemes. In Advances in Cryptology-CRYPTO’ 93, LNCS 773, Springer, Berlin (1993) 110–125.Google Scholar
- 5.Y. Desmedt and S. Jajodia. Redistributing secret shares to new access structures and its applications. Preprint (1997).Google Scholar
- 7.K.M. Martin. Untrustworthy participants in perfect secret sharing schemes. In Cryptography and Coding III, (M.J. Ganley, Ed.) Clarendon Press, Oxford (1993) 255–264.Google Scholar
- 12.G. J. Simmons. An introduction to shared secret and/or shared control schemes and their application. In Contemporary Cryptology, 441–497. IEEE Press, (1991).Google Scholar
- 14.Y. Tamura, M. Tada and E. Okamoto. Update of access structure in Shamir’s (k, n)-threshold scheme. Proceedings of The 1999 Symposium on Cryptography and Information Security, Kobe, Japan, January 26–29, (1999).Google Scholar