Abstract
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.
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References
G. R. Blakley. Safeguarding cryptographic keys. Proceedings of AFIPS 1979 National Computer Conference, 48 (1979) 313–317.
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.
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.
T.M. Cover and J.A. Thomas. Elements of Information Theory, John Wiley & Sons, New York (1991).
Y. Desmedt and S. Jajodia. Redistributing secret shares to new access structures and its applications. Preprint (1997).
E.D. Karnin, J.W. Greene and M.E. Hellman. On secret sharing systems. IEEE Trans. on Inf. Th., 29 (1983) 35–41.
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.
K.M. Martin, J. Pieprzyk, R. Safavi-Naini and H. Wang. Changing thresholds in the absence of secure channels. In Information Security and Privacy-ACISP’99, LNCS 1587, Springer, Berlin (1999) 177–191.
K.M. Martin, R. Safavi-Naini and H. Wang. Bounds and techniques for efficient redistribution of secret shares to new access structures. The Computer Journal, 42, No. 8 (1999) 638–649.
A. Shamir. How to share a secret. Communications of the ACM, 22 (1979) 612–613.
C.E. Shannon. Communication theory of secrecy systems. Bell System Tech. Journal, 28 (1949) 656–715.
G. J. Simmons. An introduction to shared secret and/or shared control schemes and their application. In Contemporary Cryptology, 441–497. IEEE Press, (1991).
D.R. Stinson. An explication of secret sharing schemes. Des. Codes Cryptogr., 2 (1992) 357–390.
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).
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© 2002 Springer-Verlag Berlin Heidelberg
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Barwick, S.G., Jackson, W.A., Martin, K.M., Wild, P.R. (2002). Size of Broadcast in Threshold Schemes with Disenrollment. In: Batten, L., Seberry, J. (eds) Information Security and Privacy. ACISP 2002. Lecture Notes in Computer Science, vol 2384. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45450-0_6
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DOI: https://doi.org/10.1007/3-540-45450-0_6
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