Abstract
In this paper, we show that there exists a t-cheater identifiable (k, n) threshold secret sharing scheme such as follows for cheating probability ε > 0. If k ≥ 3t + 1, then
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1.
Just k participants are enough to identify who are cheaters.
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2.
|V i| is independent of n. That is, |V i| = |S|(1/ε)(t+2), where S denotes the set of secrets and V i denotes the set of shares of a participant P i, respectively.
(Previously, no schemes were known which satisfy both requirements.) Further, we present a lower bound on |V i| for our model and for the model of Tompa and Woll. Our bound for the TW model is much more tight than the previous bound.
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References
A. Shamir, How to share a secret, Comm.ACM, 22(1979), pp.612–613.
G.R. Blakley, Safeguarding cryptographic keys, Proc. National Computer Conference, AFIPS Conference Proceedings, 48(1979), pp.313–317.
R.J. McEliece and D.V. Sarwate, On sharing secrets and Reed-Solomon codes, Comm.ACM, 24(1981), pp.583–584.
G. Simmons, Robust shared secret schemes or “how to be sure you have the right answer even though you don’t know the question,” Congr.Numer., 68(1989), pp.215–248.
T. Rabin and M. Ben-Or, Verifiable secret sharing and multiparty protocols with honest majority, Proc. 21st ACM Symposium on Theory of Computing (1989), pp.73–85.
E.F. Brickell and D.R. Stinson, The Detection of Cheaters in Threshold Schemes, SIAM J. DISC. MATH, Vol.4, No.4, Nov.1991, pp.502–510.
M. Tompa and H. Woll, How to share a secret with cheaters, Journal of Cryptology, vol.1(1988), pp.133–138.
Marco Carpentieri, Alfredo De Santis and Ugo Vaccaro, Size of Shares and Probability of Cheating in Threshold Schemes, Proceedings of Eurocrypt’93, Lecture Notes in Computer Science, LNCS 765, Springer Verlag (1993), pp.118–125.
E.D. Karnin, J.W. Greene, and M.E. Hellman, On Secret Sharing Systems, IEEE Trans. on Inform. Theory, Vol.IT-29 (1983), pp.35–41.
R.M. Capocelli, A. De Santis, L. Gargano and U. Vaccaro, On the size of shares for secret sharing schemes, Proceedings of Crypto’91, Lecture Notes in Computer Science, LNCS 576, Springer Verlag (1991), pp.101–113.
K. Kurosawa and K. Okada, Combinatorial interpretation of secret sharing schemes, In Pre-Proceedings of Asiacrypt’94 (1994), pp.38–48.
G.J. Simmons, A survey of Information Authentication, in Contemporary Cryptology, The science of information integrity, ed. G.J. Simmons, IEEE Press, New York (1992).
G.J. Simmons, Message authentication: a game on hypergraphs, Congr. Numer. 45 (1984), pp.161–192.
D.R. Stinson, Some constructions and bounds for authentication codes, Journal of Cryptology, vol.1 (1988), pp.37–51.
J.L. Massey, Cryptography — a selective survey, in Digital Communications, North-Holland (pub.) (1986), pp.3–21.
M. De Soete, New Bounds and Constructions for Authentication/Secrecy Codes with Splitting, Journal of Cryptology, vol.3, no.3 (1991), pp.173–186.
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© 1995 Springer-Verlag Berlin Heidelberg
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Kurosawa, K., Obana, S., Ogata, W. (1995). t-Cheater Identifiable (k, n) Threshold Secret Sharing Schemes. In: Coppersmith, D. (eds) Advances in Cryptology — CRYPT0’ 95. CRYPTO 1995. Lecture Notes in Computer Science, vol 963. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44750-4_33
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DOI: https://doi.org/10.1007/3-540-44750-4_33
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