Abstract
We derive new limitations on the information rate and the average information rate of secret sharing schemes for access structure represented by graphs. We give the first proof of the existence of access structures with optimal information rate and optimal average information rate less that 1/2 + ε, where ε is an arbitrary positive constant. We also provide several general lower bounds on information rate and average information rate of graphs. In particular, we show that any graph with n vertices admits a secret sharing scheme with information rate Ω((log n)/n).
Partially supported by Italian Ministry of University and Research (M.U.R.S.T.) and by National Council for Research (C.N.R.) under grant 91.02326.CT12.
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Blundo, C., De Santis, A., Gargano, L., Vaccaro, U. (1993). On the Information Rate of Secret Sharing Schemes. In: Brickell, E.F. (eds) Advances in Cryptology — CRYPTO’ 92. CRYPTO 1992. Lecture Notes in Computer Science, vol 740. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48071-4_11
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DOI: https://doi.org/10.1007/3-540-48071-4_11
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