scholarly journals New General Lower Bounds on the Information Rate of Secret Sharing Schemes

2007 ◽  
pp. 168-182 ◽  
Author(s):  
D. R. Stinson
Keyword(s):  
Lower Bounds ◽  
Secret Sharing ◽  
Information Rate ◽  
Secret Sharing Schemes

Combinatorial lower bounds for secret sharing schemes

1996 ◽  
Vol 60 (6) ◽  
pp. 301-304 ◽  
Author(s):  
Kaoru Kurosawa ◽  
Koji Okada
Keyword(s):  
Lower Bounds ◽  
Secret Sharing ◽  
Secret Sharing Schemes

scholarly journals Lower Bounds for Monotone Span Programs

1994 ◽  
Vol 1 (46) ◽  
Author(s):  
Amos Beimel
Keyword(s):  
Lower Bounds ◽  
Secret Sharing ◽  
Algebraic Model ◽  
New Technique ◽  
Secret Sharing Schemes ◽  
Branching Programs ◽  
Model Of Computation ◽  
Monotone Span Programs ◽  
Span Programs ◽  
A New Technique

The model of span programs is a linear algebraic model of computation. Lower bounds for span programs imply lower bounds for contact schemes, symmetric branching programs and for formula size. Monotone span programs correspond also to linear secret-sharing schemes. We present a new technique for proving lower bounds for monotone span programs. The main result proved here yields quadratic lower bounds for the size of monotone span programs, improving on the largest previously known bounds for explicit functions. The bound is asymptotically tight for the function corresponding to a class of 4-cliques.

New bounds on the information rate of secret sharing schemes

1995 ◽  
Vol 41 (2) ◽  
pp. 549-554 ◽  
Author(s):  
C. Blundo ◽  
A. De Santis ◽  
A.G. Gaggia ◽  
U. Vaccaro
Keyword(s):  
Secret Sharing ◽  
Information Rate ◽  
Secret Sharing Schemes

Secret sharing schemes on graphs

2007 ◽  
Vol 44 (3) ◽  
pp. 297-306 ◽  
Author(s):  
László Csirmaz
Keyword(s):  
Secret Sharing ◽  
Constant Factor ◽  
Information Rate ◽  
Secret Sharing Schemes ◽  
Secret Sharing Scheme ◽  
Secret Data ◽  
Sharing Scheme ◽  
Dimensional Cube ◽  
Average Size ◽  
Average Information

Given a graph G , a perfect secret sharing scheme based on G is a method to distribute a secret data among the vertices of G , the participants , so that a subset of participants can recover the secret if they contain an edge of G , otherwise they can obtain no information regarding the key. The average information rate is the ratio of the size of the secret and the average size of the share a participant must remember. The information rate of G is the supremum of the information rates realizable by perfect secret sharing schemes.Based on the entropy-theoretical arguments due to Capocelli et al [4], and extending the results of M. van Dijk [7] and Blundo et al [2], we construct a graph Gn on n vertices with average information rate below < 4/log n . We obtain this result by determining, up to a constant factor, the average information rate of the d -dimensional cube.

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