TY - GEN

T1 - On linear secret sharing for connectivity in directed graphs

AU - Beimel, Amos

AU - Paskin, Anat

PY - 2008

Y1 - 2008

N2 - In this work we study linear secret sharing schemes for s-t connectivity in directed graphs. In such schemes the parties are edges of a complete directed graph, and a set of parties (i.e., edges) can reconstruct the secret if it contains a path from node s to node t. We prove that in every linear secret sharing scheme realizing the st-con function on a directed graph with n edges the total size of the shares is Ω(n 1.5). This should be contrasted with s-t connectivity in undirected graphs, where there is a scheme with total share size n. Our result is actually a lower bound on the size monotone span programs for st∈-∈con, where a monotone span program is a linear-algebraic model of computation equivalent to linear secret sharing schemes. Our results imply the best known separation between the power of monotone and non-monotone span programs. Finally, our results imply the same lower bounds for matching.

AB - In this work we study linear secret sharing schemes for s-t connectivity in directed graphs. In such schemes the parties are edges of a complete directed graph, and a set of parties (i.e., edges) can reconstruct the secret if it contains a path from node s to node t. We prove that in every linear secret sharing scheme realizing the st-con function on a directed graph with n edges the total size of the shares is Ω(n 1.5). This should be contrasted with s-t connectivity in undirected graphs, where there is a scheme with total share size n. Our result is actually a lower bound on the size monotone span programs for st∈-∈con, where a monotone span program is a linear-algebraic model of computation equivalent to linear secret sharing schemes. Our results imply the best known separation between the power of monotone and non-monotone span programs. Finally, our results imply the same lower bounds for matching.

UR - http://www.scopus.com/inward/record.url?scp=52149106245&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-85855-3_12

DO - 10.1007/978-3-540-85855-3_12

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AN - SCOPUS:52149106245

SN - 3540858547

SN - 9783540858546

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 172

EP - 184

BT - Security and Cryptography for Networks - 6th International Conference, SCN 2008, Proceedings

T2 - 6th International Conference on Security and Cryptography for Networks, SCN 2008

Y2 - 10 September 2008 through 12 September 2008

ER -