On linear secret sharing for connectivity in directed graphs

Amos Beimel; Anat Paskin

doi:10.1007/978-3-540-85855-3_12

On linear secret sharing for connectivity in directed graphs

Amos Beimel, Anat Paskin

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

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.

Original language	English
Title of host publication	Security and Cryptography for Networks - 6th International Conference, SCN 2008, Proceedings
Pages	172-184
Number of pages	13
DOIs	https://doi.org/10.1007/978-3-540-85855-3_12
State	Published - 2008
Externally published	Yes
Event	6th International Conference on Security and Cryptography for Networks, SCN 2008 - Amalfi, Italy Duration: 10 Sep 2008 → 12 Sep 2008

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5229 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	6th International Conference on Security and Cryptography for Networks, SCN 2008
Country/Territory	Italy
City	Amalfi
Period	10/09/08 → 12/09/08

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

Cite this

Beimel, A., & Paskin, A. (2008). On linear secret sharing for connectivity in directed graphs. In Security and Cryptography for Networks - 6th International Conference, SCN 2008, Proceedings (pp. 172-184). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5229 LNCS). https://doi.org/10.1007/978-3-540-85855-3_12

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abstract = "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.",

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Beimel, A & Paskin, A 2008, On linear secret sharing for connectivity in directed graphs. in Security and Cryptography for Networks - 6th International Conference, SCN 2008, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5229 LNCS, pp. 172-184, 6th International Conference on Security and Cryptography for Networks, SCN 2008, Amalfi, Italy, 10/09/08. https://doi.org/10.1007/978-3-540-85855-3_12

On linear secret sharing for connectivity in directed graphs. / Beimel, Amos; Paskin, Anat.
Security and Cryptography for Networks - 6th International Conference, SCN 2008, Proceedings. 2008. p. 172-184 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5229 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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On linear secret sharing for connectivity in directed graphs

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