On the optimization of bipartite secret sharing schemes

Authors:
Oriol Farràs;Jessica Ruth Metcalf-Burton;Carles Padró;Leonor Vázquez
Affiliations:
Dep. de Matemàtica Aplicada 4, Universitat Politècnica de Catalunya, Barcelona, Spain;Mathematics Department, University of Michigan, Ann Arbor;Dep. de Matemàtica Aplicada 4, Universitat Politècnica de Catalunya, Barcelona, Spain;Dep. de Matemàtica Aplicada 4, Universitat Politècnica de Catalunya, Barcelona, Spain
Venue:
ICITS'09 Proceedings of the 4th international conference on Information theoretic security
Year:
2009

Citing 18
Cited 3

An explication of secret sharing schemes

Designs, Codes and Cryptography
Geometric secret sharing schemes and their duals

Designs, Codes and Cryptography
Tight Bounds on the Information Rate of Secret SharingSchemes

Designs, Codes and Cryptography
Weighted threshold secret sharing schemes

Information Processing Letters
How to share a secret

Communications of the ACM
Discrete Polymatroids

Journal of Algebraic Combinatorics: An International Journal
How to (Really) Share a Secret

CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Separating the Power of Monotone Span Programs over Different Fields

SIAM Journal on Computing
On the Power of Nonlinear Secret-Sharing

SIAM Journal on Discrete Mathematics
A First Course in Information Theory (Information Technology: Transmission, Processing and Storage)

A First Course in Information Theory (Information Technology: Transmission, Processing and Storage)
Characterizing Ideal Weighted Threshold Secret Sharing

SIAM Journal on Discrete Mathematics
Ideal Multipartite Secret Sharing Schemes

EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Secret Sharing and Non-Shannon Information Inequalities

TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
Monotone circuits for monotone weighted threshold functions

Information Processing Letters
On secret sharing schemes, matroids and polymatroids

TCC'07 Proceedings of the 4th conference on Theory of cryptography
Matroids can be far from ideal secret sharing

TCC'08 Proceedings of the 5th conference on Theory of cryptography
On matroids and non-ideal secret sharing

TCC'06 Proceedings of the Third conference on Theory of Cryptography
Secret sharing schemes with bipartite access structure

IEEE Transactions on Information Theory

Generalized oblivious transfer by secret sharing

Designs, Codes and Cryptography
Ideal secret sharing schemes for useful multipartite access structures

IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Optimal complexity of secret sharing schemes with four minimal qualified subsets

Designs, Codes and Cryptography

Quantified Score

Hi-index	0.00

Visualization

Abstract

Bipartite secret sharing schemes are those having a bipartite access structure, that is, the set of participants is divided into two parts, and all participants in each part play an equivalent role. The bipartite access structures that admit an ideal secret sharing scheme have been characterized, but it is not known which is the optimal complexity of non-ideal bipartite access structures. By using the connection between secret sharing schemes and polymatroids, we find new bounds on the optimal complexity of these acess structures and, for some of them, we find the exact value of this parameter. Some of these bounds are obtained by using a method based on linear programming.