Extending Brickell-Davenport theorem to non-perfect secret sharing schemes
Tipo de documentoArtículo
Fecha de publicación2015-02
Condiciones de accesoAcceso abierto
One important result in secret sharing is the Brickell-Davenport Theorem: every ideal perfect secret sharing scheme de nes a matroid that is uniquely determined by the access structure. Even though a few attempts have been made, there is no satisfactory de nition of ideal secret sharing scheme for the general case, in which non-perfect schemes are considered as well. Without providing another unsatisfactory de nition of ideal non-perfect secret sharing scheme, we present a generalization of the Brickell-Davenport Theorem to the general case. After analyzing that result under a new point of view and identifying its combinatorial nature, we present a characterization of the (not necessarily perfect) secret sharing schemes that are associated to matroids. Some optimality properties of such schemes are discussed.
CitaciónFarràs Ventura, O., Padro, C. Extending Brickell-Davenport theorem to non-perfect secret sharing schemes. "(0925-1022) Designs codes and cryptography", Febrer 2015, vol. 74, núm. 2, p. 495-510.