On Codes, Matroids, and Secure Multiparty Computation From Linear Secret-Sharing Schemes

Error-correcting codes and matroids have been widely used in the study of ordinary secret sharing schemes. In this paper, the connections between codes, matroids, and a special class of secret sharing schemes, namely, multiplicative linear secret sharing schemes (LSSSs), are studied. Such schemes are known to enable multiparty computation protocols secure against general (nonthreshold) adversaries. Two open problems related to the complexity of multiplicative LSSSs are considered in this paper. The first one deals with strongly multiplicative LSSSs. As opposed to the case of multiplicative LSSSs, it is not known whether there is an efficient method to transform an LSSS into a strongly multiplicative LSSS for the same access structure with a polynomial increase of the complexity. A property of strongly multiplicative LSSSs that could be useful in solving this problem is proved. Namely, using a suitable generalization of the well-known Berlekamp

• Type: Journal
• Year: 2008
• Where: TIT
• Authors: Ronald Cramer, Vanesa Daza, Ignacio Gracia, Jorge Jiménez Urroz, Gregor Leander, Jaume Martí-Farré, Carles Padró
• Keywords: Matroids, Multiplicative Lssss, Secret Sharing Schemes, TIT 2008