On Codes, Matroids and Secure Multi-party 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, we study the connections between codes, matroids, and a special class of secret sharing schemes: multiplicative linear secret sharing schemes. Such schemes are known to enable multi-party computation protocols secure against general (non-threshold) 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. We prove a property of strongly multiplicative LSSSs that could be useful in solving this problem. Namely, using a suitable generalization of the well-known Berlekamp-Welch decoder, we show that all strongly multiplicative LSS...

• Type: Conference
• Year: 2005
• Where: CRYPTO
• Authors: Ronald Cramer, Vanesa Daza, Ignacio Gracia, Jorge Jiménez Urroz, Gregor Leander, Jaume Martí-Farré, Carles Padró
• Keywords: CRYPTO 2005, Multiplicative Lssss, Secret Sharing Schemes, Self-dual Matroids