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Consider an abstract storage device Σ(G) that can hold a single element x from a xed, publicly known nite group G. Storage is private in the sense that an adversary does not have read access to Σ(G) at all. However, Σ(G) is non-robust in the sense that the adversary can modify its contents by adding some offset ∆ ∈ G. Due to the privacy of the storage… (More)

One of the main open problems in secret sharing is the characterization of the access structures of ideal secret sharing schemes. As a consequence of the results by Brickell and Davenport, every one of those access structures is related in a certain way to a unique matroid. Matroid ports are combinatorial objects that are almost equivalent to… (More)

A generalized cycle is a digraph whose set of vertices is partitioned in several parts that are cyclically ordered in such a way that the vertices in one part are adjacent only to vertices in the next part. The problems considered in this paper are: 1. To nd generalized cycles with given maximum out-degree and diameter that have large order. 2. To nd… (More)

Hierarchical secret sharing is among the most natural generalizations of threshold secret sharing, and it has attracted a lot of attention from the invention of secret sharing until nowadays. Several constructions of ideal hierarchical secret sharing schemes have been proposed , but it was not known what access structures admit such a scheme. We solve this… (More)

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… (More)

A metering scheme is a method by which an audit agency is able to measure the interaction between servers and clients during a certain number of time frames. Naor and Pinkas 21] proposed metering schemes where any server is able to compute a proof, i.e., a value to be shown to the audit agency at the end of each time frame, if and only if it has been… (More)

We study the information rate of secret sharing schemes whose access structure is bipartite. In a bipartite access structure there are two classes of participants and all participants in the same class play an equivalent role in the structure. We characterize completely the bi-partite access structures that can be realized by an ideal secret sharing scheme.… (More)

Multipartite secret sharing schemes are those having a multipartite access structure, in which the set of participants is divided into several parts and all participants in the same part play an equivalent role. In this work, the characterization of ideal multipartite access structures is studied with all generality. Our results are based on the well-known… (More)