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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)
Hierarchical secret sharing is among the most natural generalizations of threshold secret sharing, and it has attracted a lot of attention since 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)
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)
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(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 present new families of access structures that, similarly to the multilevel and compartmented access structures introduced in previous works, are natural generalizations of threshold secret sharing. Namely, they admit ideal linear secret sharing schemes over every large enough finite field, they can be described by a small number of parameters, and they(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)