In a secret sharing scheme, some participants can lie about the value of their shares when reconstructing the secret in order to obtain some illicit benefit. We present in this paper two methods to modify any linear secret sharing scheme in order to obtain schemes that are unconditionally secure against that kind of attack. The schemes obtained by the first method are robust, that is, cheaters are detected with high probability even if they know the value of the secret. The second method provides secure schemes, in which cheaters that do not know the secret are detected with high probability. When applied to ideal linear secret sharing schemes, our methods provide robust and secure schemes whose relation between the probability of cheating and the information rate is almost optimal. Besides, those methods make it possible to construct robust and secure schemes for any access structure. 相似文献
We consider solutions of a system of refinement equations written in the form
where the vector of functions is in and is a finitely supported sequence of matrices called the refinement mask. Associated with the mask is a linear operator defined on by . This paper is concerned with the convergence of the subdivision scheme associated with , i.e., the convergence of the sequence in the -norm.
Our main result characterizes the convergence of a subdivision scheme associated with the mask in terms of the joint spectral radius of two finite matrices derived from the mask. Along the way, properties of the joint spectral radius and its relation to the subdivision scheme are discussed. In particular, the -convergence of the subdivision scheme is characterized in terms of the spectral radius of the transition operator restricted to a certain invariant subspace. We analyze convergence of the subdivision scheme explicitly for several interesting classes of vector refinement equations.
Finally, the theory of vector subdivision schemes is used to characterize orthonormality of multiple refinable functions. This leads us to construct a class of continuous orthogonal double wavelets with symmetry.
The author surveys some recent progress on the Toda system on a two-dimensional surface Σ,arising in models from self-dual non-abelian Chern-Simons vortices,as well as in differential geometry.In particular,its variational structure is analysed,and the role of the topological join of the barycentric sets of Σ is shown. 相似文献
A new integrated scheme based on resource-reservation and adaptive network flow routing to alleviate contention in optical burst switching networks is proposed. The objective of the proposed scheme is to reduce the overall burst loss in the network and at the same time to avoid the packet out-of-sequence arrival problem. Simulations are carried out to assess the feasibility of the proposed scheme. Its performance is compared with that of contention resolution schemes based on conventional routing. Through extensive simulations, it is shown that the proposed scheme not only provides significantly better burst loss performance than the basic equal proportion and hop-length based traffic routing algorithms, but also is void of any packet re-orderings. 相似文献