A secret sharing scheme is a way of protecting a secret by distributing partial information to a set of participants P in such a way that only authorized subsets of P can recover the secret. The family of authorized subsets is called the access structure of the scheme. In 1979, threshold schemes were proposed to realize threshold access structures, and in 1987, multiple assignment schemes were ...

Threshold secret sharing based on the Chinese remainder theorem has been considered by Mignotte [23] and Asmuth and Bloom [1]. In this paper we demonstrate that the Chinese remainder theorem can be used for realizing more general access structures, as the compartmented or the weighted threshold ones. We also prove that there exist some non-weighted threshold access structures whose realizations...

Starting from a new relation between graphs and secret sharing schemes introduced by Xiao, Liu and Zhang, we show a method to construct more general ideal homogeneous access structures. The method has some advantages: it efficiently gives an ideal homogeneous access structure for the desired rank, and some conditions can be imposed (such as forbidden or necessary subsets of players), even if th...

We formally define and give the first construction of (leveled) threshold fully homomorphic encryption for any access structure induced by a monotone boolean formula and in particular for the threshold access structure. Our construction is based on the learning with errors assumption and can be instantiated with any existing homomorphic encryption scheme that satisfies fairly general conditions...

Many efficient secret sharing schemes for general access structures have been developed in efforts to deal with the problems of multi-party computations (MPC), threshold cryptography, and access control. In this paper, we have proposed a novel secret sharing scheme with general access structures that is based on the key-lock-pair mechanism. In our scheme, the dealer can assess a real situation ...

We present a new protocol for the verifiable redistribution of secrets from (m,n) to (m,n) access structures for threshold sharing schemes. Our protocol enables the addition or removal of shareholders and also guards against mobile adversaries that cause permanent damage. We observe that existing protocols either cannot be readily extended to allow redistribution between different access struct...

Linear Secret Sharing Scheme (LSSS) matrices are commonly used for implementing monotone access structures in highly expressive Ciphertext-Policy Attribute-Based Encryption (CP-ABE) schemes. However, LSSS matrices are much less intuitive to use when compared with other approaches such as boolean formulas or access trees. To bridge the gap between the usability of an access structure representat...

We present a new verifiable secret redistribution protocol for threshold sharing schemes that forms a key component of a proposed archival storage system. Our protocol supports redistribution from (m,n) to (m,n) threshold sharing schemes without requiring reconstruction of the original data. The design is motivated by archive systems for which the added security of threshold sharing of data mus...