Secret sharing schemes create an effective method to safeguard a secret by dividing it among several participants. By using hash functions and the herding hashes technique, we first set up a (t + 1, n) threshold scheme which is perfect and ideal, and then extend it to schemes for any general access structure. The schemes can be further set up as proactive or verifiable if necessary. The setup a...

In this paper we combine the compartmented secret sharing schemes based on the Chinese remainder theorem with the RSA scheme in order to obtain, as a novelty, a dedicated solution for compartmented threshold decryption or compartmented threshold digital signature generation. AMS Subject Classification: 94A60, 94A62, 11A07

We present group signature schemes that distribute group management using threshold encryption. To our best knowledge, we are the first to construct and analyze such schemes in detail. The threshold encryption schemes we employ to distribute group management are based on Shamir secret sharing and monotone span programs. We analyze our schemes not only in a static scenario, but also under group ...

We introduce and formally define polynomial commitment schemes, and provide two efficient constructions. A polynomial commitment scheme allows a committer to commit to a polynomial with a short string that can be used by a verifier to confirm claimed evaluations of the committed polynomial. Although the homomorphic commitment schemes in the literature can be used to achieve this goal, the sizes...

A secret sharing scheme is a method to distribute a secret among a set of participants, such that only qualified subsets of the participants can recover the secret. A secret sharing scheme is perfect if any unqualified subset obtains no information regarding the master key. The collection of qualified subsets is called access structure. In a hypergraph, if the size of edges is equal to r, the h...

A rational secret sharing scheme is a game in which each party responsible for reconstructing a secret tries to maximize his utility by obtaining the secret alone. Quantum secret sharing schemes, either derived from quantum teleportation or from quantum error correcting code, do not succeed when we assume rational participants. This is because all existing quantum secret sharing schemes conside...

Secret sharing is a cryptographic primitive, which is used to distribute a secret among participants in such a way that an authorized subset of participants can uniquely reconstruct the secret and an unauthorized subset can get no information about the secret. It is a fundamental method used in secure multiparty computations, where various distrusted participants cooperate and conduct computati...

LDPC codes, LT codes, and digital fountain techniques have received significant attention from both academics and industry in the past few years. By employing the underlying ideas of efficient Belief Propagation (BP) decoding process in LDPC and LT codes, this paper introduces three classes of secret sharing schemes called BP-XOR secret sharing schemes, pseudo-BP-XOR secret sharing schemes, and...

Secret sharing is a method of dividing a secret among n participants and allows only qualified subset to reconstruct the secret and hence provides better reliability and availability of secret data.In the generalized secret sharing scheme, a monotone access structure of the set of participants is considered. The access structure specifies a qualified subset of participants who can reconstruct t...

A well-known fact in the theory of secret sharing schemes is that shares must be of length at least as the secret itself. However, the proof of this lower bound uses the notion of information theoretic secrecy. A natural (and very practical) question is whether one can do better for secret sharing if the notion of secrecy is computational, namely, against resource bounded adversaries. In this n...