While classically cryptography is concerned with the problem of private communication among two entities, say players, in modern cryptography multi-player protocols play an important role. And among these, it is probably fair to say that secret sharing, and its stronger version verifiable secret sharing (VSS), as well as multi-party computation (MPC) belong to the most appealing and/or useful o...

A black-box secret sharing scheme for the threshold access structure Tt,n is one which works over any finite Abelian group G. Briefly, such a scheme differs from an ordinary linear secret sharing scheme (over, say, a given finite field) in that distribution matrix and reconstruction vectors are defined over Z and are designed independently of the group G from which the secret and the shares are...

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...

(t, n) threshold secret sharing is a cryptographic mechanism to divide and disseminate information among n participants in a way that at least t(t ≤ n) of them should be present for the original data to be retrieved. This has practical applications in the protection of secure information against loss, destruction and theft. In this study, the authors propose a new multi-secret sharing scheme wh...

Sharing a secret efficiently amongst a group of participants is not easy since there is always an adversary / eavesdropper trying to retrieve the secret. In secret sharing schemes, every participant is given a unique share. When the desired group of participants come together and provide their shares, the secret is obtained. For other combinations of shares, a garbage value is returned. A thres...

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 secret sharing scheme divides a secret into multiple shares by a dealer and shared among shareholders in such a way that any authorized subset of shareholders can reconstruct the secret; whereas any un-authorized subset of shareholders cannot recover the secret. If the maximal length of shares is equal to the length of the secret in a secret sharing scheme, the scheme is called ideal. If the ...

A threshold scheme, which is introduced by Shamir in 1979, is very famous as a secret sharing scheme. Dealer distribute shares of a secret value among n participants. Gathering t(≤ n) participants, a secret value can be reconstructed. This is called a (t, n) secret sharing scheme. This scheme is based on Lagrange’s interpolation formula. As regard interpolation formula, it is known not only Lag...