A secret sharing scheme is non-perfect if some subsets of participants that cannot recover the secret value have partial information about it. The information ratio of a secret sharing scheme is the ratio between the maximum length of the shares and the length of the secret. This work is dedicated to the search of bounds on the information ratio of non-perfect secret sharing schemes. To this en...

The ( ) , t n threshold secret sharing scheme proposed by Shamir (1979) encodes the secret key into n shares and those shares are distributed among the participants. Each share incorporates an x-value uniquely designated for every single participant. If the shares are distributed on insecure (or public) channels, malicious users may acquire a few (or all) shares. If the number of shares obtaine...

In anonymous secret sharing schemes, the secret can be reconstructed without knowledge of which participants hold which shares. In this paper, we derive a tighter lower bound on the size of the shares than the bound of Blundo and Stinson for anonymous (k, n)threshold schemes with 1 < k < n. Our bound is tight for k = 2. We also show a close relationship between optimum anonymous (2, n)threshold...

In a threshold scheme, the sensitivity of the secret as well as the number of players may fluctuate due to various reasons, e.g., mutual trust may vary or the structure of the players’ organization might be changed. A possible solution to this problem is to modify the threshold and/or change the secret. Moreover, a common problem with almost all secret sharing schemes is that they are “one-time...

A secret sharing scheme permits a secret to be shared among participants in such a way that only qualiied subsets of participants can recover the secret, but any non-qualiied subset has absolutely no information on the secret. In this paper we consider the problem of designing eecient secret sharing schemes having the additional feature that qualiied minorities can forbid any other set of parti...

Abstract A (t, n) secret sharing scheme permits a secret to be divided into n shares in such a way that any t or more than t shares can reconstruct the secret, but fewer than t shares cannot reconstruct the secret. Verifiable secret sharing (VSS) has been proposed to allow each shareholder to verify the validity of his own share, but not other shareholders' shares. In this paper, we propose an ...

A proactive secret sharing scheme is a method of sharing a secret among a set of participants. And, the corresponding shadows can be periodically renewed under the premise of never changing the shared secret. However, in the most existing proactive secret sharing schemes, only one secret can be shared during one secret sharing process. The proposed scheme describes PMSS, a new way to share mult...

In this paper, we investigate a new concept, called share selectable secret sharing, where no unauthorized set can obtain information of the secret (in the information-theoretic sense) even if shares are selectable as arbitrary values which are independent of the secret. We propose two totally selectable (i.e., all users’ shares are selectable) secret sharing schemes with unanimous structure. W...

Secret sharing schemes are very important techniques for the key management. To provide more efficient and flexible alternatives for the applications of secret sharing, this paper presents a dynamic multi-secret sharing scheme. A significant characteristic of the proposed scheme is that each participant has to keep only one master secret share which can be used to reconstruct different group se...