A secret sharing scheme starts with a secret and then derives from it certain shares (or shadows) which are distributed to users. The secret may be recovered only by certain predetermined groups. In case of compartmented secret sharing, the set of users is partitioned into compartments and the secret can be recovered only if the number of participants from any compartment is greater than a fixe...

For a secret sharing scheme, two parameters dmin and dcheat are defined in [12] and [13]. These two parameters measure the errorcorrecting capability and the secret-recovering capability of the secret sharing scheme against cheaters. Some general properties of the parameters have been studied in [12],[9] and [13]. The MDS secretsharing scheme was defined in [13] and it was proved that MDS perfe...

A recent work of Harn and Fuyou presents the first multilevel (disjunctive) threshold secret sharing scheme based on the Chinese Remainder Theorem. In this work, we first show that the proposed method is not secure and also fails to work with a certain natural setting of the threshold values on compartments. We then propose a secure scheme that works for all threshold settings. In this scheme, ...

A (t, n)-threshold secret sharing scheme is a method to distribute a secret among n participants in such a way that any t participants can recover the secret, but no t − 1 participants can. In this paper, we propose two secret sharing schemes using non-abelian groups. One scheme is the special case where all the participants must get together to recover the secret. The other one is a (t, n)-thr...

The algebraic setting for threshold secret sharing scheme can vary, dependent on the application. This algebraic setting can limit the number of participants of an ideal secret sharing scheme. Thus it is important to know for which thresholds one could utilize an ideal threshold sharing scheme and for which thresholds one would have to use nonideal schemes. The implication is that more than one...

A multi-secret sharing scheme is a protocol to share some arbitrarily related secrets among a set of participants. A novel ) , ( n k -threshold multi-secret sharing scheme based on an isomorphism is proposed in this paper. The maximum number of secrets that can be shared in the proposed scheme is 2 k which is larger than that of most existing efficient ) , ( n k -threshold multi-secret sharing ...

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...

A multi-secret sharing scheme (MSS) allows a dealer to share multiple secrets among a set of participants. in such a way a multi-secret sharing scheme (MSS) allows a dealer to share multiple secrets among a set of participants, such that any authorized subset of participants can reconstruct the secrets. Up to now, existing MSSs either require too long shares for participants to be perfect secur...