One important result in secret sharing is the Brickell-Davenport Theorem: every ideal perfect secret sharing scheme defines a matroid that is uniquely determined by the access structure. Even though a few attempts have been made, there is no satisfactory definition of ideal secret sharing scheme for the general case, in which non-perfect schemes are considered as well. Without providing another...

In this work we provide a framework for dynamic secret sharing and present the first dynamic and verifiable hierarchical secret sharing scheme based on Birkhoff interpolation. Since the scheme is dynamic it allows, without reconstructing the message distributed, to add and remove shareholders, to renew shares, and to modify the conditions for accessing the message. Furthermore, each shareholder...

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 publicly verifiable secret sharing (PVSS) scheme is a verifiable secret sharing (VSS) scheme in which anyone, not only the shareholders, can verify that the secret shares are correctly distributed. PVSS plays an essential role in the systems that use VSS. In this paper we present a new construction for PVSS scheme based on Paillier encryption scheme.We formalize the notion of indistinguishabi...

Secret sharing schemes are widely used now a days in various applications, which need more security, trust and reliability. In secret sharing scheme, the secret is divided among the participants and only authorized set of participants can recover the secret by combining their shares. The authorized set of participants are called access structure of the scheme. In Multi-Secret Sharing Scheme (MS...

A secret sharing scheme is a method to store information securely and reliably. Particularly, in the threshold secret sharing scheme (due to Shamir), a secret is divided into shares, encoded and distributed to parties, such that any large enough collection of parties can decode the secret, and a smaller (then threshold) set of parties cannot collude to deduce any information about the secret. W...

Proactive Secret Sharing Scheme (PSSS) is a method to periodically renew n secret shares in a (k, n) threshold-based Secret Sharing Scheme without modifying the secret or reconstructing the secret to reproduce new shares. Given enough time, a hacker may be able to compromise enough shares (k or more) to gain the secret. PSSS is a scheme that allows generating new set of shares for the same secr...

Visual Secret Sharing (VSS), first invented by Naor and Shamir, is a variant of secret sharing. In the literature, VSS schemes have many applications, including visual authentication and identification, steganography, and image encryption. Moreover, VSS schemes provide the secure services in communications. In 2010, De Prisco and De Santis deeply discussed the problem of cheating in VSS, gave t...

It is well-known that the linear secret-sharing scheme (LSSS) can be constructed from linear error-correcting codes (Brickell [1], R.J. McEliece and D.V.Sarwate [2],Cramer, el.,[3]). The theory of linear codes from algebraic-geometric curves (algebraic-geometric (AG) codes or geometric Goppa code) has been well-developed since the work of V.Goppa and Tsfasman, Vladut, and Zink( see [17], [18] a...

Weighted threshold secret sharing was introduced by Shamir in his seminal work on secret sharing. In such settings, there is a set of users where each user is assigned a positive weight. A dealer wishes to distribute a secret among those users so that a subset of users may reconstruct the secret if and only if the sum of weights of its users exceeds a certain threshold. A secret sharing scheme ...