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 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...

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...

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 ...

We present a stronger notion of veri able secret sharing and exhibit a protocol implementing it. We show that our new notion is preferable to the old ones whenever veri able secret sharing is used as a tool within larger protocols, rather than being a goal in itself.

Function sharing deals with the problem of distribution of the computation of a function (such as decryption or signature) among several parties. The necessary values for the computation are distributed to the participating parties using a secret sharing scheme (SSS). Several function sharing schemes have been proposed in the literature, with most of them using Shamir secret sharing as the unde...

A perfect secret-sharing scheme is a method to distribute a secret among a set of participants in such a way that only qualified subsets of participants can recover the secret and the joint share of participants in any unqualified subset is statistically independent of the secret. The collection of all qualified subsets is called the access structure of the perfect secret-sharing scheme. In a g...