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...

In this article, the authors propose an approach for privacy preserving distributed clustering that assumes malicious model. In the literature, there do exist, numerous approaches that assume a semi honest model. However, such an assumption is, at best, reasonable in experimentations; rarely true in real world. Hence, it is essential to investigate approaches for privacy preservation using a ma...

A publicly verifiable secret sharing (PVSS) scheme, proposed by Stadler in [Sta96], is a VSS scheme in which anyone, not only the shareholders, can verify that the secret shares are correctly distributed. PVSS can play essential roles in the systems using VSS. Achieving simultaneously the following two features for PVSS is a challenging job: – Efficient non-interactive public verification. – Pr...

Quantum secret sharing is a scheme for encoding a quantum state (the secret) into multiple shares and distributing them among several participants. If a sufficient number of shares are put together, then the secret can be fully reconstructed. If an insufficient number of shares are put together however, no information about the secret can be revealed. In quantum ramp secret sharing, partial inf...

Secret sharing is a cryptographic scheme that divides a secret key s to n participants with threshold t. Thus, assuring that no less than t shares can reconstruct the secret. The application of secret sharing also widens not only one group but several hierarchical structure. However, the group-based secret sharing proposed by Liu et al. in 2014 has some drawbacks, which are having an equal thre...

Secret-sharing schemes are an important tool in cryptography that is used in the construction of many secure protocols. However, the shares’ size in the best known secret-sharing schemes realizing general access structures is exponential in the number of parties in the access structure, making them impractical. On the other hand, the best lower bound known for sharing of an `-bit secret with re...

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...