Verifiable secret sharing schemes (VSS) are secret sharing schemes (SSS) dealing with possible cheating by participants. In this paper we use the VSS proposed by Cramer, Damgard and Maurer [6, 7, 5]. They introduced a purely linear algebraic method to transform monotone span program (MSP) based secret sharing schemes into VSS. In fact, the monotone span program model of Karchmer and Wigderson [...

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...

Secret sharing has been a subject of study for over twenty years, and has had a number of real-world applications. There are several approaches to the construction of secret sharing schemes. One of them is based on coding theory. In principle, every linear code can be used to construct secret sharing schemes. But determining the access structure is very hard as this requires the complete charac...

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 secret-sharing scheme enables a dealer to distribute a secret among n parties such that only some predefined authorized sets of parties will be able to reconstruct the secret from their shares. The (monotone) collection of authorized sets is called an access structure, and is freely identified with its characteristic monotone function f : f0; 1gn ! f0; 1g. A family of secret-sharing schemes i...

A secret-sharing scheme enables a dealer to distribute a secret among n parties such that only some predefined authorized sets of parties will be able to reconstruct the secret from their shares. The (monotone) collection of authorized sets is called an access structure, and is freely identified with its characteristic monotone function f : f0; 1gn ! f0; 1g. A family of secret-sharing schemes i...

A secret-sharing scheme enables a dealer to distribute a secret among n parties such that only some predefined authorized sets of parties will be able to reconstruct the secret from their shares. The (monotone) collection of authorized sets is called an access structure, and is freely identified with its characteristic monotone function f : {0, 1}n → {0, 1}. A family of secret-sharing schemes i...

Function secret sharing (FSS) scheme is a mechanism that calculates a function f(x) for x ∈ {0, 1} which is shared among p parties, by using distributed functions fi : {0, 1} → G (1 ≤ i ≤ p), where G is an Abelian group, while the function f : {0, 1} → G is kept secret to the parties. Ohsawa et al. in 2017 observed that any function f can be described as a linear combination of the basis functi...

In this paper we mainly focus on the fraud problem among the players and the shortcomings of multisecret sharing existed in rational secret sharing schemes. Based on the exited schemes and the related knowledge such as bit commitment agreement, we proposed a new rational multi-secret sharing scheme that has high security. In our scheme, we take an identity authentication for the dealer in distr...

Weighted threshold functions with positive weights are a natural generalization of unweighted threshold functions. These functions are clearly monotone. However, the naive way of computing them is adding the weights of the satisfied variables and checking if the sum is greater than the threshold; this algorithm is inherently non-monotone since addition is a non-monotone function. In this work w...