Secret sharing plays an important role in protecting confidential information among all participants. A fairness secret sharing scheme assures that a dishonest participant cannot get any advantages over the honest ones in the process of secret reconstruction. Though there are many secret sharing schemes available in the literature, most of them do not satisfy the requirement of fairness. In thi...

In this paper, we consider the problem of (t, δ) robust secret sharing secure against rushing adversary. We design a simple t-out-ofn secret sharing scheme, which can reconstruct the secret in presence of t cheating participants except with probability at most δ, provided t < n/2. The later condition on cheater resilience is optimal for the case of public reconstruction of the secret, on which ...

With respect to a special class of access structures based on connectivity of graphs, we start from a linear secret sharing scheme and turn it into a secret sharing scheme with perfect security and exponentially small error probability by randomizing the reconstruction algorithm through random walks on graphs. It reduces the polynomial work space to logarithmic. Then we build the corresponding ...

In Shamir’s (t, n) secret sharing (SS) scheme, the secret s is divided into n shares by a dealer and is shared among n shareholders in such a way that any t or more than t shares can reconstruct this secret; but fewer than t shares cannot obtain any information about the secret s. In this paper, we will introduce the security problem that an adversary can obtain the secret when there are more t...

An ideal secret sharing scheme is a method of sharing a secret key in some key space among a finite set of participants in such a way that only the authorized subsets of participants can reconstruct the secret key from their shares which are of the same length as that of the secret key. The set of all authorized subsets of participants is the access structure of the secret sharing scheme. In th...