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 ...

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...

The multiple assignment scheme is to assign one or more shares to single participant so that any kind of access structure can be realized by classical secret sharing schemes. We propose its quantum version including ramp secret sharing schemes. Then we propose an integer optimization approach to minimize the average share size. key words: quantum secret sharing, multiple assignment scheme, acce...

Verifiable secret sharing schemes (VSS) are secret sharing schemes dealing with possible cheating by the participants. In this paper, we propose a new unconditionally secure VSS. Then we construct a new proactive secret sharing scheme based on that VSS. In a proactive scheme, the shares are periodically renewed so that an adversary cannot get any information about the secret unless he is able t...

Secret sharing schemes are one of the most important primi-tives in distributed systems. Cumulative secret sharing schemes provide a method to share a secret among a number of participants with arbitrary access structures. This paper presents two diierent methods for constructing cumulative secret sharing schemes. The rst method produces a simple and eecient cumulative scheme. The second method...

We present a general treatment of non-cryptographic (i.e. information-theoretically secure) multi-party computation, based on underlying linear secret sharing scheme. This general approach gives pure linear-algebra conditions on the linear mappings describing the scheme. The approach establishing the minimal conditions for security, can lead to design of more efficient Multi-Party Computation (...

In this paper we study anonymous secret sharing schemes. Informally, in an anonymous secret sharing scheme the secret can be reconstructed without knowledge of which participants hold which shares. In such schemes the computation of the secret can be carried out by giving the shares to a black box that does not know the identities of the participants holding those shares. Phillips and Phillips ...