quantum information, secret sharing, quantum cryptography, quantum computation We investigate the concept of quantum secret sharing, where a secret quantum state is distributed between n parties in such a way that certain subsets of the parties can jointly recover the secret, while other subsets of the parties can acquire absolutely no information about it. In a ((k,n)) threshold scheme, any su...

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...

A (t + 1, n) proactive secret sharing is to protect a secret in long-lived system by distributing it to a group of n participants and refreshing their shares periodically in this fixed group, while any t+1 and more than t+1 shares can reconstruct the secret. In some environment, it needs to change not only the number of participants n but also the threshold value t. An adaptive proactive secret...

An n-player (t, δ)-secure robust secret sharing scheme is a (t, n)-threshold secret sharing scheme with the additional property that the secret can be recovered, with probability at least 1− δ, from the set of all shares even if up to t players provide incorrect shares. The existing constructions of robust secret sharing schemes for the range n/3 ≤ t < n/2 have the share size larger than the se...

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...

We prove that for every n and 1 < t < n any t-out-of-n threshold secret sharing scheme for one-bit secrets requires share size log(t + 1). Our bound is tight when t = n− 1 and n is a prime power. In 1990 Kilian and Nisan proved the incomparable bound log(n − t + 2). Taken together, the two bounds imply that the share size of Shamir’s secret sharing scheme (Comm. ACM ’79) is optimal up to an add...

Threshold schemes are ideally suited to situations where a group of mutually suspicious individuals with conflicting interests must cooperate. The schemes allow a user to divide portions of a secret among a participants group. Any t or more participants from a participants group of n members can cooperate to regain the original secret while (t-1) or fewer participants cannot reveal anything abo...

Although secret sharing techniques have been applied to implement secure electronic sealed-bid auction for a long time, problems and attacks still exist in secret-sharing-based electronic sealed-bid auction schemes. In this paper, a new secret-sharing-based first-bid e-auction scheme is designed to achieve satisfactory properties and efficiency. Correctness and fairness of the new auction are b...

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...

The ( ) , t n threshold secret sharing scheme proposed by Shamir (1979) encodes the secret key into n shares and those shares are distributed among the participants. Each share incorporates an x-value uniquely designated for every single participant. If the shares are distributed on insecure (or public) channels, malicious users may acquire a few (or all) shares. If the number of shares obtaine...