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 ...

In general, every linear code can be used to construct a secret sharing scheme. However, determining the access structure of the secret sharing scheme based on a linear code is a very difficult problem. In this paper, we first construct a class of two-weight linear code over finite chain ring Fq[u]/⟨u⟩. Then, we present an access structure of the secret sharing scheme based on the two-weight li...

In this paper, we construct an authentication scheme for multi-receivers and multiple messages based on a linear code C. This construction can be regarded as a generalization of the authentication scheme given by Safavi-Naini and Wang [8]. Actually, we notice that the scheme of Safavi-Naini and Wang is constructed with Reed-Solomon codes. The generalization to linear codes has the similar advan...

Secret sharing is one of the branches of threshold cryptography. Secret sharing is intended to secure a secret key s among a group G with n participants. Thus, the secret key s can be reconstructed by collecting shares of t or more participants. Recently, the secret sharing concept has been applied in securing DNSsec root key. However, the idea of DNSsec root key security is based on Shamir’s (...

In this paper, we propose a verifiable (t,n)-threshold multi-secret sharing scheme, based on one-dimensional cellular automata where the number of secrets is not restricted by n or t. We show that our scheme can be used to solve an open problem proposed recently in Alvarez et al. (2008) [G. Alvarez, L. Hernández Encinas, A. Martín del Rey, A multisecret sharing scheme for color images based on ...

We consider the standard secure multi-party multiplication protocol due to M. Rabin. This protocol is based on Shamir’s secret sharing scheme and it can be viewed as a practical variation on one of the central techniques in the foundational results of Ben-Or, Goldwasser, and Wigderson and Chaum, Crépeau, and Damgaard on secure multi-party computation. Rabin’s idea is a key ingredient to virtual...

Considering the case of players’ deceptions, traditional secret sharing scheme can not resolve the security issues. To address these security issues, the paper proposes a rational secret sharing scheme against cheating based on game theory. Under the conditions of the rational, applying the idea of threshold, the scheme is composed of key generation, share encryption, verification and secret re...