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 ...

Secret sharing schemes as basic building blocks for many applications in distributed systems should be efficient and robust to any possible attacks. Based on bilinear pairing, this paper will propose a new (t, n) threshold verifiable multi-secret sharing scheme and a GGOC verifiable multi-secret sharing scheme that improve the security and minimizes the number of published values.

In this paper, we investigate how threshold cryptography can be conducted with the Asmuth-Bloom secret sharing scheme and present three novel function sharing schemes for RSA, ElGamal and Paillier cryptosystems. To the best of our knowledge, these are the first provably secure threshold cryptosystems realized using the Asmuth-Bloom secret sharing. Proposed schemes are comparable in performance ...

In Shamir’s (t, n) threshold secret sharing scheme, one secret s is divided into n shares by a dealer and all shares are shared among n shareholders, such that knowing t or more than t shares can reconstruct this secret; but knowing fewer than t shares cannot reveal any information about the secret s. The secret reconstruction phase in Shamir’s (t, n) threshold secret sharing is very simple and...

A necessary and sufficient condition for the asymptotic idealness of the AsmuthBloom threshold secret sharing scheme is proposed. Apart from this, a comprehensive analysis of the known variants of the Asmuth-Bloom threshold secret sharing scheme is provided, clarifying the security properties achieved by each of them.

A multi-secret sharing scheme allows several secrets to be shared amongst a group of participants. In 2005, Shao and Cao developed a verifiable multi-secret sharing scheme where each participant’s share can be used several times which reduces the number of interactions between the dealer and the group members. In addition, some secrets may require a higher security level than others involving t...

After any distribution of secret sharing shadows in a threshold changeable secret sharing scheme, the threshold may need to be adjusted to deal with changes in the security policy and adversary structure. For example, when employees leave the organization, it is not realistic to expect departing employees to ensure the security of their secret shadows. Therefore, in 2012, Zhang et al. proposed ...

How to construct an ideal multi-secret sharing scheme for general access structures is difficult. In this paper, we solve an open problem proposed by Spiez et al.recently [Finite Fields and Their Application, 2011(17) 329-342], namely to design an algorithm of privileged coalitions of any length if such coalitions exist. Furthermore, in terms of privileged coalitions, we show that most of the e...

In many pairing-based cryptosystems, the secret keys are elements of bilinear groups. For safeguarding such secret keys or decrypting or signing in a threshold manner, Verifiable Secret Sharing (VSS) in bilinear groups is required. In this paper, we show a method of verifiably sharing a random secret in a bilinear group. Our method is simple and practical. It can be regarded as a generalisation...

Function sharing deals with the problem of distribution of the computation of a function (such as decryption or signature) among several parties. The necessary values for the computation are distributed to the participating parties using a secret sharing scheme (SSS). Several function sharing schemes have been proposed in the literature, with most of them using Shamir secret sharing as the unde...