Leakproof secret sharing protocols with applications to group identification scheme

In a traditional (t, n)-threshold secret sharing scheme, t or more honest participants can reconstruct the secret K. In the reconstruction process, the individual shares and the secret key K are revealed, hence K is shared once only. In this paper, we firstly give the definition of leakproof secret sharing scheme which is composed of a distribution protocol and a proof protocol, then propose two leakproof secret sharing protocols, a computationally secure protocol and an information-theoretically secure protocol. In our protocols, t or more participants can jointly prove that they hold the secret K by using a multi-prover zero-knowledge argument of knowledge. As a result, the secret K will be shared for as many times as desired. Furthermore, each participant can detect the dealer in the distribution protocol from cheating, and any verifier can prevent non-qualified set of participants in proof protocol from cheating. As an example of the practical impact of our work we use our techniques to construct group identification schemes with zero-knowledge.

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