Design and analysis of a verifiable secret sharing scheme

As the further expansion of the multiple secret sharing scheme,the multi-secret sharing scheme can share any number of secrets in one sharing session.In order to prevent the secret dealer's and the participant's cheating attacks like those in the existing multi-secret sharing schemes,a new verifiable threshold multi-secret sharing scheme is proposed.Each participant's secret shadow is selected by himself and it can be transmitted to the secret dealer over a public channel.The shadow can be used in multiple sharing sessions without the need to be updated.At the same time,it is allowed to check whether each cooperative participant and the secret dealer have taken a legal action or not.The security of the proposed scheme is based on that of Shamir's secret sharing scheme and that of the ECIES cryptosystem,and the difficulty in solving the elliptic curve discrete logarithm.