Secure Publicly Verifiable Threshold Multi-secret Sharing Scheme

Abstract

A publicly verifiable multi-secret sharing scheme is proposed, using non-interactive zero-knowledge proof protocol and Shamir’s sharing system. The security of the scheme is based on the intractability of integer factorization problem and discrete logarithm problem. The validity of the sharing distributed by the dealer can be verified by anyone. Recovering the secret, participants only need to provide a shadow of the sharing. It is difficult to get the sharing from the shadow. So the sharing can be reused to share the multi-secret. Moreover, the validity of the shadow can also be verified by anyone. So the scheme is secure, efficient, and can prevent both dealer and participant from cheating.