Threshold verifiable multi-secret sharing based on elliptic curves and Chinese remainder theorem

In this study, the authors propose a new protocol to share secret shadows for verifiable (t, n) secret sharing (VSS) schemes. Unlike traditional VSS schemes, whose communications between the dealer and the participants require a secure channel, the authors' new scheme relies on the elliptic curve cryptosystem and the Chinese remainder theorem operates over a public channel. The security of the secret shadows and the verification algorithm are based on the hardness of the elliptic curve discrete logarithm problem. They also extend the proposed scheme to an efficient verifiable multi-secret sharing (VMSS) scheme, particularly when the number of secrets is more than the threshold. As a result, their scheme is a multi-use and efficient VMSS on the public channel which provides the same level of security as traditional VMSS schemes with much shorter keys.