Efficient cloud-aided verifiable secret sharing scheme with batch verification for smart cities

With the wide usage of the information and communication technology (ICT) in smart cities, people's lives become easier and more convenient. Cloud computing, as a burgeoning technology of the ICT, provides consumers with unlimited computing capabilities and storage resources. Using the cloud to promote the progress of the ICT-based applications meets the requirement of the practical usage, and is also in line with the sustainable development. As we all know, the secret sharing is a hot topic in the security community. Many security-assurance applications can be realized with the assistance of secret sharing. In this paper, an efficient cloud-aided verifiable secret sharing scheme is proposed based on the polynomial commitment for smart cities, which can be used in a variety of practical applications such as electronic voting and revocable electronic cash. In the proposed scheme, users can verify the received shares from the cloud. Moreover, in order to meet the requirement of the real-world usage, we extend our scheme to support the batch verification with the aid of a third-party arbitration center. In addition, the aggregate signature is used to verify whether a subset of users possess the shares that indeed sent by the cloud. The security analysis shows that the proposed scheme can satisfy the security requirements of the verifiable secret sharing (VSS) and the performance analysis shows that our scheme is more efficient than previous schemes in terms of the communication and the computation.