Server-aided multi-secret sharing scheme for weak computational devices

In the setting of (t, n) threshold secret sharing, at least t parties can reconstruct the secret, and fewer than t parties learn nothing about the secret. However, to achieve fairness, the existing secret sharing schemes either assume a trusted party exists or require running multi-round, which is not practical in a real application. In addition, the cost of verification grows dramatically with the number of participants and the communication complexity is O(t), if there is not a trusted combiner in the reconstruction phase. In this work, we propose a fair server-aided multi-secret sharing scheme for weak computational devices. The malicious behavior of clients or server providers in the scheme can be verified, and the server provider learns nothing about the secret shadows and the secrets. Unlike other secret sharing schemes, our scheme does not require interaction among users and can work in asynchronous mode, which is suitable for mobile networks or cloud computing environments since weak computational mobile devices are not always online. Moreover, in the scheme, the secret shadow is reusable, and expensive computation such as reconstruction computation and homomorphic verification computation can be outsourced to the server provider, and the users only require a small amount of computation.