Outsourcing secret sharing scheme based on homomorphism encryption

Secret sharing is an important component of cryptography protocols and has a wide range of practical applications. However, the existing secret sharing schemes cannot apply to computationally weak devices and cannot efficiently guarantee fairness. In this study, a novel outsourcing secret sharing scheme is proposed. In the setting of outsourcing secret sharing, clients only need a small amount of decryption and verification operations, while the expensive reconstruction computation and verifiable computation can be outsourced to cloud service providers (CSP). The scheme does not require complex interactive argument or zero‐knowledge proof. The malicious behaviour of clients and CSP can be detected in time. Moreover, the CSP cannot get any useful information about the secret, and it is fair for every client to obtain the secret. At the end of this study, the authors prove the security of the proposed scheme and compare it with other secret sharing schemes.