Open-refreshing verifiable secret sharing scheme in asynchronous system

Verifiable secret-sharing scheme is a basic primitive in cryptography, it has found numerous application to secure multi-party computation and threshold cryptosystems. However, the threshold may be corrupted in a longer operating period, refreshing shares are the main methods used to deal with this problem. Many proposed schemes have less efficient in computation and communication, and are affected also by the communication model. In this paper, a new verifiable secret sharing is proposed via a public refreshing phrase. Contract to the other proposed schemes, it achieves both forward and backward security, and it has high computational efficiency and can be applied to asynchronous communication model.