A new (t, n) multi-secret sharing scheme based on Shamir's secret sharing

In 2000, Chien et al. proposed a (t, n) multi-secret sharing scheme. At least t of the n participants can easily reconstruct p secrets at the same time. But the secret reconstruction needs to solve simultaneous equations, which is a complex process. In order to reduce the complexity of the secret reconstruction, Yang et al. proposed an alternative scheme based on Shamir's secret sharing in 2004. But there are more public values required in Yang's scheme than in Chien's scheme when p < t. Motivated by these concerns, a new (t, n) multi-secret sharing scheme is proposed in this paper, which is as easy as Yang's scheme in the secret reconstruction and requires the same number of public values as Chien's scheme.