On the Construction and Analysis of Verifiable Multi-secret Sharing Based on Non-homogeneous Linear Recursion

We shall propose two verifiable multi-secret sharing schemes based on novel non homogeneous linear recursions. In the initial phase, the secret shadow of each participant is selected by himself. In the construction phase, the dealer puts the information of shared secrets in the initialization vector of non-homogeneous linear recursions of degree t - 1. In the verification phase, verification algorithms based on elliptic curve are designed to resist a variety of cheating actions or attacks. In the recovery phase, each participant just needs to provide secret share instead of secret shadow. The proposed schemes have the following features: verifiability, the reuse of secret shadows and shared secrets is possible, only public channels are needed. Compared with previous schemes, they have better performance, fewer public values, lower computation complexity, shorter key length and less running time.