Efficient and verifiable threshold multi-secret sharing scheme

Most previous secret sharing schemes have some problems in which the schemes can not deter the cheating of the dealer and secret shadowholders simultaneously,and the computation in a secret recovery is overhead.A secure and efficient solving scheme was proposed.Each participant can share many secrets with other participants by holding only one shadow in the proposed scheme.This new scheme provides efficient solutions againstcheating of the dealerand cheating ofany participant.The security of the proposed scheme is based on the difficulty of computing the discrete logarithm modulo for a composite number and the factorization problem of a large in-teger.Compared with the other existing schemes,the proposed scheme has the advantages of lower computation and the parallel recon-struction in a secret recovery phase.