A Generalized Multi-secret Sharing Scheme to Identify Cheaters

Secret sharing is an important research area in information security and cryptography,which is significant to managing communication keys and ensuring the safety of computer networks.Most previous multi-secret sharing schemes have problems in efficiently detecting the cheating of either the dealer or shadowholders and in carrying out complex and large-amount computation for secret recovery.The authors have designed an efficient multi-secret sharing scheme with a generalized access structure on the basis of dealing with the difficulty of computing the discrete logarithm modulo for a composite number and the factorization problem of a large integer.The proposed scheme has the following properties:(1)Cheating of the dealer or any participant can be detected efficiently;(2)a new secret can be added on the bulletin by the dealer at any time on condition that small-amount of data are made public;(3) the participants can reconstruct a secret with the parallel procedure in a secret recovery phase;(4)the shadows of the participants will not change when the system accepts a new participant or fires an old participant.This scheme will find wide applications in conferences distributed secretly,securely-distributed computation and electronic commerce.