Study On Secret Sharing Schemes

With the development of information technology,the scale of encryption system is also expanding,and the shortcomings of traditional methods on secret management are increasingly prominent.Therefore,as a safe and efficient secret management method,secret sharing has attracted more and more attention.Secret sharing is to share a secret among some participants,so that some sets of pariticipants can recover the secret,while other sets cannot get any information about the secret.In this paper,we focus on the problem of secret sharing given the storage capacity of each participant.To derive and optimize the upper bound of the secret sharing rate,we propose a linear programming scheme,which add the common information property into the constraints.Compared with the typical scheme,the new scheme in this paper effectively enhances the constraints,and a better upper bound of the linear secret sharing rate can be derived,which can be used to improve some cases where the linear secret sharing rate is not achievable.Then,we give the upper bound of the new linear secret sharing rate for all cases of five participants,and construct the corresponding linear schemes.Thus,all the optimal linear secret sharing rates of five participants are determined.To determine the optimal linear secret sharing rate,we propose an algorithm.The algorithm is based on the fact that the existence of a linear secret sharing scheme is equivalent to the existence of solutions to a quadratic system of equations.It constructs a linear secret sharing scheme with an optimal linear secret sharing rate and the size of the secret is an arbitrary integer.Compared with the existing linear secret sharing scheme with secret sizes of unit size,the linear secret sharing scheme determined by the algorithm in this paper can achieve the optimal linear secret sharing rate when the storage capacity of each participant is given,which shows a better performance.