Design And Analysis On Several Secret Sharing Schemes

Secret sharing is a kind of classical and important multi-party cryptographic protocols,and is applied in many scenarios,such as key management,etc.Secret sharing is to divide a secret into multiple shares,and the secret can be reconstructed through some shares.Considering some applications,the efficiency of the secret sharing is one of the important factors.From sharing a secret to sharing a number of secrets,scholars have built multi-secret sharing schemes to improve the overall efficiency of the scheme.At the same time,it is necessary to consider how to improve the efficiency of all aspects of the secret sharing scheme,such as communication efficiency and channel efficiency.In this thesis,from the perspective of improving the efficiency of secret sharing,and based on some of the tools in finite field,we will design three secret sharing schemes:a cheating immune multi-secret sharing scheme without pre-defined order of secrets,a secret reconstruction scheme with optimal communication efficiency,and a secret sharing scheme for the general access structure with partial broadcast channels.The main contributions are as follows:(1)An efficient cheating immune multi-secret sharing scheme is built without pre-defined order of secrets.This scheme is a new multi-secret sharing scheme based on some special tools.We construct the pseudo shares by combining the technology of shift value and bivariate polynomials,which implies the proposed scheme have the following three properties:the cheaters is detected thanks to hash function,each share is reused in secret reconstruction,and the order of recovery of secrets is not pre-defined.In addition,there is no any secure channels between the dealer and the participants.(2)A secret reconstruction scheme with optimal communication efficiency is con-structed.First,a new method,called "jumping skill",is given.That is,the share is consisted of multiple components,and each participant in secret re-construction phase will select components of share in discontinued way.A new secret reconstruction scheme then is constructed by using this method,and we explore the relationship between the number of participants involved in secret reconstruction and the number of steps.It is theoretically proved that the com-munication efficiency of the scheme is optimal.Finally,extensive simulation are conducted,and the results indicate that the upper bound of the communication efficiency can be achieved in our scheme.(3)A partial broadcast secret sharing scheme for the general access structure is proposed.First,we generalized the main results given by Wang and Wong.Secondly,the secret sharing scheme for general access structure with partial broadcast channels is constructed from the largest unauthorized set.In the end,the proposed scheme is compared with existing schemes in details in aspects of channel efficiency and information transmission cost.The comparison results imply that the proposed scheme decreases the number of channels and reduces the cost of information transfer.