Secret Sharing Scheme Based On Multilinear Map And Its Research

Secret sharing is the core underlying protocol for many cryptographic systems,and it has a wide range of applications in secure communication in a network environmenr,whose gole is to share a secret among multiple participants.Information rate is one of the most important factors to measure the efficiency of secret sharing.Existing secret sharing schemes for the realization of verifiability,public verifiability and other security needs,resulting in its information rate is relatively low,which seriously restricted the application efficiency of secret sharing schemes.Thus,it is necessary to research the optimization problem of secret sharing efficiency.Based on the multilinear map,this paper studies the verifiability,public verifiability and the efficiency optimization problem of secret sharing.The research focuses on verifiable secret sharing and publicly verifiable secret sharing based on multilinear map,secret sharing of universally composable security,and the application of public verifiability secret sharing in data storage.The specific works are as follows:(1)Verifiable secret sharing based on multilinear map.We use the multilinear map to design a commitment scheme,and based on this scheme designed a verifiable secret sharing scheme,by using the multilinearity of multilinear map,the verifiable function of the scheme is realized.Finally,the efficiency of the scheme is optimized,the design method of verifiable secret sharing scheme with optimal information rate is proposed,and we analyze the security and performance of the scheme.(2)Publicly verifiable secret sharing based on multilinear map.Firstly,we construct a publicly verifiable secret sharing scheme based on a commitment scheme which is designed by multiple linear pair,our scheme allows any one who has public information to verify the secret sharing process publicly.Secondly,by using the multiple linearity of the multilinear map,the efficiency of the scheme is optimized,and the publicly verifiable secret sharing scheme with progressive optimal information rate is established.Finally,the performance analysis results show the security and effectiveness of the scheme.(3)Secert sharing secret with universally composable security.Firstly,an ideal function of the verifiable secret sharing is proposed under the universally composable framework.Secondly,we combine the composable security theory,discuss the universally composable security model and method which is suitable for secret sharing scheme.Finally,a secret sharing scheme is proposed under the multilinear Diffie-Hellman assumption.(4)The application of publicly verifiable secret sharing based on multilinear map in data storage.A secure and verifiable data storage scheme is proposed by using multiple linear technology and verifiable secret sharing scheme.The security of each stage of data storage is analyzed and the corresponding architecture is designed.