Construction And Application Of A Class Of Vector Space Secret Sharing Scheme

In1989, a novel ideal secret sharing scheme is proposed by Brickell, this scheme is named vector space construction. It’s interesting that Shamir (t,n) threshold schemes is a special case of vector space construction. Shamir secret sharing scheme is proposed by A.Schinzel and S.Spiez in2010, and left a problem that is structure the algorithm to find privileged coalitions of any length if such coalitions exist. In order to solve this problem, in this paper we constuct a kind of vector space secret sharing scheme. In this scheme, we first construct a φ function, and then to solve the access structures of this scheme. We design a effective algorithm that can solve the access structures of this scheme, and proved that this algorithm can calculate the privileged coalitions of Shamir secret sharing scheme. At last, we propose a verifiable and dynamic multi-secret sharing scheme based on Shamir’s secret sharing schemes and NTRU algorithm.The research results of this paper are showed in the following:1.We proved that Shamir secret sharing scheme is a special case of this kind of vector space secret sharing scheme, and by using the above algorithm give the method to calculate the privileged coalitions of Shamir secret sharing scheme, so effectively solved open question that is proposed by S.Spiez.2.We proposed a new multi-secret sharing scheme based on Shamir’s secret sharing schemes. The access structures of this scheme are non-threshold access structures, and NTRU algorithm can ensure that the security an verifiability of the scheme. Compared with other verifiable multi-secret sharing schemes, this scheme is simple in design and requires small calculation and low storage space, and it can detect effectively a variety of cheating or forgery behaviors and guarantee that the reconstruction of the secret is correct.