On some properties of the (t, n) threshold secret sharing schemes based on the generalized vector space construction

In this paper some of the properties of the (t, n) threshold secret sharing schemes, based on the generalized vector space construction, are discussed. The relations between the size of the shares and the number of the users n in the (t, n) threshold secret sharing schemes are presented. Moreover, it is shown how a qualified set of users can efficiently recover the secret in case of (2, n) and (3, n) threshold secret sharing schemes, exploiting the regular structure of the matrices corresponding to each of the n users.