Some democratic secret sharing schemes

In this paper, we consider the problem of constructing secret sharing schemes without the assistance of a Dealer. We show how to implement Brickellʹs Vector space construction as a democratic secret sharing scheme. As a special case, we construct democratic threshold schemes by using Sharmirʹs method. In our democratic secret sharing schemes, the participants need no more information to be kept secret (shares) than they would need in the case where the schemes are constructed by a Dealer.