Some democratic secret sharing schemes

The paper considers the problem of constructing secret sharing schemes without the assistance of a Dealer. It shows how to implement Brickell’s Vector space construction as a democratic secret sharing scheme. As a special case, the paper construct democratic threshold schemes by using Sharmir’s method. In the present 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.