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UWEETR-2003-0014 Author(s): Keywords: Abstract Blakley, Blakley, Chan and Massey conjectured a lower bound on the entropy of broadcast messages in threshold schemes with disenrollment. In an effort to examine the conjecture, we identify their original scheme definition has a limitation: a coalition of participants can reconstruct all shared secrets without broadcast from the dealer, and hence render the dealer no control over disenrollment. We introduce a constraint that delays this lack of control of dealer over the disenrollment. We also establish the lower bounds on the entropy of broadcast messages in such a model. We demonstrate the need for new models by presenting a construction under open problems. |