How to avoid the cheaters succeeding in the key sharing scheme

In this paper the Rational Interpolation is presented as a solution to the problem caused by a cheater using the Threshold Scheme. We will implement this scheme by using the Berlekamp-Massey algorithm.The first version we present does not try to detect the cheaters, as in 3], 9] or 10]. This version tries to prevent their knowledge of the correct keyD while the other participants are aware only of the false keyD computed in the threshold scheme.The second version we present is to detect the existence of cheaters.This work was partially supported by Spanish CICYT Grant TIC91-0472.