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 key D while the other participants are aware only of the false key D′ computed in the threshold scheme. The second version we present is to detect the existence of cheaters. © 1993 Kluwer Academic Publishers.