Steven H. Low and Nicholas F. Maxemchul formulated in 1998 a collusion problem, which is to determine whether it is possible for a group of colluders to reveal secret data by combining their knowledge. However, their formulation models attackers to collude after the communication has finished, so it cannot take into consideration more effective attack, which is performed during protocol execution. Therefore we propose a collusion model which enables to carry out the collusion attack during the communication protocol runs. Furthermore, we present an algorithm that determines whether the collusion succeeds or not.
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