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    "A study on Modeling of the Collusion Problem and its Evaluation"

    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 of collusion has some drawbacks that each colluder must expose her own secret key, so that it cannot properly express the way how collusion is formed. Fortheremore, their formulation models attakers to collude after the communication has finished, so it cannot take into considerration more effective attack, which is perfomed during protocol execution. Therefore we propose two collusion models, the one is introduced that the secret keys of colluders are not shared and the collusion condition is represented in a directed graph, the other enables to carry out the collusion attack during the communication protocol runs.

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