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Efficient Multicast Key Distribution (MKD) is essential for secure multicast communications. Although Sherman et al. claimed that their MKD scheme - OFT (One-way Function Tree) achieves both perfect forward and backward secrecy, several types of collusion attacks on it still have been found. Solutions to prevent these attacks have also been proposed, but at the cost of a higher communication overhead. In this paper, the authors prove falsity of a recently-proposed necessary and sufficient condition for existence of collusion attack on the OFT scheme by a counterexample and give a new necessary and sufficient condition for nonexistence of any type of collusion attack on it.
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