Cryptanalysis of a polynomial-based key management scheme for secure group communication

Piao et al. proposed a polynomial-based key management scheme for secure intra-group and inter-group communication. In this note, we present a simple attack on this scheme and show that it does not satisfy group forward and backward secrecy. In other words, we show that when a node leaves a group, it can easily compute the new intra-group key based on its old key and the publicly broadcasted data. Similarly, we also show that when a node joins a group, it can discover the old keys.