Secured erasure broadcast channels with state feedback: An arbitrarily number of colluding receivers

In this paper, we study the secure communication in a K-user erasure broadcast channel (EBC) with state feedback. Assuming that each message must be kept secret to a set of J colluding receivers, we present an achievable rate region as a function of J = 1,..., K - 1. Similarly to the case J = K - 1 studied in the literature, our proposed scheme consists of three phases: initial secret key generation (phase 0), encrypted broadcasting (phase 1), and multicasting (phase 2). However, with J < K - 1, we show that a larger number of secret keys can be generated by smartly combining and reusing packets overheard during phases 0 and 1. Interestingly, it is found that the sum secrecy rate scales with the number of users only if the number of colluding receivers J remains constant.