| Abstract |
The compound secure groupcast problem is considered, where the key variables at $K$ receivers are designed so that a transmitter can securely groupcast a message to {\em any} $N$ out of the $K$ receivers through a noiseless broadcast channel. The metric is the information theoretic tradeoff between key storage $\alpha$, i.e., the number of bits of the key variable per message bit, and broadcast bandwidth $\beta$, i.e., the number of bits of the broadcast information per message bit. We present two results. First, when broadcast bandwidth is minimized, i.e., when $\beta = 1$, we show that the minimum key storage is $\alpha = N$. Second, when key storage is minimized, i.e., when $\alpha = 1$, we show that broadcast bandwidth $\beta = \min(N, K-N+1)$ is achievable.
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