Compound Secure Groupcast: Key Assignment for Selected Broadcasting
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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 any N out of the K receivers through a noiseless broadcast channel. The metric is the information theoretic tradeoff between key storage α, i.e., the number of bits of the key variable per message bit, and broadcast bandwidth β, i.e., the number of bits of the broadcast information per message bit. We have three main results. First, when broadcast bandwidth is minimized, i.e., when β = 1, we show that the minimum key storage is α = N. Second, when key storage is minimized, i.e., when α = 1, we show that broadcast bandwidth β = min(N, K-N+1) is achievable and is optimal (minimum) if N=2 or K-1. Third, when N=2, the optimal key storage and broadcast bandwidth tradeoff is characterized as α+β≥ 3, α≥ 1, β≥ 1.
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