Compound Secure Groupcast: Key Assignment for Selected Broadcasting
Hua Sun · IEEE Journal on Selected Areas in Information Theory · 2022
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$\alpha $, i.e., the number of bits of the key variable stored at each receiver per message bit, and broadcast bandwidth$\beta $, i.e., the number of bits of the broadcast information sent by the transmitter per message bit. We have three main results. First, when broadcast bandwidth is minimized, i.e., when$\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)$is achievable and is optimal (minimum) if$N=2$or$K-1$. Third, when$N=2$, the optimal key storage and broadcast bandwidth tradeoff is characterized as$\alpha +\beta \geq 3, \alpha \geq 1, \beta \geq 1$.