复合安全组播：选择广播的密钥分配
Compound Secure Groupcast: Key Assignment for Selected Broadcasting
摘要：
复合安全组播问题被认为是，在$K$接收机的关键变量的设计，使发送器可以安全地组播消息的任何$N$出的$K$接收机通过无噪声的广播信道。该度量是密钥存储$α$之间的信息理论折衷，即，每个消息比特的密钥变量的比特数，以及广播带宽$β$，即，每个消息比特的广播信息的比特数。我们有三个主要结果。首先，当广播带宽被最小化时，即，当$β= 1$时，我们证明了最小密钥存储是$α= N$ .第二，当密钥存储最小化时，即，当$α= 1$时，我们表明广播带宽$β= \min(N, K-N+1)$是可实现的，并且如果是$N=2$或$K-1$，则是最优的（最小值）。第三，当$N=2$时，最优密钥存储和广播带宽折衷被表征为$α+β\geq 3, α\geq 1, β\geq 1$。
英文摘要：
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 $α+β\geq 3, α\geq 1, β\geq 1$.
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