论文标题
使用共享密钥安全组播放
Secure Groupcast with Shared Keys
论文作者
论文摘要
我们考虑一个发射器和$ K $接收器，每个接收器都与发射器共享一个密钥变量。通过无噪声的广播频道，发射器希望将通用的消息$ w $安全地发送到$ k $接收器中的$ n $，而其余的$ k-n $接收器则学习有关$ w $的信息。我们对最大消息率感兴趣，即，可以将最大的$ w $位数量固定到每个密钥块的合法接收器和最小广播带宽，即，将最小广播信息的最小钻头数量确保分组到消息位所需的广播信息。 我们专注于组合键的设置，其中$ k $接收器的每个子集都共享一个任意大小的独立钥匙。在此组合关键设置下，以下方案的最大消息率是特征的-1）$ n = 1 $或$ n = k-1 $，即用$ k-1 $ k-1 $ evappers或安全的goupdroppers或$ k-1 $ k-1 $接收器的1 $ k-1 $接收器的安全单次，带有$ 1 $ neveropper，2）$ n = 2 $ n = 2 $ n = 4 $ n = $ 2 $ 2 $ 2）对于任何$ n，k $，同一基数的任何子集的密钥大小都相等。此外，对于后两种情况，最大消息率的最小广播带宽是特征的。
We consider a transmitter and $K$ receivers, each of which shares a key variable with the transmitter. Through a noiseless broadcast channel, the transmitter wishes to send a common message $W$ securely to $N$ out of the $K$ receivers while the remaining $K-N$ receivers learn no information about $W$. We are interested in the maximum message rate, i.e., the maximum number of bits of $W$ that can be securely groupcast to the legitimate receivers per key block and the minimum broadcast bandwidth, i.e., the minimum number of bits of the broadcast information required to securely groupcast the message bits. We focus on the setting of combinatorial keys, where every subset of the $K$ receivers share an independent key of arbitrary size. Under this combinatorial key setting, the maximum message rate is characterized for the following scenarios - 1) $N=1$ or $N=K-1$, i.e., secure unicast to 1 receiver with $K-1$ eavesdroppers or secure groupcast to $K-1$ receivers with $1$ eavesdropper, 2) $N=2, K=4$, i.e., secure groupcast to $2$ out of 4 receivers, and 3) the symmetric setting where the key size for any subset of the same cardinality is equal for any $N,K$. Further, for the latter two cases, the minimum broadcast bandwidth for the maximum message rate is characterized.
