A novel private communication framework is proposed where privacy is induced by transmitting over a channel instances of linear inverse problems that are identifiable to the legitimate receiver but unidentifiable to an eavesdropper. The gap in identifiability is created in the framework by leveraging secret knowledge between the transmitter and the legitimate receiver. Specifically, the case where the legitimate receiver harnesses a secret block structure to decode a transmitted block-sparse message from underdetermined linear measurements in conditions where classical compressed sensing would provably fail is examined. The applicability of the proposed scheme to practical multiple-access wireless communication systems is discussed. The protocol's privacy is studied under a single transmission, and under multiple transmissions without refreshing the secret block structure. It is shown that, under a specific scaling of the channel dimensions and transmission parameters, the eavesdropper can attempt to overhear the block structure from the fourth-order moments of the channel output. Computation of a statistical lower bound suggests that the proposed fourth-order moment secret block estimation strategy is near optimal. The performance of a spectral clustering algorithm is studied to that end, defining scaling laws on the lifespan of the secret key before the communication is compromised. Finally, numerical experiments corroborating the theoretical findings are conducted.

中文翻译：

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通过秘密块结构保证私密通信


提出了一种新颖的私有通信框架，其中通过在合法接收者可识别但窃听者无法识别的线性逆问题的信道实例上传输来诱导隐私。通过利用发送者和合法接收者之间的秘密知识，在框架中产生了可识别性的差距。具体来说，检查了合法接收器利用秘密块结构在经典压缩感知可能失败的条件下根据未确定的线性测量来解码传输的块稀疏消息的情况。讨论了所提出的方案在实际多址无线通信系统中的适用性。在单次传输和不刷新秘密块结构的多次传输下研究协议的隐私性。结果表明，在信道维度和传输参数的特定缩放下，窃听者可以尝试从信道输出的四阶矩中偷听到块结构。统计下界的计算表明所提出的四阶矩秘密块估计策略接近最优。为此，研究了谱聚类算法的性能，定义了通信受到损害之前密钥寿命的缩放法则。最后，进行了数值实验证实了理论结果。