A novel private communication framework is proposed where privacy is induced by transmitting over 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.

翻译：本文提出了一种新型隐私通信框架，通过在线性逆问题的信道实例上传输信息来产生隐私性，这些实例对合法接收者可识别，但对窃听者不可识别。该框架利用发射机与合法接收机之间的秘密知识来创造可识别性差距。具体而言，研究了在经典压缩感知会必然失效的条件下，合法接收者利用秘密块结构从欠定线性测量中解码所传输的块稀疏消息的情况。讨论了所提方案在实际多址无线通信系统中的适用性。分析了在单次传输以及不更新秘密块结构的多次传输下的协议隐私性。研究表明，在信道维度与传输参数的特定缩放条件下，窃听者可通过信道输出的四阶矩尝试窃听块结构。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，定义了通信被攻破前密钥寿命的缩放律。最后，通过数值实验验证了理论结果。