Physical Layer Security for Computation Over Unreliable Transmission Channels

几乎所有新兴技术（例如工业4.0、智能电网、5G、触觉互联网、移动人群传感、电子健康）的一个组成部分，都将是依赖于空间分布式终端/代理上可用数据的可靠、高效、尤其是安全的功能计算。例如，感兴趣的功能可以是用于火灾探测的建筑物中的最大烟气浓度，智能电网中的最大频率漂移，通过移动人群传感技术实现的城市地区的平均噪声水平，5G移动网络中的最佳资源分配或网络控制系统中的控制器输出。与现有的网络解决方案相比，这将导致范式的转变，因为原始数据的有效传输不再是最高优先级。在通信信道和网络上的分布式计算以及安全多方计算领域有许多正在进行的研究活动。关于后者，几乎所有发表的结果都是从标准密码学的角度来看的，而只有极少数的工作遵循物理层安全方法（即香农方法）。然而，这几部作品始终假设任何一对给定的发射器和接收器之间的通信在时间或频率上是分开的，并且在无限容量的无噪声信道上进行。因此，通信在安全协议的设计中只起很小的作用。对于任何实际的相关计算方案，这些都是过于理想化的假设，因为除了安全要求之外，每个终端还必须处理噪声、信道波动以及有限的功率和带宽等通信约束。因此，在附加保密约束的不可靠信道上可靠有效地计算函数的基本信息理论极限仍然是未知的。缺乏基本限制阻碍了对现有权衡的彻底理解，这对于推导在噪声信道上进行安全计算的条件是必不可少的。由于不可信甚至损坏的计算结果在上述每种技术中都可能产生灾难性的后果，因此本研究的主要目标是为不可靠传输通道上的分布式计算提供信息理论基础的第一个要素。在此基础上，推导出最优策略并对其性能进行分析。

An integral part of nearly every emerging technology such as, for instance, Industry 4.0, Smart Grids, 5G, Tactile Internet, Mobile Crowd Sensing, eHealth, will be the reliable, efficient, and especially secure computation of functions that depend on the data available at spatially distributed terminals/agents. Functions of interest can be, for instance, the maximum flue gas concentration in a building for fire detection, the maximum frequency drift in a Smart Grid, the average noise level in an urban area by means of Mobile Crowd Sensing, the optimal resource allocation in a 5G mobile network, or the controller output in a networked control system. Compared with existing network solutions, this will result in a paradigm shift as the efficient transmission of raw data is no longer of highest priority. There are many ongoing research activities in the area of distributed computation over communication channels and networks as well as in the area of secure multi-party computation. With regard to the latter, almost all published results are from a standard cryptographic perspective while only very few works exist that follow a physical layer security approach (i.e., Shannon approach). These few works, however, consistently assume that the communication between any given pair of transmitters and receivers is separated in time or frequency and takes place over a noiseless channel of unlimited capacity. Thus, the communication plays only a very minor role in the design of security protocols. For any practical relevant computation scheme, these are too idealistic assumptions as in addition to the security requirements, each terminal also has to deal with noise, channel fluctuations, and communication constraints such as limited power and bandwidth. As a consequence, the fundamental information theoretic limits of reliably and efficiently computing functions over unreliable channels under additional secrecy constraints are still unknown. The lack of fundamental limits prevents a thorough understanding of the existing trade-offs, which is indispensable for deriving conditions under which secure computation over noisy channels is possible. As untrusted or even corrupted computation results can have catastrophic consequences in each of the above-mentioned technologies, the main goal of this research fellowship is to provide the first elements of an information theoretic foundation of distributed computation over unreliable transmission channels. Based on this, optimal strategies will be derived and its performance analyzed.