Physical Layer Security for Computation Over Unreliable Transmission Channels

几乎每一种新兴技术的组成部分，例如工业4.0、智能电网、5G、触觉互联网、移动的人群感应、电子健康，都将是依赖于空间分布的终端/代理处可用数据的功能的可靠、高效和特别安全的计算。感兴趣的功能可以是例如用于火灾检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、借助于移动的人群感测的城市区域中的平均噪声水平、5G移动的网络中的最优资源分配、或者联网控制系统中的控制器输出。与现有的网络解决方案相比，这将导致模式转变，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领域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，而只有很少的作品遵循物理层安全方法（即，Shannon方法）。然而，这些少数作品始终假设任何给定的发射机和接收机之间的通信在时间或频率上是分开的，并且发生在无限容量的无噪声信道上。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，因为除了安全性要求之外，每个终端还必须处理噪声、信道波动以及诸如有限功率和带宽的通信约束。因此，在额外的保密约束下，在不可靠的信道上可靠和有效地计算函数的基本信息理论限制仍然是未知的。缺乏基本的限制，防止彻底了解现有的权衡，这是必不可少的推导条件下，安全的计算噪声信道是可能的。由于不可信甚至损坏的计算结果可能会在上述每种技术中产生灾难性的后果，因此本研究金的主要目标是提供不可靠传输信道上分布式计算的信息理论基础的第一要素。在此基础上，将推导出最优策略，并分析其性能。

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.