CIF: Small: Best Wiretap Codes for Real-world Physical-layer Security

低功耗设备在现代通信系统中的无处不在的特性，在当今不断连接的世界中带来了许多新的和令人兴奋的可能性，也带来了一些挑战。用户现在可以通过各种网络结构永久访问数据和信息；然而，保护个人数据从未像现在这样具有挑战性。由于许多网络由低功率设备组成(例如，在物联网中)，目前需要传统密码术的低功率安全替代方案。有一种技术显示出解决这些需求的巨大前景，那就是使用窃听编码的物理层安全。然而，尽管经过了几十年的基础理论研究，人们仍在继续寻找能够应对现代网络安全挑战的实用编码方案。该项目在物理层安全的窃听编码领域具有变革性的潜力。提出的研究目标是一种简单而又新颖的窃听编码方法，该方法将在各种窃听信道模型上产生可证明是最佳的编码结构。这样的代码可能会指导适用于物联网和其他应用的安全标准和协议。该项目寻求通过完全纳入杨百翰大学的特殊本科生研究和推广计划来招募一个多样化的研究团队。研究小组的学生将发展技能和专业网络，使他们能够继续在STEM专业人员中建立更大的多样性。开发和采用窃听编码的关键限制因素是：当前的设计理论寻求实现保密的代码，因为块长度趋于无穷大，并且假设设计者完全了解窃听者的信道状态信息。本项目试图通过将物理层安全问题重塑为联合信令/编码问题来克服这两个问题，其中信令和信道探测提供具有高保密容量的环境，然后窃听编码通过采用特定的有限块长度窃听代码在该环境中最大限度地提高安全性。该方法要求研究团队为窃听者的信道的所有可能状态找到最佳代码。该项目解决了联合设计问题的编码方面的问题，并将通过寻找和/或设计能够证明最适合其大小的窃听代码来确定有限块长度制度下的安全吞吐量的基本限制。该项目主要研究以下三个方面的工作：1)研究简单信道最优安全(最佳)窃听码的基本代数性质；2)寻找并设计简单信道的显式、最优、二进制码结构；3)将最佳二进制编码结果扩展到更困难、更真实的信道模型，并设计最优的非二进制窃听码。预计大量当前已知的代数码结构将被证明是它们的大小参数的最佳。还将寻求为块长度和维度产生最佳(或接近最佳)代码的通用算法，其中不存在已知的最佳代数结构。如果成功，这些结果将改变有限块长度窃听代码的设计。这种突破性成果的集合将使通信专家能够在充分了解有限块长窃听代码的安全吞吐量的可实现速率的情况下，开始在现代通信网络中采用物理层安全码。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The pervasive nature of low-power devices in modern communication systems has introduced scores of new and exciting possibilities as well as several challenges in today's continuously connected world. Users now enjoy perpetual accessibility to data and information through various network structures; however, securing personal data has never been more challenging. Due to many networks being comprised of low-power devices (e.g., as in the Internet of Things), low-power secure alternatives to traditional cryptography are currently in demand. One technique that shows immense promise for addressing these needs is physical-layer security with wiretap coding. However, despite the several decades of fundamental theoretical research, the search continues for practical coding schemes that can address the security challenges of modern networks. This project has the potential to be transformative in the field of wiretap coding for physical-layer security. The proposed research targets a straightforward and yet novel approach to wiretap coding that will produce provably-best coding structures over various wiretap channel models. Such codes are likely to direct security standards and protocols adapted to the Internet of Things and other applications. The project seeks to recruit a diverse research team through full inclusion in special undergraduate research and outreach programs at Brigham Young University. Students from the research group will develop skills and professional networks that allow them to go on to build greater diversity in STEM professions.Key limiting factors in the development and adoption of wiretap coding are: the current design theory seeks codes that achieve secrecy as blocklength tends to infinity, and it is assumed that the designer has full knowledge of the eavesdropper's channel state information. This project seeks to overcome both of these problems by recasting the physical-layer security problem as a joint signaling/coding problem, where signaling and channel sounding provide an environment with high capacity for secrecy, and wiretap coding then maximizes security in that environment through adoption of specific finite blocklength wiretap codes. The approach requires the research team to find the best codes for all possible states of the eavesdropper's channel. This project addresses the coding side of the joint design problem, and will identify fundamental limits of secure throughput in the finite blocklength regime by finding and/or designing wiretap codes that can be proved to be best for their size. The project addresses the following three main research tasks: 1) characterize fundamental algebraic properties of optimally-secure (best) wiretap codes for simple channels; 2) find and design explicit, optimal, binary code structures for simple channels; and 3) expand best binary coding results to more difficult and realistic channel models and design optimal non-binary wiretap codes. It is anticipated that a host of currently known algebraic code structures will prove to be best for their size parameters. Generic algorithms will also be sought that produce best (or nearly-best) codes for blocklengths and dimensions where no known best algebraic structures exist. If successful, these results will transform finite blocklength wiretap code design. Such a collection of breakthrough results would empower communication experts to begin adopting physical-layer security codes in modern communication networks with full knowledge of the achievable rates of secure throughput for finite blocklength wiretap codes.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.