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

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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.