Emily McMillon

Department of Mathematics, College of Science

Support

NSF Mathematical Sciences Postdoctoral Research Fellowship

Faculty Mentor

Gretchen Matthews, Professor of Mathematics

Briefly describe the research project you are planning to contribute to and lead as a postdoctoral associate at Virginia Tech. What is the problem you are addressing? What is the expected impact of your work?

Broadly speaking, my project is looking at codes and decoding algorithms for use in cryptography that are resilient against attack via a quantum computer.

Code-based cryptography works by disguising confidential data by adding noise (errors) in ways that an authorized user can remove via decoding. This system is believed to resist quantum attack when used with certain codes, but improvements are needed to facilitate replacement of today’s algorithms with this more secure technology.

I will consider quasi-cyclic moderate-density parity-check (QC-MDPC) codes for use in post-quantum cryptography. These codes use iterative decoding algorithms similar to low-density parity-check (LDPC) codes, but these decoding algorithms do not produce the same behavior for MDPC codes. Decoder failure rates cannot be calculated explicitly; extensive simulation results to try to extrapolate them. Therefore, I will work to determine how graph substructures affect the error floor of MDPC codes by understanding and characterizing the connection between decoder failure and syndrome decoding errors of low weights. A second research goal is to study quantum LDPC codes.

Why did you choose to pursue postdoctoral training at Virginia Tech?

Virginia Tech is home to one of the top coding/cryptography groups in the US, making this the ideal location for me to grow as a researcher and mathematician. More generally, I also appreciate the level of institutional support for research in quantum, security, and cybersecurity - fields that are all closely connected to my research.

What are you most looking forward to as you begin in this fellowship at Virginia Tech?

I am looking forward to getting to work closely with Dr. Matthews and the fantastic applied algebra group here at Virginia Tech.