William Youmans, Ph.D., a postdoctoral fellow in the Department of Mathematics and Statistics at Florida Atlantic University, will soon begin a new postdoctoral position at Clemson University, where he will continue his research in post-quantum cryptography in collaboration with the Savannah River National Laboratory.
Dr. Youmans joined FAU in 2023 as a postdoctoral researcher under the supervision of Dr. Edoardo Persichetti, supported by National Security Agency grant H98230-22-1-0328, and later continued his work under Dr. Shi Bai, supported by National Science Foundation grant 2044855 "CAREER grant: Concrete Hardness in Lattice-based Cryptography". His research focuses on developing both classical and quantum algorithms to analyze the hardness of the mathematical problems that underpin the security of modern cryptographic protocols.
With the advent of practical quantum computing on the horizon, traditional cryptographic systems such as RSA and elliptic curve cryptography face serious threats from quantum algorithms—most notably Shor’s algorithm, which can efficiently factor large integers and compute discrete logarithms. This presents a significant risk to data privacy and secure communication on a global scale.
To address these challenges, the cryptographic community has turned to post-quantum cryptography, a field dedicated to designing and analyzing cryptographic systems capable of resisting attacks from quantum-capable adversaries. Dr. Youmans’ work contributes directly to this effort by developing and analyzing algorithms that test the resilience of proposed post-quantum schemes, helping to identify vulnerabilities and strengthen the cryptographic standards currently under consideration by organizations such as NIST.
A notable example of his recent work is the article “A Quasi-Polynomial Time Algorithm for the Extrapolated Dihedral Coset Problem,” co-authored with Dr. Shi Bai, Dr. Elena Kirshanova of the Technology Innovation Institute, and FAU graduate students Hansraj Jangir and Tran Ngo. The paper has been accepted to Crypto 2025, one of the top conferences in the field of cryptography. This work advances our understanding of quantum attacks on the Learning with Errors (LWE) problem—a core hardness assumption underlying many lattice-based cryptographic systems. This research enhances the broader effort to evaluate the true quantum security of LWE-based schemes.
By deepening our understanding of the computational complexity behind post-quantum cryptographic primitives, Dr. Youmans plays an important role in shaping the future of secure digital infrastructure in the quantum era.
