I am currently a post-doctoral research fellow in the Department of Mathematics and Statistics at Florida Atlantic University under the supervision of Shi Bai. I am a member of the cryptography group at FAU.

I received my PhD in mathematics from the University of South Florida in 2023 under the supervision of Jean-François Biasse, where I was a member of the USF Center for Cryptographic Research.

My research interests are centered around post-quantum cryptography, lattice-based cryptography, quantum algorithms, and number theory.

Publications

A quasi-polynomial time algorithm for the extrapolated dihedral coset problem. S. Bai, H. Jangir, E. Kirshanova, T. Ngo, W. Youmans. Submitted.
An algebraic algorithm for breaking NTRU with multiple keys. S. Bai, H. Jangir, T. Ngo, W. Youmans. Designs Codes and Cryptography, 92(12):3895-3918, 2024. pdf. code.
An algorithm for solving the principal ideal problem with subfields. J.-F. Biasse, C. Fieker, T. Hofmann, W. Youmans. Advances in Mathematics of Communications, early access, 2023. pdf.
Mildly short vectors in ideals of cyclotomic fields without quantum computers. J.-F. Biasse, M. R. Erukulangara, C. Fieker, T. Hofmann, W. Youmans. Mathematical Cryptology, 2(1):84-107, 2022. pdf.
A trade-off between classical and quantum circuit size for an attack against CSIDH. J.-F. Biasse, X. Bonnetain, B. Pring, A. Schrottenloher, W. Youmans. Mathematical Cryptology, 15(1):4-17, 2021. pdf
Generating sets of Reidemeister moves of oriented singular links and quandles. K. Bataineh, M. Elhamdadi, M. Hajij, W. Youmans. Knot Theory and its Ramifications, 27(14):1850064, 2018. pdf.

Other research

Recovering generators of principal ideals using subfield structure and applications to cryptography. PhD dissertation. University of South Florida, 2023. pdf.
Anonymity preserving data collection using homomorphic encryption. J.-F. Biasse, S. Chellappan, N. Fisk, N. Khan, W. Youmans. US Patent No. 11,809,597 B2, 2023.
Privacy preserving prescription drug management using fully homomorphic encryption. White paper from Microsoft Private AI Bootcamp, 2019. A. Shahverdi, N. Trieu, C. Weng, W. Youmans. Protecting Privacy through Homomorphic Encryption, 169-176, 2021.

An algorithm for solving the principal ideal problem with subfields. Joint Mathematical Meetings, 2024. link.
An algorithm for solving the principal ideal problem with subfields. FAU CryptoCafe Seminar, 2023. video.
Mildly short vectors in ideals of cyclotomic fields without quantum computers. MathCrypt, 2022. video.
Privacy preserving prescription drug management using fully homomorphic encryption. With A. Shahverdi, N. Trieu, C. Weng. Microsoft Private AI Bootcamp, 2019.
Computing the regulator of a real quadratic order using p-adic methods. Applied Mathematics, Modeling and Computational Science, 2019.

Check out my GitHub! Some relevant projects are listed here:

arora-ge-ntru - A C++ implementation of the Arora-Ge algorithm for breaking NTRU with multiple keys.
NormRelations - A Julia package for exploiting subfield structure to recursively solve problems in number fields.
CycloDB - A searchable database of cyclotomic field invariants (class groups, regulators, and more) for certain cyclotomic fields of degree up to 576 and conductor 2730.

Address:
William Youmans
Department of Mathematics and Statistics
777 Glades Road
Boca Raton, FL 33431
Office: Charles E. Schmidt College of Science building, room 217.
Email: youmans.wj@gmail.com