William Youmans

Mathematician and cryptographer. Postdoc at Clemson University.

I am currently a post-doctoral researcher in the School of Mathematical and Statistical Sciences at Clemson University, under the supervision of Ryann Cartor and Felice Manganiello. I am working in collaboration with the Savannah River National Laboratory on applications of post-quantum cryptography to real-world problems.

Previously I was a post-doctoral research fellow in the Department of Mathematics and Statistics at Florida Atlantic University under the supervision of Shi Bai and Edoardo Persichetti, working alongside 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.

Refereed research publications

  • A quasi-polynomial time algorithm for the extrapolated dihedral coset problem over power-of-two moduli. S. Bai, H. Jangir, E. Kirshanova, T. Ngo, W. Youmans. Advances in Cryptology – CRYPTO 2025. pdf preprint
  • 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 preprint.

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.

Invited talks

  • A quasi-polynomial time algorithm for the extrapolated dihedral coset problem over power-of-two moduli. ACCESS, online, 2025. program
  • A quasi-polynomial time algorithm for the extrapolated dihedral coset problem over power-of-two moduli. AMS Fall Southeastern Sectional Meeting, Tulane University, 2025. program
  • A quasi-polynomial time algorithm for the extrapolated dihedral coset problem over power-of-two moduli. Applied Algebra Days Workshop, Florida Atlantic University, 2025. program
  • Solving the principal ideal problem with subfields. CHARM Workshop, Institut de Mathématiques de Bordeaux, 2025. program slides
  • An algebraic algorithm for breaking NTRU with multiple keys. AMS Spring Southeastern Sectional Meeting, Clemson University, 2025. program
  • An algorithm for solving the principal ideal problem with subfields. Joint Mathematical Meetings, 2024. program.
  • 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.

Teaching

Florida Atlantic University:
  • Methods of Calculus. Fall 2023.
University of South Florida:
  • Introduction to Cryptography and its Applications (co-instructor). Spring 2023.
  • Cryptography and Coding Theory (teaching assistant). Fall 2019 - 2022.
  • Elementary Number Theory (teaching assistant). Fall 2018.

Code

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.

Contact

  • Address:
    William Youmans
    School of Mathematical and Statistical Sciences
    105 Sikes Hall
    Clemson, SC 29634

  • Office: Martin Hall, room O13.

  • Email: youmans.wj@gmail.com