Research
The development of quantum computers gives rise to new technical and theoretical problems. I use number theory to research these problems, driving the field forward.
I am working on mathematics behind cryptographic protocol which is proposed to be safe for the quantum work. In ranked choice order:
Isogeny-based cryptography
Code-based cryptography
Lattice-based cryptography
I am also interested in problems at the intersection of algebraic number theory and algebraic geometry. In particular, I have current collaborative work studying the geometry of monogenicity.
Accepted & Published Papers
Adventures in Supersingularland. Experimental Mathematics, 2021. Joint with Catalina Camacho-Navarro, Kristin Lauter, Joelle Lim, Kristina Nelson, Travis Scholl, Jana Sotáková.
On the arithmetic of a family of superelliptic curves. Manuscripta Mathematica, 2022. Joint with Richard Griffon, Libby Taylor, Nicholas Triantafillou. arxiv version.
A Study of Error Floor Behavior in QC-MDPC Codes. PQCrypto, 2022. Joint with Tyler Raven Billingsley, Daniel Raynor Hast, Jun Bo Lau, Ray Perlner, Angela Robinson.
The Scheme of Monogenic Generators I: Representability. Joint with Sebastian Bozlee, Leo Herr, Hanson Smith. Research in Number Theory, 2023. arxiv version.
The Scheme of Monogenic Generators II: Local Monogenicity and Twists. Joint with Sebastian Bozlee, Leo Herr, Hanson Smith. Research in Number Theory, 2023. arxiv version.
Orienteering with one endomorphism. Joint with Mingjie Chen, Kristin E. Lauter, Renate Scheidler, Katherine E. Stange, Ha T. N. Tran. La Matematica, 2023. arxiv version.
Orientations and cycles in supersingular isogeny graphs. Joint with Mingjie Chen, Kristin E. Lauter, Renate Scheidler, Katherine E. Stange, Ha T. N. Tran. Research Directions in Number Theory. Assoc. Women Math. Ser., 2024. arxiv version.
Finding Orientations of Supersingular Elliptic Curves and Quaternion Orders. Joint with James Clements, Pierrick Dartois, Jonathan Komada Eriksen, Péter Kutas, Benjamin Wesolowski. Designs, Codes and Cryptography, to appear.
Adding Level Structure to Supersingular Elliptic Curve Isogeny Graphs. Journal de Théorie des Nombres de Bourdeaux, to appear.
Generalized class group actions on oriented elliptic curves with level structure. Joint with Wouter Castryck, Jonathan Komada Eriksen, Gioella Lorenzon and Frederik Vercauteren. To appear at the International Workshop for the Arithmetic of Finite Fields.
Submitted Articles
Preprints
Expository Notes
Code
Code to accompany the WIN5 project "Orientations and cycles in supersingular isogeny graphs" (Magma) (code not vetted by my collaborators - not guaranteed to be error-free)
Code to accompany the WIN5 project "Orienteering with one endomorphism" (SageMath)
Code to accompany the QC-MDPC Codes project (SageMath)
Code to accompany the Adventures in Supersingularland project (SageMath)
Code to generate supersingular elliptic curve ell-isogeny graphs with level-N structure (SageMath)