Code

I maintain some computer code for computations relating to my research.  These scripts are mostly for the computer algebra systems Pari/GP and Sage.  You are welcome to download and use these scripts; they and the software to run them (Pari & Sage) are free. Please let me know if you encounter errors.

Notes on usage

• To use a Pari/GP script, load the script by typing “\r filename” at the prompt, where filename includes the path, then see the script for descriptions of functions;
• To use a Sage script, type “attach(‘filename’)” at the prompt; it also works simply to cut and paste the text of the script file into the first cell of a notebook;
• To use a Sage notebook, upload it to the notebook interface.

Illustrating Number Theory

I’ve taken an interest in the illustration of number theory with computers and 3d printing, etc.  Click here to view my gallery.

SIDH

Isogeny-based cryptography is a primary candidate for post-quantum cryptography. 

• Attacking SIDH variants [ github ] – This code demonstrates the attacks in our paper, Improved torsion point attacks on SIDH variants with Victoria de Quehen, Péter Kutas, Chris Leonardi, Chloe Martindale, Lorenz Panny, and Christophe Petit.  

Ring Learning with Errors

Ring Learning with Errors is a front-runner for a hard problem upon which to base post-quantum cryptography.  Here are some algorithms for attempting to solve it.

• Ring-BKW [ Code etc. ] – This code supports my paper Algebraic aspects of solving Ring-LWE, including ring-based improvements in the Blum-Kalai-Wasserman algorithm.
• Ring-LWE and Poly-LWE attack [ Sage Notebook ] – This implements the algorithms in our paper Provably weak instances of Ring-LWE (with Yara Elias, Kristin E. Lauter and Ekin Ozman).

Schmidt Arrangements

• Apollonian-like packings and Schmidt Arrangements [ Sage Notebook | Interactive Web Page ] – This draws pictures of Schmidt Arrangements and K-Apollonian circle packings as described in my papers Visualizing the arithmetic of imaginary quadratic fields and The Apollonian structure of Bianchi groups.
• My graduate student, Daniel Martin, has some remarkable code for Schmidt arrangements and his own generalizations.