David Urbanik

Math post-doc at the IHES.

urbanik at ihes dot fr

About Me

Auxiliary Work

(Extra) Isogeny-based Cryptography

Here is a collection of various non-published work related to isogeny-based cryptography. This does not include my published work in this area.


This is a list of articles I have written on various miscellaneous topics, usually with the aim of presenting an original perspective on existing work. Given in reverse chronological order.




Abstract and Explicit Constructions of Jacobian Varieties

Masters Thesis. Contains the results of my paper on the group law for hyperelliptic Jacobians, as well as an introduction to the mathematics necessary to describe the abstract construction of the Jacobian in modern scheme-theoretic language.




A Brief Introduction to Schemes and Sheaves

Written to provide intuition, background, and motivation that I feel is lacking in most introductions. Best viewed as a supplement to a more detailed resource.




Reductions Between Families of Polynomials in Theory and in Practice

Written as an undergraduate CS thesis. Covers some results of Valiant, and some inconsequential computational work of my own.




A Friendly Introduction to Supersingular Isogeny Diffie-Hellman

For readers with a mathematical background of at least a first course in group theory.




On Notation in Multivariable Calculus

A detailed study of the function f(x,y)=x2 + y2 .