David Urbanik

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

• My talk on SIDH on Youtube, with slides. Given at the University of Waterloo on July 12, 2016.
• A library for compressing and decompressing SIDH keys. This work led to a joint collaboration and was accepted to Eurocrypt 2017.
• Hand-optimized ARM64 assembler for SIDH finite field arithmetic, which has been incorporated into the Microsoft SIDH Library.
• My friendly introduction to Supersingular Isogeny Diffie-Hellman.

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.

'18	Aug	10	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.
'18	May	10	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.
'17	May	5	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.
'17	Mar	10	A Friendly Introduction to Supersingular Isogeny Diffie-Hellman For readers with a mathematical background of at least a first course in group theory.
'17	Feb	11	On Notation in Multivariable Calculus A detailed study of the function f(x,y)=x2 + y2 .
'16	Nov	29	Quantum Physics and the Representation Theory of SU(2) Written as a project for a class on representation theory.