About Me

I am a mathematician studying cryptography and verifiable computation. I am currently interested in interactive proof systems, succinct arguments, and zero-knowledge protocols, particularly as they relate to cryptocurrency and blockchain applications. My academic background is in theoretical mathematics in the areas of algebraic combinatorics and commutative algebra, and I am currently a visiting research associate at Colorado State University. I received my PhD in mathematics from U.C. Berkeley in 2018, advised by Olga Holtz.


For a complete list of my academic papers and presentations, see my CV — preprints are available online at arXiv.org.

Lecture notes covering some of the mathematical background needed to carry out zk-SNARK constructions, which I prepared for a recent course on verifiable computation, are available on the course website. I also recently wrote down some concrete details on efficient evaluation of multilinear polynomials.


I recently prepared and taught an undergraduate topics course, MATH 480A2: Mathematics of Blockchain Protocols, at Colorado State University in Fall 2022. The course focused on zero-knowledge and verifiable computation protocols and underlying mathematical primitives, using Justin Thaler's book "Proofs, Arguments, and Zero-Knowledge" as a primary reference.

An archive of course websites from my previous teaching as a grad student at U.C. Berkeley can be found here.


Most of my software projects can be found at my GitHub. Some highlights include:

  • pazk-rs: a Rust library implementing protocols from Justin Thaler's book "Proofs, Arguments, and Zero-Knowledge"
  • shamir: a python script to split and combine BIP 39 seed phrases using Shamir secret sharing
  • Zonotopal Spaces: Sage code for explicitly generating the zonotopal spaces described in Olga Holtz and Amos Ron's 2011 publication "Zonotopal Algebra" and related literature.
  • Voter Model (interactive): an interactive simulation of the voter model, a probabilistic model for opinion dynamics on a graph.
  • Tableau Combinatorics (interactive): a basic tool for more easily manipulating Young tableaux and Young diagrams. Also available in English notation.


Email IconBryan.Gillespie@colostate.edu

Twitter Icon@bryan_gillespie

Github Icongithub.com/bgillesp