# Recent Research

## 2021: Multicolor Ramsey numbers for Berge cycles

### Villanova University and NYU

In this paper, for small uniformities, we determine the order of magnitude of the multicolor Ramsey numbers for Berge cycles of length 4, 5, 6, 7, 10, or 11. Our result follows from a more general setup which can be applied to other hypergraph Ramsey problems. Using this, we additionally determine the order of magnitude of the multicolor Ramsey number for Berge-K a,b for certain a, b, and uniformities.

The paper can be downloaded from here.

## 2020: Privacy Preserving, Distributed, and Verifiable Machine Learning for COVID-19 Identification using ZKPs

### Los Alamos National Laboratory

We developed an efficient and succinct zero-knowledge proof application (with differential privacy) using zkSNARKs for distributed and verifiable machine learning with an additional focus on COVID-19 data. The goal of the project was to develop a the capability to remotely train neural networks with a large array of untrusted edge nodes, each with their own secret data, and to produce a succinct proof that attests to the correctness of the entire chain of computation and the output trained parameters. Using recent techniques for recursive proof composition, proof carrying data, differential privacy, distributed neural network training, and zkSNARKs, we wrote an application in C++ (using the libsnark library) that demonstates the capacity for researchers to now perform privacy preserving, distributed, and verifiable ML.

Download the slides that I presented at CLSAC 2020 here.

## 2019: Design and Implementation of a Secure Neural Network Verification System Using zkSNARKs

### Los Alamos National Laboratory

We present an efficient and succinct zero-knowledge proof application using zkSNARKs for remotely verifying the forward-pass execution of an arbitrarily-sized neural network with hidden inputs and model parameters. Our zero-knowledge guarantee allows the prover to hide information about the input and model parameters from the verifier while being able to attest to the integrity of these parameters and the model's execution.

Our approach is transformative for various applications such as nuclear treaty verification without the need to disclose sensitive data, security camera auditing without the need to leak footage, and secure patient diagnosis without the need to disclose individually identifiable health information. We demonstrate an end-to-end implementation of this proof system using custom gadgets in libsnark on a neural network for the classification of MNIST handwritten digits.

Download the full research poster here.

## 2018: N-Player Hackenbush: Theory, Approximation, and Implementation

### Villanova University

This project generalizes game sums (the main tool used for analyzing positions in combinatorial games) in 2-Player Hackenbush and proposes a theory for analyzing N-Player combinatorial games including N-Player Hackenbush. This project proposes a new way to quantify the advantages to each of the players given any game position, provides a fast method for the approximation of this sum, and demonstrates an example implementation of this algorithm on arbitrary input. This algorithm is demonstrated by an application to N-Player Hackenbush.

Download the resulting research poster here.

zachdestefano (at) gmail (dot) com