Probabilistic Zero-Knowledge Proofs for Neural Network Robustness Pubblico

Abstract

As machine learning (ML) models are increasingly deployed in high-stakes domains,

ensuring their robustness has become critical. However, verifying these properties

often requires access to models’ secrets, which poses a privacy risk. This thesis

proposes a novel cryptographic approach that uses Zero-Knowledge Succinct Non-

Interactive Arguments of Knowledge (zk-SNARKs) to certify the robustness of neural

networks without revealing their internal parameters. Building on prior work such

as FairProof and GeoCert, we present a scalable and privacy-preserving method that

uses verifiable randomness and circuit-based forward propagation to simulate and

prove neural network behavior. Our approach introduces a probabilistic strategy that

avoids the computational complexity of exact robustness verification and supports

real-world scenarios. Experiments on synthetic multilayer perceptrons demonstrate

that our zk-SNARK-based system can distinguish between fair and unfair models

while maintaining constant-time verification and manageable proof sizes. This work

achieves a practical and scalable method for zero-knowledge verification of machine

learning models, enabling secure and privacy-preserving model validation.

Table of Contents

Contents

1 Introduction 1

2 Background 3

2.1 zk-SNARK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.2 Things Behind the Scenes . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2.1 Writing the Circuit . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.2 Arithmetic Circuit . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.3 Introduction to Rank-1 Constraint System (R1CS) . . . . . . 6

2.2.4 Example of R1CS . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.5 Trusted Setup and Groth16 in zk-SNARK . . . . . . . . . . . 9

2.3 Robustness of Machine Learning Model . . . . . . . . . . . . . . . . . 11

2.4 FairProof and GeoCert . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.5 Randomness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3 Approach 15

3.1 Public and Private Inputs in the Proof System . . . . . . . . . . . . . 16

3.2 Verifiable Randomness . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.3 Inputs Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.4 Real World Scenario Simulation . . . . . . . . . . . . . . . . . . . . . 19

3.5 Forward Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.6 Number Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . 23

i

4 Experiments 25

4.1 Fairness Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2 Feasibility Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5 Conclusion 29

A Source Code 31

A.1 Code For Verifiable Randomness: . . . . . . . . . . . . . . . . . . . . 31

A.2 Code for Forward Propagation and Rounding . . . . . . . . . . . . . 33

Bibliography 36

About this Honors Thesis

Rights statement

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School	Emory College
Department	Mathematics and Computer Science
Degree	B.S.
Submission	Honors Thesis
Language	English
Research Field	Computer Science
Parola chiave	Machine Learning Robustness Gnark Zero-Knowledge Proof
Committee Chair / Thesis Advisor	Michelangelo Grigni, Emory University
Committee Members	Jinho Choi, Emory University Bree Danielle Ettinger, Emory University

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