Probabilistic Zero-Knowledge Proofs for Neural Network Robustness Público

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

• Permission granted by the author to include this thesis or dissertation in this repository. All rights reserved by the author. Please contact the author for information regarding the reproduction and use of this thesis or dissertation.

School	Emory College
Department	Mathematics and Computer Science
Degree	B.S.
Submission	Honors Thesis
Language	English
Research Field	Computer Science
Palavra-chave	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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