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PAC to the Future: Zero-Knowledge Proofs of PAC Private Systems

Guilhem Repetto, Nojan Sheybani, Gabrielle De Micheli, Farinaz Koushanfar

TL;DR

This paper tackles verifiable privacy in outsourced computations by marrying PAC Privacy with zero-knowledge proofs, enabling users to verify both the correct application of privacy-preserving noise and the integrity of outsourced computations. It leverages non-interactive zk-STARKs within the RISC-Zero framework to produce publicly verifiable proofs without revealing private parameters. The authors instantiate the framework on K-means, SVM, and database-statistics tasks, showing predictable proof-generation overhead and near-plaintext utility for small-to-medium workloads. The work advances trust in privacy-preserving cloud services by delivering verifiable privacy guarantees that remain robust in a post-quantum setting and without relying on trusted setups.

Abstract

Privacy concerns in machine learning systems have grown significantly with the increasing reliance on sensitive user data for training large-scale models. This paper introduces a novel framework combining Probably Approximately Correct (PAC) Privacy with zero-knowledge proofs (ZKPs) to provide verifiable privacy guarantees in trustless computing environments. Our approach addresses the limitations of traditional privacy-preserving techniques by enabling users to verify both the correctness of computations and the proper application of privacy-preserving noise, particularly in cloud-based systems. We leverage non-interactive ZKP schemes to generate proofs that attest to the correct implementation of PAC privacy mechanisms while maintaining the confidentiality of proprietary systems. Our results demonstrate the feasibility of achieving verifiable PAC privacy in outsourced computation, offering a practical solution for maintaining trust in privacy-preserving machine learning and database systems while ensuring computational integrity.

PAC to the Future: Zero-Knowledge Proofs of PAC Private Systems

TL;DR

This paper tackles verifiable privacy in outsourced computations by marrying PAC Privacy with zero-knowledge proofs, enabling users to verify both the correct application of privacy-preserving noise and the integrity of outsourced computations. It leverages non-interactive zk-STARKs within the RISC-Zero framework to produce publicly verifiable proofs without revealing private parameters. The authors instantiate the framework on K-means, SVM, and database-statistics tasks, showing predictable proof-generation overhead and near-plaintext utility for small-to-medium workloads. The work advances trust in privacy-preserving cloud services by delivering verifiable privacy guarantees that remain robust in a post-quantum setting and without relying on trusted setups.

Abstract

Privacy concerns in machine learning systems have grown significantly with the increasing reliance on sensitive user data for training large-scale models. This paper introduces a novel framework combining Probably Approximately Correct (PAC) Privacy with zero-knowledge proofs (ZKPs) to provide verifiable privacy guarantees in trustless computing environments. Our approach addresses the limitations of traditional privacy-preserving techniques by enabling users to verify both the correctness of computations and the proper application of privacy-preserving noise, particularly in cloud-based systems. We leverage non-interactive ZKP schemes to generate proofs that attest to the correct implementation of PAC privacy mechanisms while maintaining the confidentiality of proprietary systems. Our results demonstrate the feasibility of achieving verifiable PAC privacy in outsourced computation, offering a practical solution for maintaining trust in privacy-preserving machine learning and database systems while ensuring computational integrity.
Paper Structure (30 sections, 2 theorems, 12 equations, 6 figures, 3 algorithms)

This paper contains 30 sections, 2 theorems, 12 equations, 6 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Zero-Knowledge Proofs
  4. PAC Privacy
  5. Related Works
  6. Methodology
  7. Threat Model
  8. Global Flow
  9. Choice of mechanisms
  10. $K$-means
  11. SVMs
  12. Database statistics
  13. Implementation
  14. Non-Interactive ZK
  15. RISC-Zero
  16. ...and 15 more sections

Key Result

lemma 1

If $\Sigma$ is symmetric definite-positive, then there exists a unique real matrix $A$ that is lower triangular with positive diagonal entries, such that

Figures (6)

  • Figure 1: PAC game
  • Figure 2: Evolution of the centroids after some iterations of the Risc-Zero implementation of $4$-means ($K=4$)
  • Figure 3: Execution $K$-means with different number of samples. The database consists of $1000$ points, and $500$ random points are used for each training.
  • Figure 4: Execution $K$-means with different values of $K$, and dimensions of the points, and number of iterations in the training phase. The database consists of $1000$ points, and $500$ random points are used for each training.
  • Figure 5: Number of Risc0 cycles needed to compute the noise generating algorithm for SVM. Each sample consists of $50$ datapoints are of dimensions $2,6$ and $10$. The SVM algorithm executes $1000$ epochs.
  • ...and 1 more figures

Theorems & Definitions (2)

  • lemma 1: Choleski decomposition
  • lemma 2: Noise generation