An Algorithm for Persistent Homology Computation Using Homomorphic Encryption

TL;DR

This paper introduces a novel algorithm that enables the computation of persistent homology, a key topological data analysis tool, directly on encrypted data using homomorphic encryption, facilitating privacy-preserving data analysis.

Contribution

It presents the first algorithm for computing persistent homology on encrypted data, integrating topological data analysis with homomorphic encryption for secure analysis.

Findings

First implementation of PH computation on encrypted data

Demonstrates feasibility of privacy-preserving topological analysis

Lays groundwork for secure TDA in sensitive data applications

Abstract

Topological Data Analysis (TDA) offers a suite of computational tools that provide quantified shape features in high dimensional data that can be used by modern statistical and predictive machine learning (ML) models. In particular, persistent homology (PH) takes in data (e.g., point clouds, images, time series) and derives compact representations of latent topological structures, known as persistence diagrams (PDs). Because PDs enjoy inherent noise tolerance, are interpretable and provide a solid basis for data analysis, and can be made compatible with the expansive set of well-established ML model architectures, PH has been widely adopted for model development including on sensitive data, such as genomic, cancer, sensor network, and financial data. Thus, TDA should be incorporated into secure end-to-end data analysis pipelines. In this paper, we take the first step to address this challenge and develop a version of the fundamental algorithm to compute PH on encrypted data using homomorphic encryption (HE).