An Algorithm for Persistent Homology Computation Using Homomorphic Encryption

This research presents a new method for performing topological data analysis (TDA, a technique that finds shape-based patterns in complex data) on encrypted information using homomorphic encryption (HE, a type of encryption that lets computers process data without decrypting it first). The authors adapted a fundamental TDA algorithm called boundary matrix reduction to work with encrypted data, proved it works correctly mathematically, and tested it using the OpenFHE framework to show it functions properly on real encrypted data.