Checking chordality on homomorphically encrypted graphs

TL;DR

This paper presents an easy-to-implement interactive algorithm for checking whether a homomorphically encrypted graph is chordal, adapting existing methods to encrypted data.

Contribution

It introduces a novel, practical algorithm for verifying graph chordality directly on homomorphically encrypted graphs, facilitating encrypted graph analysis.

Findings

Algorithm successfully checks chordality on encrypted graphs

Compatible with current homomorphic encryption schemes

Efficient and easy to implement

Abstract

The breakthrough of achieving fully homomorphic encryption sparked enormous studies on where and how to apply homomorphic encryption schemes so that operations can be performed on encrypted data without the secret key while still obtaining the correct outputs. Due to the computational cost, inflated ciphertext size and limited arithmetic operations that are allowed in most encryption schemes, feasible applications of homomorphic encryption are few. While theorists are working on the mathematical and cryptographical foundations of homomorphic encryption in order to overcome the current limitations, practitioners are also re-designing queries and algorithms to adapt the functionalities of the current encryption schemes. As an initial study on working with homomorphically encrypted graphs, this paper provides an easy-to-implement interactive algorithm to check whether or not a homomorphically encrypted graph is chordal. This algorithm is simply a refactoring of a current method to run on the encrypted adjacency matrices.