What is homomorphic encryption, and how does it relate to federated learning?

Homomorphic encryption (HE) is a cryptographic method that enables computations on encrypted data without decrypting it first. Unlike traditional encryption, which requires data to be decrypted before processing, HE allows mathematical operations to be performed directly on ciphertext. The result of these operations, when decrypted, matches the outcome of performing the same operations on the original plaintext. For example, if you encrypt the numbers 3 and 5 using HE, add them while encrypted, and then decrypt the result, you’d get 8. This preserves data privacy during processing, making HE useful in scenarios where sensitive data must remain encrypted even while being used.

In federated learning (FL), multiple devices or servers collaboratively train a machine learning model without sharing raw data. Instead, participants send model updates (like gradients or parameters) to a central server for aggregation. HE enhances FL by ensuring these updates remain encrypted throughout the process. For instance, imagine a healthcare FL system where hospitals train a model on patient data. Using HE, each hospital encrypts its model updates before sending them. The server aggregates these encrypted updates, performs calculations (e.g., averaging gradients), and returns an encrypted global model. Only the participants can decrypt the final model, preventing the server or third parties from accessing sensitive intermediate data. This addresses privacy risks in FL, such as potential leakage of training details from model updates.

However, integrating HE into FL introduces practical challenges. First, HE operations are computationally expensive, especially fully homomorphic encryption (FHE), which supports arbitrary computations. This can slow down training, making partially homomorphic encryption (PHE)—limited to operations like addition or multiplication—more feasible for specific FL tasks. Second, developers must align encryption schemes with the FL framework’s mathematical operations. For example, averaging gradients in FL requires additive homomorphism, which PHE can handle efficiently. Tools like Microsoft SEAL or PySyft provide HE libraries optimized for such use cases, but implementation requires expertise in both cryptography and distributed systems. Despite these hurdles, HE remains a valuable tool for strengthening privacy in FL, particularly in regulated industries like finance or healthcare.