PryML: Privacy-Preserving Federated Learning under Data Heterogeneity using CKKS Encryption

Abstract

Federated Learning enables collaborative model training across distributed clients without centralizing raw data, offering privacy advantages for sensitive domains such as healthcare and finance. However, recent work has shown that standard federated protocols remain vulnerable to gradient inversion attacks, where a malicious aggregator can reconstruct private training samples from shared model updates. Homomorphic Encryption provides a cryptographic solution by allowing computation on encrypted data, but existing encrypted federated systems have not been rigorously evaluated under realistic data heterogeneity, a condition where clients hold non-identically distributed data. We present PryML, a privacy-preserving federated learning framework that integrates CKKS approximate homomorphic encryption with the Flower federated learning ecosystem. We provide a formal convergence analysis proving that CKKS encryption noise contributes additively rather than multiplicatively to heterogeneity-induced convergence error, meaning encryption does not amplify the degradation caused by skewed data distributions. Experimental validation on the MNIST dataset with 10 clients over 20 communication rounds demonstrates 99.0 percent accuracy under uniform data distribution and 98.0 percent under extreme label skew with a heterogeneity index of approximately 0.69, maintaining less than 0.1 percentage point gap compared to unencrypted baselines across all tested conditions. Security evaluation confirms resistance to gradient inversion attacks, reducing reconstruction similarity from 40 percent to 2.1 percent, with ciphertext entropy reaching 7.95 bits per byte. PryML provides practical encrypted federated learning for privacy-critical applications requiring regulatory compliance.