Privacy-Preserving Federated Learning with Verifiable Fairness Guarantees

TL;DR

This work addresses the pressing need to perform fairness verification in privacy-preserving federated learning. It introduces CryptoFair-FL, a protocol that fuses additively homomorphic encryption with secure MPC to compute and verify demographic parity and equalized odds while preserving data privacy, and it formalizes $(\dparam,\deltap)$-differential privacy guarantees. A batched, $\mathcal{O}(n \log n)$-complexity verification scheme, along with information-theoretic lower bounds and adaptive composition, characterizes the privacy-fairness tradeoffs and near-optimality. Extensive experiments on healthcare, finance, CelebA, and synthetic FedFair-100 datasets demonstrate substantial fairness improvements with modest overhead and strong defenses against attribute inference attacks, offering a practical path to regulated, accountability-ready fairness in federated systems.

Abstract

Federated learning enables collaborative model training across distributed institutions without centralizing sensitive data; however, ensuring algorithmic fairness across heterogeneous data distributions while preserving privacy remains fundamentally unresolved. This paper introduces CryptoFair-FL, a novel cryptographic framework providing the first verifiable fairness guarantees for federated learning systems under formal security definitions. The proposed approach combines additively homomorphic encryption with secure multi-party computation to enable privacy-preserving verification of demographic parity and equalized odds metrics without revealing protected attribute distributions or individual predictions. A novel batched verification protocol reduces computational complexity from BigO(n^2) to BigO(n \log n) while maintaining (\dparam, \deltap)-differential privacy with dparam = 0.5 and deltap = 10^{-6}. Theoretical analysis establishes information-theoretic lower bounds on the privacy cost of fairness verification, demonstrating that the proposed protocol achieves near-optimal privacy-fairness tradeoffs. Comprehensive experiments across four benchmark datasets (MIMIC-IV healthcare records, Adult Income, CelebA, and a novel FedFair-100 benchmark) demonstrate that CryptoFair-FL reduces fairness violations from 0.231 to 0.031 demographic parity difference while incurring only 2.3 times computational overhead compared to standard federated averaging. The framework successfully defends against attribute inference attacks, maintaining adversarial success probability below 0.05 across all tested configurations. These results establish a practical pathway for deploying fairness-aware federated learning in regulated industries requiring both privacy protection and algorithmic accountability.

Figures (5)

• Figure 1: CryptoFair-FL system architecture. Institutional participants $P_1, \ldots, P_n$ maintain local datasets $D_i$, compute encrypted statistics $\mathsf{Enc}(s_i)$, and transmit ciphertexts to the Secure Aggregator. The Fairness Verifier computes demographic parity ($\hat{\Delta}_{\text{DP}}$) and equalized odds ($\hat{\Delta}_{\text{EO}}$) violations. Dashed arrow indicates fairness feedback for model adjustment.
• Figure 2: Privacy-fairness tradeoff analysis. The theoretical lower bound from Theorem \ref{['thm:lower_bound']} establishes fundamental limits. CryptoFair-FL achieves near-optimal tradeoffs, with empirical measurements across datasets confirming theoretical predictions within 20% margin.
• Figure 3: Computational scaling analysis on log-log axes. Naïve homomorphic encryption exhibits quadratic growth $\mathcal{O}(n^2)$, while CryptoFair-FL demonstrates sub-quadratic $\mathcal{O}(n \log n)$ complexity. Reference lines confirm theoretical predictions.
• Figure 4: Empirical fairness-privacy tradeoff across benchmark datasets. Smaller privacy budget $\varepsilon$ (stronger privacy protection) increases noise in fairness verification, resulting in higher residual fairness violations. The tradeoff curves follow the theoretical prediction from Theorem \ref{['thm:accuracy']}.
• Figure 5: Training convergence for ICU mortality prediction across the 30-hospital MIMIC-IV federation. Model utility (AUROC) and fairness ($\Delta_{\text{DP}}$) improve simultaneously. The demographic parity violation decreases from 0.248 to 0.031, satisfying the 0.05 fairness threshold by round 60.

Theorems & Definitions (22)

• Definition 1: Demographic Parity Violation
• Definition 2: Equalized Odds Violation
• Definition 3: Additively Homomorphic Encryption
• Definition 4: Differential Privacy
• Lemma 1: Batching Complexity Reduction
• proof : Proof Sketch
• Theorem 2: Privacy Lower Bound for Fairness Verification
• proof : Proof Sketch
• Proposition 3: Composition for Fairness Verification
• Definition 5: Attribute Inference Attack