Zero-Knowledge Federated Learning with Lattice-Based Hybrid Encryption for Quantum-Resilient Medical AI

Federated learning (FL) has become a foundational paradigm for multi-institutional medical AI, allowing hospitals and research centers to jointly train diagnostic models without exchanging patient records. This privacy promise, however, is increasingly contested: a malicious or honest-but-curious server can launch model inversion attacks (MIAs) that reconstruct private patient images directly from shared model updates, and recent scalable, closed-form attacks penetrate even secure aggregation at clinically realistic batch sizes. Existing defenses face an unsatisfactory dilemma. Gradient-perturbation methods such as differential privacy and pruning trade away the diagnostic accuracy on which clinical reliability depends, while cryptographic protocols add system complexity yet still leave updates exposed to these scalable attacks. We propose Aegis, a principled client-side defense that breaks this dilemma without perturbing patient data or modifying the FL protocol. Our key insight is that the success of every known MIA is fundamentally bounded by the local batch size relative to the model's leakage capacity; once this limit is exceeded, distinct samples collide and reconstructions collapse into indistinguishable mixtures. Aegis turns this universal bottleneck into a defense: each client superimposes onto its real update a masking gradient computed on locally synthesized, task-relevant data, deliberately pushing the effective batch beyond the attack's recovery capacity. We complement the design with theoretical convergence guarantees under standard convex assumptions and evaluate Aegis on MNIST, CIFAR-10, and three MedMNIST modalities (chest X-ray, abdominal CT, colon pathology). Aegis neutralizes three state-of-the-art MIAs while preserving model utility and incurring only modest overhead, offering a practical privacy primitive for medical FL.

Encrypted training relies on keeping server-side updates low-degree. This constraint traditionally excludes models whose weights inhabit a compact Lie group (notably variational quantum circuits, where every trainable weight is an $\mathrm{SU(2)}$ rotation). Expressed in Euler angles or discrete alphabets, these updates appear transcendental, historically demanding prohibitive costs: one client--server round per gate, or upwards of $25{,}000$ operations per weight. This penalty is strictly an artefact of coordinates. In the unit-quaternion (spin) chart, group composition is exactly bilinear (degree two, with coefficients in $\{-1,0,+1\}$). Consequently, encrypted rotation updates cost one multiplicative level and federated averaging costs zero in any levelled homomorphic scheme, completely eliminating bootstrapping. This implementation-independent algebraic property is confirmed across two cryptographic backends, introducing only $0.0$ and $-2.0\times10^{-12}$ rad of aggregation error. Leveraging this reduction yields a non-interactive protocol for encrypted federated training of hybrid quantum--classical networks. It includes correctness proofs for aggregation and sign handling, plus a compilation lemma proving parameterised entanglers add only constant-factor overhead without altering the depth class. Empirically, a paired five-seed study confirms zero measurable utility tax ($Δ=+9\times10^{-6}$ MSE, $p=0.92$), and a noise-budget ablation falsifies the hypothesis that encryption noise regularises. These convergence trends replicate across datasets and scale to $20$ clients. Finally, hardware validation on a $156$-qubit processor achieves $0.9918$ fidelity against a $0.99957$ unencrypted control.

Federated learning (FL) is vulnerable to multi-level attacks. However, existing methods address them separately, leaving FL exposed to data leakage, unauthorized reuse, and malicious gradient manipulation. In this work, we propose an FL framework that couples keyed context-provenance watermarking with verifiable lattice-based secure aggregation of Real-World Anchored Watermarking and Lattice-Based Zero-Knowledge Secure Aggregation. At the data layer, we propose a Kerckhoffs-compliant scheme that utilizes Physical Anchor Metadata (PAM) to ensure data provenance. PAM is defined as a context-provenance token derived from trusted infrastructure data (time, location, and server ID) and then subjected to a keyed HMAC-SHA-256 transformation to produce a watermark payload that cannot be generated without the client's secret key. We further design FMGAN, a GAN-based robust image watermarking framework that embeds this transformed payload using a feature fusion module and a Mamba-guided linear attention mechanism. At the computation layer, we adopt a lattice-based zero-knowledge secure aggregation (LZKSA) protocol that verifies key correctness, L2 norm bounds, and cosine similarity constraints over committed gradients without revealing private updates. The RLWE-based design guarantees post-quantum security. Extensive experiments validate the complementary protection of the two layers under composite attack scenarios. To our knowledge, no prior verification workflow has jointly evaluated both layers in a hybrid, end-to-end trustworthy FL framework.