Hybrid Poly Commitments for Scalable Binius Zero-Knowledge Proofs in Federated Learning

Federated learning enables collaborative model training without sharing raw data, but practical deployments increasingly require verifiable guarantees that clients compute updates correctly. Zero-knowledge proofs can provide such guarantees, yet existing approaches face scalability limits due to the combined cost of polynomial commitments and FFT-intensive verification. Pairing-based schemes offer compact proofs but incur high prover and verifier overhead, while hash-based constructions reduce algebraic cost at the expense of rapidly growing proof sizes. This paper propose Hybrid-Commit, a polynomial commitment architecture for Binius zero-knowledge proofs that aligns cryptographic primitives with the algebraic structure of federated learning workloads. The scheme separates verification into additive and multiplicative phases: linear aggregation is handled using batched additive commitments optimized for binary fields, while non-linear constraints are verified via hash-based commitments over sparsely selected FFT domains. Proofs from multiple clients are combined through recursive aggregation while preserving non-interactivity. Experiments show near-constant prover time with respect to client count, over 90% reduction in FFT computation and memory usage, sublinear proof-size growth, and under 5% end-to-end training overhead with no impact on model accuracy, indicating that workload-aware commitment design can improve the scalability of zero-knowledge verification in federated learning systems.