HaloMed: Efficient Recursive Zero-Knowledge Proofs Using Pasta Curves for Privacy-Preserving Healthcare Data Verification

Proofs Zero-Knowledge Succinct Non-Interactive Argument of Knowledge (ZK-SNARK) have emerged as a promising solution for safeguarding privacy in healthcare data systems.However, existing implementations still face challenges related to trusted setup requirements and computational inefficiencies in recursive proof composition.This paper presents HaloMed, an innovative solution implementing the Halo2 proof system without trusted setup for healthcare data verification.By leveraging the Pasta curves (Pallas/Vesta) in a 2-cycle configuration, HaloMed recursive composition achieves O(1) constant constant verification complexity regardless of batch size-enabling scalability from individual records to 10,000-record batches without performance degradation.The system employs Inner Product Arguments (IPA) to eliminate trusted setup and implements a Merkle tree structure for recursive proof aggregation.Experimental evaluation demonstrates that through recursive proof aggregation, HaloMed achieves 890 ms proof generation for large datasets with 8× throughput improvement over individual proofs, while maintaining constant 15 ms verification and 82% proof size reduction-enabling real-time healthcare operations at scale.HaloMed addresses the limitations of existing ZK-SNARK systems-namely, trusted setup requirements (Groth16, PLONK), recursive composition inefficiency, and performance bottlenecks.A five-layer architecture enforces Health Insurance Portability and Accountability Act compliance through cryptographic guarantees of minimum disclosure and role-based access control without trusted intermediaries.The main contributions include the first Halo2 implementation in healthcare, recursive proof composition via Pasta curves enabling linear-time aggregation of up to 10,000 medical records with constant O(1) verification, and practical performance suitable for real-time operations at scale.This system paves the way for widespread adoption of zero-knowledge technology in digital healthcare ecosystems.