FM3H-MH: An Efficient Large-Scale Privacy Amplification Scheme for Quantum Key Distribution

Privacy amplification (PA) is a critical process in quantum key distribution (QKD) systems, essential for eliminating information leakage to eavesdroppers and extracting unconditionally secure keys. In practical high-speed QKD systems, a large input size enables the PA scheme to approach the asymptotic limit of the secure-key rate. Concurrently, the throughput of the PA scheme must keep pace with the GHz-level clock rates of modern QKD systems to prevent it from becoming a systemic bottleneck. To globally optimize these objectives, this paper proposes a scalable and highly efficient PA scheme combining a novel δ-almost-universal hash family (FM3H) with modular arithmetic hashing (MH), and proves the security of this hybrid scheme, within the information-theoretic and quantum-side framework. The proposed scheme achieves a throughput of 283 Mbps on a common mobile CPU with an input size of 1010 bits. NIST statistical tests and avalanche-effect measurements are reported as characterizations of the statistical properties of the output sequences. To our knowledge, this work presents the first FPGA-based implementation of a modular hashing-based PA scheme, thereby breaking the dependence of modular hashing schemes on general software platforms. In DV-QKD systems, the FPGA-based scheme achieves a throughput of 1.706 Gbps while maintaining low resource overhead.