Quantum proof and high-speed privacy amplification for quantum key distribution

Privacy amplification (PA) is a vital step in the postprocessing stage of quantum key distribution, which can extract a secure key from a source partially leaked to the environment. We propose a PA scheme that uses the square hash (SQH)--modular arithmetic hash (MH) function. In consideration of a potential quantum attacker, we use the trace distance as a metric to measure the closeness between two classical-quantum states. We transform a raw key state to a processed state using this scheme and derive the trace distance between the processed state and the ideal target state. It is proven that the trace distance can be reached as small as desired. Additionally, our approach accelerates the SQH-MH function through the number-theoretic transform, reducing the computational complexity to $O(n\mathrm{log}n)$. On the basis of a CPU, a maximum throughput rate of 1.06 Gbit/s is achieved, and the results show that our algorithm demonstrates good stability of the throughput rate when handling tasks with different compression ratios.