  Privacy amplification (PA) is a vital procedure in quantum key distribution
(QKD) to generate the secret key that the eavesdropper has only negligible
information from the identical correcting key for the communicating parties.
With the increase of repeat frequency of discrete-variable QKD (DV-QKD) system,
the processing speed of PA has become the bottle neck restricting DV-QKD's
secure key rate. The PA using Toeplitz-based Hash function is adopted widely
because of its simplicity and parallel feature. Because this algorithm can be
accelerated with Fast Fourier Transform (FFT), an improved scheme PA for
Field-programmable Gate Array (FPGA) based on this is proposed. This paper
improves the custom FFT-based algorithm by reducing the number of computations
and read/write memory operations significantly. The correctness is verified
when implemented in a Xilinx Virtex-6 FPGA. Meanwhile, the processing speed of
improved scheme can nearly double the classical Toeplitz Hashing scheme on FPGA
through the actual experiment.
