  Quantum key distribution (QKD) is a cryptographic system that generates an
information-theoretically secure key shared by two legitimate parties. QKD
consists of two parts: quantum and classical. The latter is referred to as
classical post-processing (CPP). Information reconciliation is a part of CPP in
which parties are given correlated variables and attempt to eliminate the
discrepancies between them while disclosing a minimum amount of information.
The elegant reconciliation protocol known as \emph{Cascade} was developed
specifically for QKD in 1992 and has become the de-facto standard for all QKD
implementations. However, the protocol is highly interactive. Thus, other
protocols based on linear block codes such as Hamming codes, low-density
parity-check (LDPC) codes, and polar codes have been researched. In particular,
reconciliation using LDPC codes has been mainly studied because of its
outstanding performance. Nevertheless, with small block size, the bit error
rate performance of polar codes under successive-cancellation list (SCL)
decoding with a cyclic redundancy check (CRC) is comparable to state-of-the-art
turbo and LDPC codes. In this study, we demonstrate the use of polar codes to
improve the performance of information reconciliation in a QKD system with
small block size. The best decoder for polar codes, a CRC-aided SCL decoder,
requires CRC-precoded messages. However, messages that are sifted keys in QKD
are obtained arbitrarily as a result of a characteristic of the QKD protocol
and cannot be CRC-precoded. We propose a method that allows arbitrarily
obtained sifted keys to be CRC precoded by introducing a virtual string. Thus
the best decoder can be used for reconciliation using polar codes and improves
the efficiency of the protocol.
