Hidden-Markov-model-based calibration-attack recognition for continuous-variable quantum key distribution

The quadrature values of a continuous-variable quantum key distribution system could be disturbed by many interferences in practice, such as environmental disturbance, imperfect devices, and attacks. It's hard to identify which values were affected by the attack by directly observing the measured quadrature values. In order to determine the occurrence of a calibration attack without increasing the complexity of the system, we propose a hidden-Markov model (HMM) to learn the correspondence between the interferences and the measurement results of the receiver, which regards different interferences of the system as the hidden states and the processed measurement values as the observation sequence of the HMM. The legitimate parties can recognize calibration attack by using the proposed methods without any additional devices and complex excess noise evaluation procedure. The paper addresses the learning process and recognition mechanism of the HMM for calibration attack, verifies the effectiveness of this proposal based on a group of samples that consist of normal and abnormal measurement values, and discusses the excess noise of the system after attack recognition. Results show that the eavesdropping by Eve can be exactly recognized with a precision of $98.735%$ when the attack ratio is $50%$ and transmission distance $L=25\phantom{\rule{4pt}{0ex}}\mathrm{km}$. Meanwhile, the false positive rate is as low as $1.28%$ and the false negative rate reaches $0.08%$ under the same conditions.