Study on the security of the authentication scheme with key recycling in QKD

In quantum key distribution (QKD), the information theoretically secure authentication is necessary to guarantee the integrity and authenticity of the exchanged information over the classical channel. In order to reduce the key consumption, the authentication scheme with key recycling (KR), in which a secret but fixed hash function is used for multiple messages while each tag is encrypted with a one-time pad (OTP), is preferred in QKD. Based on the assumption that the OTP key is perfect, the security of the authentication scheme has be proved. However, the OTP key of authentication in a practical QKD system is not perfect. How the imperfect OTP affects the security of authentication scheme with KR is analyzed thoroughly in this paper. In a practical QKD, the information of the OTP key resulting from QKD is partially leaked to the adversary. Although the information leakage is usually so little to be neglected, it will lead to the increasing degraded security of the authentication scheme as the system runs continuously. Both our theoretical analysis and simulation results demonstrate that the security level of authentication scheme with KR, mainly indicated by its substitution probability, degrades exponentially in the number of rounds and gradually diminishes to zero.