Security of a control key in quantum key distribution

Quantum key distribution (QKD) schemes rely on the randomness to exchange secret keys between two parties. A control key to generate the same (pseudo)-randomness for the key exchanging parties increases the key exchange rate. However, the use of pseudo randomness where true randomness is required makes a classical system vulnerable to the known plain-text attack. Contrary to the belief of unavailability of this attack in QKD, we show that this attack is actually possible whenever a control key is employed. In this paper, we show that it is possible to make use of the uncertainty principle to not only avoid this attack, but also remove the hazards of photon-number splitting attack in quantum setting. We define the secrecy of control key based on the guessing probability, and propose a scheme to achieve this defined secrecy. We show the general applicability of our framework on the most common QKD schemes.