Analysis of the Security of BB84 by Model Checking

Quantum Cryptography or Quantum key distribution (QKD) is a technique that allows the secure distribution of a bit string, used as key in cryptographic protocols. When it was noted that quantum computers could break public key cryptosystems based on number theory extensive studies have been undertaken on QKD. Based on quantum mechanics, QKD offers unconditionally secure communication. Now, the progress of research in this field allows the anticipation of QKD to be available outside of laboratories within the next few years. Efforts are made to improve the performance and reliability of the implemented technologies. But several challenges remain despite this big progress. The task of how to test the apparatuses of QKD For example did not yet receive enough attention. These devises become complex and demand a big verification effort. In this paper we are interested in an approach based on the technique of probabilistic model checking for studying quantum information. Precisely, we use the PRISM tool to analyze the security of BB84 protocol and we are focused on the specific security property of eavesdropping detection. We show that this property is affected by the parameters of quantum channel and the power of eavesdropper.

💡 Research Summary

The paper addresses a gap in the practical verification of quantum key distribution (QKD) systems by applying probabilistic model checking to the seminal BB84 protocol. Using the PRISM model‑checking tool, the authors construct a formal Markov Decision Process (MDP) that captures the essential steps of BB84: Alice’s random choice of bits and bases, photon transmission, Bob’s random basis measurement, and the public discussion phase where bases are compared and the error rate is estimated. Two sources of stochasticity are introduced: (1) channel noise, represented by a parameter p_noise that modifies the transition probabilities of the MDP, and (2) an eavesdropper (Eve) who can either perform a full intercept‑resend attack on every photon or a partial attack affecting only a fraction p_eve of the transmitted photons.

Security is expressed as a Probabilistic Computation Tree Logic (PCTL) property: “Whenever Alice and Bob happen to use the same basis, the observed error rate exceeds a predefined threshold θ, then an eavesdropping attempt is detected.” By issuing PRISM queries of the form P=?