Security evaluation of quantum distance-bounding protocols via semidefinite programming

Comparing the security of quantum distance-bounding (QDB) protocols is notoriously difficult because optimal attack strategies depend heavily on the specific structure of each protocol. The authors seek to establish a uniform, rigorous framework to evaluate and compare the security of various QDB protocols against distance-fraud (DF) and mafia-fraud (MF) attacks.

To achieve a uniform comparison, the authors isolate the 'fast phase' of QDB protocols—the timed quantum communication rounds used to verify proximity. They formalize these as one-round games where the adversary's success probability is the primary metric. By leveraging the QDB security framework, they show that for discrete-variable protocols, these games reduce to convex optimization problems. This allows them to use semidefinite programming (SDP) to compute exact optimal attack values. Each mafia-fraud value is accompanied by an explicit attack strategy and a mathematical certificate proving that no better attack exists.

Findings

Across the discrete-variable protocols studied, the best one-round distance-fraud attack consistently succeeds with a probability of 0.5. In contrast, mafia-fraud resistance varies significantly between protocols, allowing for a clear ranking of their security. The authors report the first known one-round attack values for two of the four protocols examined and identify stronger mafia-fraud attacks for the others than previously reported. For continuous-variable protocols, they provide estimates using a calibrated Gaussian model, as exact SDPs are not currently feasible in that setting.

This work provides a standardized, computationally tractable method for benchmarking QDB protocols. By moving from protocol-specific analyses to a unified SDP-based framework, researchers can now obtain exact security bounds rather than relying on loose relaxations. This is particularly important for verifying that new quantum communication designs are truly resistant to relay and impersonation attacks.