Distance-bounding protocols are security protocols with a time measurement phase used to detect relay attacks, whose security is typically measured against mafia-fraud and distance-fraud attacks. A prominent subclass of distance-bounding protocols, known as lookup-based protocols, use simple lookup operations to diminish the impact of the computation time in the distance calculation. Independent results have found theoretical lower bounds [Formula presented] and [Formula presented], where n is the number of time measurement rounds, on the security of lookup-based protocols against mafia and distance-fraud attacks, respectively. However, it is still an open question whether there exists a protocol achieving both security bounds. This article closes this question in two ways. First, we prove that the two lower bounds are mutually exclusive, meaning that there does not exist a lookup-based protocol that provides optimal protection against both types of attacks. Second, we provide a lookup-based protocol that approximates those bounds by a small constant factor. Our experiments show that, restricted to a memory size that linearly grows with n, our protocol offers strictly better security than previous lookup-based protocols against both types of fraud.

peer reviewed