Complexity of distance fraud attacks in graph-based distance bounding

TL;DR

This paper analyzes the complexity of distance fraud attacks in graph-based distance bounding protocols, proving the problem's NP-hardness and providing a more efficient algorithm for a specific protocol variant.

Contribution

It proves the NP-hardness of the distance fraud security problem in graph-based DB protocols and introduces a more efficient algorithm for a tree-based approach.

Findings

NP-hardness of the MFS problem in graph-based DB protocols

Improved algorithm reduces complexity from exponential to manageable levels

Suggests real-world protocols may be more secure than theoretical models

Abstract

Distance bounding (DB) emerged as a countermeasure to the so-called \emph{relay attack}, which affects several technologies such as RFID, NFC, Bluetooth, and Ad-hoc networks. A prominent family of DB protocols are those based on graphs, which were introduced in 2010 to resist both mafia and distance frauds. The security analysis in terms of distance fraud is performed by considering an adversary that, given a vertex labeled graph $G = (V, E)$ and a vertex $v \in V$, is able to find the most frequent $n$-long sequence in $G$ starting from $v$ (MFS problem). However, to the best of our knowledge, it is still an open question whether the distance fraud security can be computed considering the aforementioned adversarial model. Our first contribution is a proof that the MFS problem is NP-Hard even when the graph is constrained to meet the requirements of a graph-based DB protocol. Although this result does not invalidate the model, it does suggest that a \emph{too-strong} adversary is perhaps being considered (i.e., in practice, graph-based DB protocols might resist distance fraud better than the security model suggests.) Our second contribution is an algorithm addressing the distance fraud security of the tree-based approach due to Avoine and Tchamkerten. The novel algorithm improves the computational complexity $O(2^{2^n+n})$ of the naive approach to $O(2^{2n}n)$ where $n$ is the number of rounds.