Post-collusion security and distance bounding

Verification of cryptographic protocols is traditionally built upon the assumption that participants have not revealed their long-term keys. However, in some cases, participants might collude to defeat some security goals, without revealing their long-term secrets. We develop a model based on multiset rewriting to reason about collusion in security protocols. We introduce the notion of post-collusion security, which verifies security properties claimed in sessions initiated after the collusion occurred. We use post-collusion security to analyse terrorist fraud on protocols for securing physical proximity, known as distance-bounding protocols. In a terrorist fraud attack, agents collude to falsely prove proximity, whilst no further false proximity proof can be issued without further collusion. Our definitions and the Tamarin prover are used to develop a modular framework for verification of distance-bounding protocols that accounts for all types of attack from literature. We perform a survey of over 25 protocols, which include industrial protocols such as Mastercard's contactless payment PayPass and NXP's MIFARE Plus with proximity check. For the industrial protocols we confirm attacks, propose fixes, and deliver computer-verifiable security proofs of the repaired versions.