Gracefully Degrading Fair Exchange with Security Modules

The fair exchange problem is key to trading electronic items in systems of mutually untrusted parties. In modern variants of such systems, each party is equipped with a security module. The security modules trust each other but can only communicate by exchanging messages through their untrusted host parties, that could drop those messages. We describe a synchronous algorithm that ensures deterministic fair exchange if a majority of parties are honest, which is optimal in terms of resilience. If there is no honest majority, our algorithm degrades gracefully: it ensures that the probability of unfairness can be made arbitrarily low. Our algorithm uses, as an underlying building block, an early-stopping subprotocol that solves, in a general omission failure model, a specific variant of consensus we call biased consensus. Interestingly, this modular approach combines concepts from both cryptography and distributed computing, to derive new results on the classical fair exchange problem.