Interdomain routing involves coordination among mutually distrustful parties, leading to the requirements that BGP provide policy autonomy, flexibility, and privacy. BGP provides these properties via the distributed execution of policy-based decisions during the iterative route computation process. This approach has poor convergence properties, makes planning and failover difficult, and is extremely difficult to change. To rectify these and other problems, we propose a radically different approach to interdomain-route computation, based on secure multi-party computation (SMPC). Our approach provides stronger privacy guarantees than BGP and enables the deployment of new policy paradigms. We report on an initial exploration of this idea and outline future directions for research.