The growing relevance of Internet eXchange Points (IXPs), where an increasing number of networks exchange routing information, poses fundamental questions regarding the privacy guarantees of confidential business information. To facilitate the exchange of routes among their members, IXPs provide Route Server (RS) services to dispatch the routes according to each member's export policies. Nowadays, to make use of RSes, these policies must be disclosed to the IXP. This state of affairs raises privacy concerns among network administrators and even deters some networks from subscribing to RS services. We design SIXPACK (which stands for "Securing Internet eXchange Points Against Curious onlooKers"), a RS service that leverages Secure Multi-Party Computation (SMPC) techniques to keep export policies confidential, while maintaining the same functionalities as today's RSes. We assess the effectiveness and scalability of our system by evaluating our prototype implementation and using traces of data from one of the largest IXPs in the world.