Network outages are an important issue for Internet Service Providers (ISPs) and, more generally, online service providers, as they can result in major financial losses and negatively impact relationships with their customers. Troubleshooting network outages is a complex and time-consuming process. Network administrators are overwhelmed with large volumes of monitoring data and are limited to using very basic tools for debugging, e.g., ping and traceroute. Intelligent correlation of measurements from different Internet locations is very useful for analyzing the root cause of outages. However, correlating measurements of user traffic across domains is largely avoided as it raises privacy concerns. A possible solution is secure multi-party computation (MPC), a set of cryptographic methods that enable a number of parties to aggregate data in a privacy-preserving manner. In this work, we describe a novel system that helps diagnose network outages by correlating passive measurements from multiple ISPs in a privacy-preserving manner. We first show how MPC can be used to compute the scope (local, global, or semi-global) and severity (number of affected hosts) of network outages. To meet near-real-time monitoring guarantees, we then present an efficient protocol for MPC multiset union that uses counting Bloom filters (CBF) to drastically accelerate MPC comparison operations. Finally, we demonstrate the utility of our scheme using real-world traffic measurements from a national ISP and we discuss the trade-offs of the CBF-based computation.