Privacy-preserving federated learning enables a population of distributed clients to jointly learn a shared model while keeping client training data private, even from an untrusted server. Prior works do not provide efficient solutions that protect against collusion attacks in which parties collaborate to expose an honest client's model parameters. We present an efficient mechanism based on oblivious distributed differential privacy that is the first to protect against such client collusion, including the "Sybil" attack in which a server preferentially selects compromised devices or simulates fake devices. We leverage the novel privacy mechanism to construct a secure federated learning protocol and prove the security of that protocol. We conclude with empirical analysis of the protocol's execution speed, learning accuracy, and privacy performance on two data sets within a realistic simulation of 5,000 distributed network clients.