Network virtualization is one of the promising technologies that can increase flexibility, diversity, and manageability of networks. Building optimal virtual networks across multiple domains is getting much attention, but existing studies were based on an unrealistic assumption, that is, providers' private information can be disclosed; as is well known, providers never actually do that. In this paper, we propose a new method that solves this multi-domain problem without revealing providers' private information. Our method uses an advanced secure computation technique called multi-party computation (MPC). Although MPC enables existing unsecured methods to optimize virtual networks securely, it requires very large time to finish the optimization due to the MPC's complex distributed protocols. Our method, in contrast, is designed to involve only a small number of MPC operations to find the optimal solution, and it allows providers to execute a large part of the optimization process independently without heavy distributed protocols. Evaluation results show that our method is faster than an existing method enhanced with MPC by several orders of magnitude. We also unveil that our method has the same level of embedding cost.