Secure aggregation of high-dimensional vectors is a fundamental primitive in federated statistics and learning. A two-server system like PRIO enables scalable aggregation of secret-shared vectors. Adversarial clients may attempt to manipulate the aggregation, so it is important to ensure that each contribution (shared with secrets) is well-formed. In this work, we focus on the important and well-studied goal of ensuring that each contribution vector has a bounded Euclidean norm. Existing protocols for ensuring contributions with bounded norms either incur large communication overhead or only allow approximate norm bound verification. We propose the Private Enforcement of Economic Norms (PINE): a new protocol that allows exact norm bound verification with little communication overhead. For high-dimensional vectors, our approach has a communication overhead of a few percent, compared to the 16- to 32-fold overhead of previous approaches.
