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