PINE: Efficient Verification of a Euclidean Norm Bound of a Secret-Shared Vector

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.