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.

翻译：高维向量的安全聚合是联邦统计与学习中的基本原语。基于双服务器系统（如PRIO）可实现秘密共享向量的可扩展聚合。恶意客户端可能试图操纵聚合结果，因此确保每个（秘密共享）贡献的合规性至关重要。本研究聚焦于一个重要的经典目标——确保每个贡献向量具有有界欧几里得范数。现有协议在保证范数有界贡献时，要么产生较大的通信开销，要么仅允许对范数边界进行近似验证。我们提出私有廉价范数执行（PINE）协议：一种能以极低通信开销实现精确范数验证的新方案。对于高维向量，我们的方法通信开销仅为几个百分点，而先前方法的开销高达16-32倍。