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础原语。以PRIO为代表的双服务器系统能够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（秘密共享的）贡献向量格式正确至关重要。本研究聚焦于确保每个贡献向量具有有界欧几里得范数这一重要且被深入研究的课题。现有确保贡献向量范数有界的协议要么产生较大的通信开销，要么仅支持范数边界的近似验证。我们提出私有低成本范数强制协议（PINE）：该新协议能以极低的通信开销实现精确的范数验证。对于高维向量，相较于先前方法16-32倍的通信开销，本方案的通信开销仅需增加几个百分点。