# PINE: Efficient Norm-Bound Verification for Secret-Shared Vectors

arXiv: https://arxiv.org/abs/2311.10237 · HTML: https://mlsanity.com/paper/2311.10237/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Nov 2023.

## Built on by (most cited first, 1 of 1)

- [Private Vector Mean Estimation in the Shuffle Model: Optimal Rates Require Many Messages](https://mlsanity.com/paper/2404.10201/) (2024)

## Abstract (arXiv)

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.