# On the Communication–Key Rate Region of Hierarchical Vector Linear Secure Aggregation

## TL;DR

This paper explores secure aggregation in a two-hop hierarchical network for federated learning, ensuring privacy while optimizing communication rates.

## Contribution

The paper introduces a novel hierarchical secure aggregation framework with optimal communication rates and explicit linear coding.

## Key findings

- Hierarchical architectures achieve optimal communication rates for secure aggregation.
- The proposed coding scheme reduces the server-side masking burden significantly.
- Information-theoretic bounds are derived and matched with an achievable scheme.

## Abstract

Motivated by heterogeneous data distributions and task-dependent aggregation requirements in federated learning, we study information-theoretic secure aggregation of linear functions over a two-hop hierarchical network. The system comprises an aggregation server, an intermediate layer of U relays, and UV users, where each relay serves a disjoint cluster of V users. Each relay observes all uplink transmissions within its cluster and forwards a coded message to the server. The server is authorized to compute a prescribed linear function F of the users’ inputs with zero error, while being prevented from learning any additional information about an unauthorized linear function G. Moreover, each relay must obtain no information about any non-trivial linear function Bu of the inputs in its own cluster. We define the communication rates on both hops as the number of transmitted symbols per input symbol. By deriving matching information-theoretic converse and achievability bounds, we fully characterize the optimal communication rates and propose an explicit linear coding scheme that achieves the resulting optimal region. Our results demonstrate that hierarchical architectures can attain optimal communication rates while substantially reducing the server-side masking burden, thereby enabling scalable secure aggregation of authorized linear functions.