On the Fundamental Limits of Hierarchical Secure Aggregation with Dropout and Collusion Resilience

TL;DR

This paper investigates the fundamental communication limits of hierarchical secure aggregation in networks with dropouts and collusion, establishing optimal rates and conditions for feasibility using advanced coding schemes.

Contribution

It introduces a comprehensive rate characterization for secure aggregation in hierarchical networks, including necessary and sufficient conditions and a novel coding scheme for security and efficiency.

Findings

Secure aggregation feasible if surviving users exceed collusion threshold

Optimal first-round communication rates fully characterized

Bounds on relay-to-server rate are tight in certain regimes

Abstract

We study the fundamental communication limits of information-theoretic secure aggregation in a hierarchical network consisting of a server, multiple relays, and multiple users per relay. Communication proceeds over two rounds and two hops, and the system is subject to arbitrary user and relay dropouts. Up to $T$ users may collude with either the server or any single relay. The server aims to recover the sum of the inputs of all users that survive the first round, while learning no additional information beyond the aggregate sum and the inputs of the colluding users. Each relay, however, must learn nothing about the users' inputs except for the information revealed by the inputs of the colluding users under the same collusion model. We introduce a four-dimensional rate tuple that captures the communication cost across rounds and hops. Under a delayed message availability model, we establish necessary and sufficient conditions for feasibility and fully characterize the optimal first-round communication rates. For the second round, we characterize the optimal user-to-relay rate and derive lower and upper bounds on the relay-to-server rate. While these bounds do not coincide in general, they are tight in certain regimes of interest. Our results reveal a sharp threshold phenomenon: secure aggregation is feasible if and only if the total number of surviving users across surviving relays exceeds the collusion threshold. Achievability is established via a vector linear coding scheme with carefully structured correlated randomness exhibiting MDS-like properties, ensuring correctness and information-theoretic security under all possible dropout patterns. Entropic converse bounds are also derived.