Multi-Server Secure Aggregation with Arbitrary Collusion and Heterogeneous Security Constraints

TL;DR

This paper investigates the fundamental limits of multi-server secure aggregation with heterogeneous security constraints and arbitrary collusion, providing tight bounds and schemes across various regimes.

Contribution

It introduces a general model for secure aggregation with diverse security requirements and characterizes the optimal communication and key rates, extending prior homogeneous security results.

Findings

Characterized communication rates for all parameter regimes.

Determined minimum key rates in most regimes.

Established tight bounds and achievable schemes in broad settings.

Abstract

We study the fundamental limits of multi-server secure aggregation over a two-hop network where multiple servers, each connected to a disjoint subset of users, jointly compute the sum of all users' inputs. The goal is to ensure that no server can infer any information about prescribed subsets of inputs beyond the desired aggregate, even when colluding with an arbitrary subset of users. Existing works largely focus on homogeneous security requirements, where all inputs are protected against colluding sets up to a given size. Such formulations are insufficient to capture more general scenarios in which different subsets of inputs may require protection against different collusion patterns. In this paper, we consider a general model with heterogeneous security requirements and arbitrary user collusion. We characterize the communication rates for all parameter regimes, and determine the minimum key rate required for secure aggregation in most regimes. In particular, we establish tight information-theoretic lower bounds and matching achievable schemes in a broad class of regimes. For the remaining regime, we derive a general lower bound together with an achievable scheme that attains it within a bounded gap. Our results reveal how the interplay between network topology and heterogeneous security constraints fundamentally determines the communication and key generation requirements, and generalize existing results on secure aggregation.