Information-Theoretic Decentralized Secure Aggregation with User Dropouts

2026-05-21

AI Summary

This work addresses the problem of securely aggregating private inputs from at least $U$ active users in a decentralized network without a central server, where up to $T$ users may collude and arbitrary users may drop out. The authors propose a two-round communication protocol that fully characterizes the optimal communication rate region under this setting. They establish that the problem is infeasible when $U \leq T+1$, and prove a lower bound of $1/(U - T - 1)$ on the second-round communication rate, which depends solely on the effective redundancy $U - T - 1$. By constructing a secret-sharing scheme based on $(T+1)$-private MDS matrices, the protocol achieves information-theoretic security and robustness against user dropouts. The proposed scheme is shown to be optimal, achieving rates $R_1 \geq 1$ and $R_2 \geq 1/(U - T - 1)$, with optimality confirmed via a tight converse bound.

Abstract

This paper investigates the fundamental limits of information-theoretic decentralized secure aggregation (DSA) with user dropouts. We consider a fully decentralized network where $K$ users communicate over broadcast channels without a trusted aggregation server. Each user holds a private input and aims to recover the sum of the surviving users' inputs (users may drop) while ensuring that no additional information about individual inputs is revealed to that user, even if it can collude with other users. A two-round communication protocol is considered, where we assume at least $U$ users survive and each user can collude with at most $T$ other users. For this setting, the optimal communication rate region is fully characterized: we show that DSA is infeasible if $U\le T+1$; otherwise, the optimal rate region is given by $R_1\geq 1$ and $R_2\geq \frac{1}{U-T-1}$, where $R_1$ and $R_2$ denote the first- and second-round communication rates, respectively. The proposed aggregation scheme is based on correlated secret keys constructed from $(T+1)$-private maximum distance separable (MDS) matrices, which simultaneously provide robustness against user dropouts and security against collusion. We also derive tight converse bounds that establish the optimality of the proposed scheme. Our result shows that the optimal second-round communication rate depends only on the effective redundancy level $U-T-1$ regardless the total number of users.

Problem

• secure aggregation
• user dropouts
• decentralized network
• information-theoretic security
• collusion resistance

Innovation

• decentralized secure aggregation
• user dropouts
• collusion security
• MDS codes
• information-theoretic privacy