Information-Theoretic Decentralized Secure Aggregation with Passive Collusion Resilience

Abstract

In decentralized federated learning (FL), multiple clients collaboratively learn a shared machine learning (ML) model by leveraging their privately held datasets distributed across the network, through interactive exchange of the intermediate model updates. To ensure data security, cryptographic techniques are commonly employed to protect model updates during aggregation. Despite growing interest in secure aggregation, existing works predominantly focus on protocol design and computational guarantees, with limited understanding of the fundamental information-theoretic limits of such systems. Moreover, optimal bounds on communication and key usage remain unknown in decentralized settings, where no central aggregator is available. Motivated by these gaps, we study the problem of decentralized secure aggregation (DSA) from an information-theoretic perspective. Specifically, we consider a network of $K$ fully-connected users, each holding a private input -- an abstraction of local training data -- who aim to securely compute the sum of all inputs. The security constraint requires that no user learns anything beyond the input sum, even when colluding with up to $T$ other users. We characterize the optimal rate region, which specifies the minimum achievable communication and secret key rates for DSA. In particular, we show that to securely compute one symbol of the desired input sum, each user must (i) transmit at least one symbol to others, (ii) hold at least one symbol of secret key, and (iii) all users must collectively hold no fewer than $K - 1$ independent key symbols. Our results establish the fundamental performance limits of DSA, providing insights for the design of provably secure and communication-efficient protocols in decentralized learning.