Li Zhou

Zhou Li, Xiang Zhang, Jiawen Lv et al.

Motivated by federated learning (FL), secure aggregation (SA) aims to securely compute, as efficiently as possible, the sum of a set of inputs distributed across many users. To understand the impact of network topology, hierarchical secure aggregation (HSA) investigated the communication and secret key generation efficiency in a 3-layer relay network, where clusters of users are connected to the aggregation server through an intermediate layer of relays. Due to the pre-aggregation of the messages at the relays, HSA reduces the communication burden on the relay-to-server links and is able to support a large number of users. However, as the number of users increases, a practical challenge arises from heterogeneous security requirements--for example, users in different clusters may require varying levels of input protection. Motivated by this, we study weakly-secure HSA (WS-HSA) with collusion resilience, where instead of protecting all the inputs from any set of colluding users, only the inputs belonging to a predefined collection of user groups (referred to as security input sets) need to be protected against another predefined collection of user groups (referred to as collusion sets). Since the security input sets and collusion sets can be arbitrarily defined, our formulation offers a flexible framework for addressing heterogeneous security requirements in HSA. We characterize the optimal total key rate, i.e., the total number of independent key symbols required to ensure both server and relay security, for a broad range of parameter configurations. For the remaining cases, we establish lower and upper bounds on the optimal key rate, providing constant-factor gap optimality guarantees.

Xiang Zhang, Zhou Li, Shuangyang Li et al.

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 distributed learning systems.