Haiqiang Chen

Minyang Lu, Zhou Li, Haiqiang Chen et al.

We study the hierarchical secure aggregation problem with groupwise keys. The problem consists of an aggregation server, $U$ relays, and $UV$ users, where each relay serves $V$ disjoint users, and each subset of $G$ users shares an independent groupwise key. Two security requirements are imposed: relay security and server security. Specifically, each relay must not learn any information about the users' inputs, and the server must not learn any additional information beyond the recovered sum of all inputs. We first show that the problem is infeasible when $G = 1$. For the feasible regime $1 < G \le UV$, we fully characterize the optimal rate region. In particular, we prove that both each user and each relay must transmit at least one symbol per input symbol. Furthermore, we characterize the minimum required groupwise key rate as $\max\left\{\frac{V}{\binom{UV}{G} - \binom{(U-1)V}{G}},\; \frac{U - 1}{\binom{UV}{G} - U \binom{V}{G}}\right\},$ where the two terms correspond to the constraints imposed by relay security and server security, respectively. For achievability, we propose an explicit linear coding scheme based on structured precoding matrices, and show that it satisfies both correctness and security requirements. The construction avoids permutation-based symmetrization by leveraging sufficiently generic matrix designs over large fields. Finally, we establish a matching converse, thereby characterizing the optimal rate region.

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.